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STAAD Foundation Advanced V8i
Verification Manual DAA039800-1/0001 Last updated: 26 July 2011
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Verification Manual — i
Chapter 2
ii — (Undefined variable: Primary.ProductName)
Table of Contents Introduction
1
Section 1 Australian Code (AS3600-2001[AMnd 2004])
3
1.1 General Isolated Foundation 1
3
1.2 General Isolated Foundation 2
6
1.3 General Combined Foundation 1
14
1.4 General Combined Foundation 2
16
Section 2 British Code (BS8110-1-1997)
23
2.1 General Isolated Foundation 1
23
2.2 General Isolated Foundation 2
26
2.3 General Isolated Foundation 3
32
2.4 General Isolated Foundation 4
38
2.5 General Isolated Foundation 5
44
2.6 General Isolated Foundation 6
53
2.7 General Isolated Foundation 7
62
2.8 General Combined Foundation 1
71
2.9 General Combined Foundation 2
77
2.10 Mat Combined Foundation
83
2.11 General Isolated Foundation with Eccentricity
88
Section 3 Canadian Code (CSA A23.3-2004)
99
3.1 CSA General Isolated Foundation 1
99
3.2 CSA General Isolated Foundation 2
105
3.3 CSA General Isolated Foundation 3
112
3.5 CSA Pilecap Foundation 1
115
3.4 CSA General Combined Foundation s1
122
Section 4 Indian Code (IS 456 -2000)
125
4.1 IS General Isolated Foundation 1
125
4.2 IS General Isolated Foundation 2
129
4.3 IS General Isolated Foundation 3
133
4.4 IS General Isolated Foundation 4
138
4.5 IS General Isolated Foundation 5
140
4.6 IS General Isolated Foundations 6
145
4.7 IS General Isolated Foundation 7
150 Verification Manual — iii
Chapter — 3
4.8 IS Toolkit Combined 1
158
4.9 IS Toolkit Combined Foundation 2
164
4.10 IS Toolkit Combined Foundation 3
170
4.11 IS Toolkit Combined Foundation 4
176
4.12 IS Pilecap 1
182
4.13 IS Pilecap 2
189
4.14 IS Mat Combined Foundation 1
197
Section 5 United States Code (ACI 318 -2005)
201
5.1 US General Isolated Foundation 1
201
5.2 US General Isolated Foundation 2
206
5.3 US General Isolated Foundation 3
211
5.4 US General Isolated Foundation 4
215
5.5 US General Isolated Foundation 5
220
5.6 US General Isolated Foundation 6
229
5.7 US General Isolated Foundation 7
233
5.8 US General Combined Foundation 1
241
5.9 US General Combined Foundation 2
247
5.10 US General Combined Foundation 3
253
5.11 US General Combined Foundation 4
258
5.12 US Pilecap Foundation 1
264
5.13 US Pilecap Foundation 2
271
5.14 US Pilecap Foundation 3
280
5.15 US Pilecap Foundation 4
287
5.16 US Mat Combined Foundation 1
295
5.17 US General Isolated Foundation with Sliding & Overturning
302
5.18 US General Isolated Foundation with Eccentric Loading
311
Section 6 Deadman Anchors (ACI 318 -2005)
321
6.1 Deadman Guy Anchor US 1
321
6.2 Deadman Guy Anchor US 2
330
6.3 Deadman Guy Anchor US 3
338
6.4 Deadman Guy Anchor US 4
347
Section 7 Drilled Pier Foundations
357
7.1 Drilled Pier Foundation 1 API
357
7.2 Drilled Pier Foundation 2 API
361
7.3 Drilled Pier Foundation 3 FHWA
366
iv — STAAD Foundation Advanced V8i
7.4 Drilled Pier Foundation 4 FHWA
371
7.5 Drilled Pier Foundation 5 VESIC
375
7.6 Drilled Pier Foundation 6 Vesic
380
Section 8 Plant Foundation
385
8.1 Vertical Vessel Foundation 1
385
8.2 Vertical Vessel Foundation Design
394
8.3 Vertical Vessel Foundation Design
403
8.4 Vertical Vessel Seismic Load Generation 1
412
8.5 Vertical Vessel Seismic Load Generation 2
413
8.6 Vertical Vessel Seismic Load Generation 3
414
8.7 Vertical Vessel Seismic Load Generation 4
415
8.8 Vertical Vessel Seismic Load Generation 5
416
8.9 Vertical Vessel Seismic Load Generation 6
418
8.10 Vertical Vessel Seismic Load Generation 7
419
8.11 Vertical Vessel Seismic Load Generation 8
420
8.12 Vertical Vessel Seismic Load Generation 9
421
8.13 Vertical Vessel Wind Load Generation 1
422
8.14 Vertical Vessel Wind Load Generation 2
423
8.15 Vertical Vessel Wind Load Generation 3
424
8.16 Vertical Vessel Wind Load Generation 4
426
8.17 Horizontal Vessel Applied Loads 1
427
8.18 Horizontal Vessel Applied Loads 2
431
Section 9 Chinese Code (GB50007-2002)
437
9.1 Cone Footing Design
437
9.2 PKPM Isolated Footing Design
445
9.3 Stepped Foundation Design
449
9.4 PKPM Stepped Footing Design
457
9.5 Combined Foundation
461
9.6 Pile Foundation Design
470
Section 10 Technical Support
485
Index
487
List of Figures & Tables
489
Figures
489
Tables
493 Verification Manual — v
Chapter 3
vi — (Undefined variable: Primary.ProductName)
Introduction This document is intended to use as a hand calculation reference for STAAD Foundation Advanced V8i (Release 6.0) verification problems. Verification Problems can be found under Start Page > Example > Verification. Each section in this manual represents either specific design code (e.g., AS3600-2001) or particular foundation type (e.g., Dead Man Anchor Guy Foundation). Hand calculation title (e.g., AS GEN ISO 1) indicates corresponding STAAD Foundation file name. At end of each hand calculation a comparison table between hand calculations and program results is provided for various output parameters like bearing pressure, overturning and sliding factor of safety, shear force, etc.
Verification Manual — 1
Chapter 4
2 — (Undefined variable: Primary.ProductName)
Section 1
Australian Code (AS36002001[AMnd 2004]) 1.1 General Isolated Foundation 1 1.1.1 Reference 1.1.2 Problem Design an isolated footing with the given data: Load Fy = 500 KN, fc = 25 MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 110 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, and FOS against overturning =1.5. Height of soil above footing = 500 mm, GWT is 200 mm from GL. Surcharge= 10 KN/m2
Verification Manual — 3
Chapter — 1 1.1 General Isolated Foundation 1 Figure 1-1: Australian code General isolated foundation
1.1.3 Solution Approximate area of footing required = 500/110 m2 = 4.545 m2 Assuming 2.4 m x 2.4 m x 0.400 m footing dimension, Weight of footing = 2.4 x 2.4 x 0.400 x 25 KN = 57.6 KN Weight of above soil = 2.4 x 2.4 x 0.500 x 18 KN = 51.84 KN Reduction of Weight due to buoyancy = 2.4 x 2.4 x (0.500+0.400-0.200) x 9.81 KN = 39.554 KN Load due to surcharge = 2.4 x2.4 x 10 KN =57.6 KN Therefore, total load on the footing = (500+57.6 +51.84+57.6 -39.554 ) KN = 627.486 KN Maximum pressure = 627.486 /(2.4x2.4) = 108.94 KN/ m2 108.94 KN/m2 1.5 Hence OK
Factored Design Axial Load = 292 KN + 1.4(1,500 KN) = 2,392 KN MX =1.4 x 50 =70 KNm MZ =1.4 x 50 =70 KNm
Check For Trial Depth against moment about Z Axis Average Base Pressure along one edge = 156.07 KN/m2 (left end) Average Base Pressure along other edge = 142.93 KN/m2 (right end) Approximate Base Pressure at the left critical section = 150 KN/m2 Approximate Base Pressure at the right critical section = 149.01 KN/m2 Hence, the moment at the left critical section Mu (Left) F = (156.07 + 150.0)/2 (1.85 m) (4 m) = 1,132.46 KN LA = (150.0 + 2 · 156.07) (1.85 m) /[3(150.0 + 156.07)] = 0.932 m Mu(left) = F · LA = 1,132.46 KN (0.932 m) = 1,055.4 KNm Similarly, the moment at the right critical section Mu (Right): F = (142.93 + 149.01)/2 (1.85 m) (4 m) = 1,080.2 KN LA = (142.93 + 2 · 149.01) (1.85 m) /[3(142.93 + 149.01)] = 0.919 m Mu(right) = F · LA = 1,080.2 KN (0.919 m) = 992.7 KNm So max moment with respect to the Z axis, Mu(Z) = 1,056 KNm
8 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.2 General Isolated Foundation 2
Assuming 50 mm clear cover and 16 mm bar, effective depth d
eff
= (730 - 50 - 0.5 x 16) mm = 672 mm
m= fc/fy =0.0555 γ = 0.85 - 0.007(fc - 28) = 0.871 (Take γ = 0.85 per Clause 8.1.2.2 K
= 0.4 (Clause 8.1.3)
umax
Ku = 0.34 · γ · (1 - 0.2 · γ) = 0.24 R
umax
M
= 0.85 · fc · γ · K
umax
= φ [R
umax
·b
· (1 - K
umax · d 2] =
umax
/2) = 3.891
5,622.7 KNm
Mu < M
umax
Hence OK
Check For Trial Depth against moment about X Axis Average Base Pressure along one edge = 142.93 KN/m2(left end) Average Base Pressure along other edge = 156.07 KN/m2 (right end) Approximate Base Pressure at the left critical section = 149.01 KN/m2 Approximate Base Pressure at the right critical section = 150.0 KN/m2 Hence, the moment at the critical section Mu (left) F = (142.93 + 149.01)/2 (1.85 m) (4 m) = 1,080.2 KN LA = (142.93 + 2 · 149.01) (1.85 m) /[3(142.93 + 149.01)] = 0.919 m Mu(right) = F · LA = 1,080.2 KN (0.919 m) = 992.7 KNm Similarly, the moment at the right critical section Mu (Right): F = (156.07 + 150.0)/2 (1.85 m) (4 m) = 1,132.46 KN LA = (150.0 + 2 · 156.07) (1.85 m) /[3(150.0 + 156.07)] = 0.932 m Verification Manual — 9
Chapter — 1 1.2 General Isolated Foundation 2
Mu(left) = F · LA = 1,132.46 KN (0.932 m) = 1,055.4 KNm So max moment with respect to the X axis, Mu(X) = 1,056 KNm
Assuming 50 mm clear cover and 16 mm bar, effective depth d
eff
= (730 - 50 - 0.5 x 16) mm = 672 mm
m= fc/fy =0.0555 γ = 0.85 - 0.007(fc - 28) = 0.871 (Take γ = 0.85 per Clause 8.1.2.2 K
= 0.4 (Clause 8.1.3)
umax
Ku = 0.34 · γ · (1 - 0.2 · γ) = 0.24 R
umax
M
= 0.85 · fc · γ · K
umax
= φ [R
umax
·b
· (1 - K
umax · d 2] =
umax
/2) = 3.891
5,622.7 KNm
Mu < M
umax
Hence OK
Area of Steel Required along X dir Calculation required steel for balanced section, Ast x = 4,427 m2m Minimum area of steel Ast min = 0.002 · b · d = 5,376 mm2 So, provided area of steel = 5,376 mm2
Area of Steel Required along Z dir Calculation required steel for balanced section, Ast x = 4,427 m2m Minimum area of steel Ast min = 0.002 · b · d = 5,376 mm2 So, provided area of steel = 5,376 mm2
10 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.2 General Isolated Foundation 2
Check for One-Way Shear Along X Direction Critical section for moment is at a distance, d, away from the face of column Average Base Pressure along one edge = 142.93 kN/m2 Average Base Pressure along other edge = 156.07 kN/m2 Approximate Base Pressure at the left critical section = 156.07 + (142.93 - 156.07) · 1.178/4= 152.2 kN/m2 Approximate Base Pressure at the right critical section = 156.07 + (142.93 - 156.07) · (4 1.178)/4 = 146.8 kN/m2 Hence, the SF at the left critical section: F = (156.07 + 152.2)/2 (1.178 m) (4 m) = 726.3 kN Shear at the right critical section: F = (142.93 + 146.8)/2 (1.178 m) (4 m) = 682.6 kN Critical shear is 727 kN Developed shear stress, τv = 726.3 kN (103)/[4,000 (672)] = 0.44 N/mm 2 τc
max
= 0.2 · fc = 5 N/mm 2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 672/1,000) = 1.021 ß2 = 1 ß3 = 1 τ = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)] 1/3 = 0.75{1.021(1)(1)[5,376 · 25/(4,000 · 672)] 1/3} = 0.282 c N/mm 2 Hence OK
Verification Manual — 11
Chapter — 1 1.2 General Isolated Foundation 2
Along Z Direction Critical section for moment is at a distance, d, away from the face of column Average Base Pressure along one edge = 142.93 kN/m2 Average Base Pressure along other edge = 156.07 kN/m2 Approximate Base Pressure at the left critical section = 156.07 + (142.93 - 156.07) · (4 1.178)/4 = 146.8 kN/m2 Approximate Base Pressure at the right critical section = 156.07 + (142.93 - 156.07) · 1.178/4= 152.2 kN/m2 Hence, the SF at the left critical section: F = (142.93 + 146.8)/2 (1.178 m) (4 m) = 682.6 kN Shear at the right critical section: F = (156.07 + 152.2)/2 (1.178 m) (4 m) = 726.3 kN Critical shear is 727 kN Developed shear stress, τv = 726.3 kN (103)/[4,000 (672)] = 0.27 N/mm 2 τ
cmax
= 0.2 · fc = 5 N/mm 2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 672/1,000) = 1.021 ß2 = 1 ß3 = 1 τ = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)] 1/3 = 0.75{1.021(1)(1)[5,376 · 25/(4,000 · 672)] 1/3} = c 0.282 N/mm 2 Hence OK
Punching Shear Punching Shear is checked on a perimeter 0.5 · d from the column face. 12 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.2 General Isolated Foundation 2
Pm = 3,888 mm Vmax = 2,251 kN τ = Vmax/(Pm · d) = 2,251 kN (10)3/(3,888 mm · 672 mm) = 0.862 N/mm 2 v
Punching shear stress capacity τ = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm 2 c
τv < τc Hence safe
Verification Manual — 13
Chapter — 1 1.3 General Combined Foundation 1
1.2.4 Comparison Table 1-2: Australian verification example 2 comparison STAAD FounReference Percent DifValue of… dation Result ference Result Corner Pressure, KN/m2 112 111.9 None
Resisting force for sliding, KN Resisting Moment for Overturning, KNm Shear Force (One-Way), KN Resisting Shear Stress (OneWay), N/mm2 Shear Force (Two-Way), KN Resisting Shear Stress (TwoWay), N/mm2 Governing Flexural Moment, KNm Resisting Flexural Moment, KNm Reinforcement provided in design, mm2
102.6
102.6
112
111.9
102.6 896
121.32 895.6
None
896 3,584
895.6 3,582.3
None
3,584 727
3,582.3 726
Negligible
727 0.284
735 0.284
None
0.284 2251 1.19
0.284 2250 1.19
None None
1,056
1,054
None
1,056 5,622
1,054 5,622
None
5,622 5,376 ea. way
5,622 5,376 ea. way
None
1.3 General Combined Foundation 1 1.3.1 Reference 1.3.2 Problem Design a combined footing with the given data: Load Fy = 600 KN each column., fc = 25 MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm. and C/C column distance = 3,000 mm . Bearing Capacity of Soil = 105 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5 Ht of soil =450 mm. Depth of GWT=250 mm.
14 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.3 General Combined Foundation 1 Figure 1-3: Plan and Elevation
1.3.3 Solution Approximate area of footing required = 2(600)/115 m2 = 10.435 m2 Assuming 5 m x 2.8 m x 0.600 m footing dimension, ( left overhang=right overhang = 1 m) Weight of footing = 5 (2.8) (0.600) (25) = 210 KN Weight of pedestal=2(0.3)(0.3)(0.5)(25) = 2.25 KN Weight of soil above footing = [5(2.8) - 2(0.3)(0.3)] · 0.450 · 18 = 111.9 KN Reduction of Weight due to buoyancy = 5(2.8) · (0.45 + 0.6 - 0.25) · 9.81 KN = 109.9 KN Therefore, total load on the footing = (2 · 600 + 210 + 2.25 + 111.9 - 109.9) KN = 1,414.3 KN Maximum pressure= 1,414.3 /(5 · 2.8) = 101.0 KN/ m2 101 KN/ m2 < 105 KN/m2 (Hence safe)
Critical load case and the governing factor of safety for overturning About Z Direction Overturning Moment =0 Total Service load on foundation = 1,414.3 KN Verification Manual — 15
Chapter — 1 1.4 General Combined Foundation 2 max resisting Moment = 5 m · 1,414.3 KN /2 =3,535.6 KNm Hence OK
About X Direction Overturning Moment = 0 max resisting Moment = 2.8 m · 1,414.3 KN /2 = 1,980 KNm Hence OK
1.3.4 Comparison Table 1-3: Australian verification example 3 comparison STAAD FounReference Percent DifValue of… dation Result ference Result Bearing Pressure, KN/m2 101 101 None Resisting Moment for 3,535.8 3,535 None Overturning (Z), KNm Resisting Moment for 1,980 1,980 None Overturning (X), KNm
1.4 General Combined Foundation 2 1.4.1 Reference 1.4.2 Problem Design a combined footing with the given data: Load Fy = 600 KN and 550 KN on two col., fc = 25 MPa, fy = 450 MPa, Column Dimension = 300 mm x 300 mm, Pedestal height-500 mm. and C/C column distance=3000 mm . Bearing Capacity of Soil = 100 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
16 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.4 General Combined Foundation 2 Figure 1-4: Plan and Elevation
1.4.3 Solution Approximate area of footing required = (600+550)/100 m2 = 11.5 m2 Assuming 5 m x 3 m x 0.500 m footing dimension, ( left overhang = right overhang = 1 m) Weight of footing = 5 m · 3 m · 0.500 m · 25 = 187.5 KN Weight of pedestal = 2(0.3)(0.3)(0.5)(25) = 2.25 KN Therefore, total load on the footing = (600 + 550 + 187.5 + 2.25) KN = 1,339.8 KN Pressure from axial load = 1,339.8 KN/(5 m · 3 m) = 89.3 KN/ m2 CG of foundation raft = 5/2= 2.5 m from left end CG of load = (1 m · 600 KN + 4 m · 550 KN)/(600 KN + 550 KN) = 2.435 m Eccentricity= 2.5 - 2.435 = 0.065 m So Moment Mz = P · e = 1,150 KN (0.065 m) = 75 KNm Zz = 3 · 52/6 = 12.5 m 3 stress due to moment = M/Z = 75 KNm/12.5 m3 = 6 KN/m2 Stress at left end = P/A + M/Z = 89.3 + 6 = 95.3 KN/m2 Stress at right end = P/A - M/Z = 89.3 - 6 = 83.3 KN/m2 So, Maximum stress 95.3 KN/m2 < 100 KN/m2 (Hence safe)
Verification Manual — 17
Chapter — 1 1.4 General Combined Foundation 2
Critical load case and the governing factor of safety for overturning About Z Direction Overturning Moment =0 max resisting Moment = 5 m (1,339.8 KN) /2 = 3,349.5 KNm Hence OK
Wrt X Direction Overturning Moment =0 max resisting Moment = 3 m (1,339.8 KN) /2 = 2,009.7 KNm Hence OK
Check For Trial Depth Moment About Z Axis (sagging) Bending moment at critical section, Muz = 172 KNm Assuming 50 mm clear cover and 12 mm bar, effective depth d
eff
= (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556 γ = 0.85 - 0.007 · (fc - 28) = 0.87 take γ = 0.85 ( Clause 8.1.2.2) K
umax
= 0.4 (Clause 8.1.3)
K = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24 u
R = 0.85 · fc · γ · K · (1 - γ · K /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891 umax u u N/mm 2 M = φ [R · b · d 2] =0.80 [3.891 N/mm 2 · 3,000 mm · (444 mm)2]10-6 = 1,840 umax umax KNm Muz < Mumax Hence OK
Moment About Z Axis (hogging) Bending moment at critical section, Muz = 201 KNm Assuming 50 mm clear cover and 12 mm bar, effective depth d
eff
= (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556 γ = 0.85 - 0.007 · (fc - 28) = 0.87 18 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.4 General Combined Foundation 2
take γ = 0.85 ( Clause 8.1.2.2) K
umax
= 0.4 (Clause 8.1.3)
K = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24 u
R = 0.85 · fc · γ · K · (1 - γ · K /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891 umax u u N/mm 2 M = φ [R · b · d 2] =0.80 [3.891 N/mm 2 · 3,000 mm · (444 mm)2]10-6 = 1,840 umax umax KNm Muz < Mumax Hence OK
Moment About X Axis Cantilever length = (3 - 0.3)/2 = 1.35 m Bending moment at critical section, Mux = 107.34 N/mm2 (5 m) (1.35 m)2/2 =489.1 KNm Assuming 50 mm clear cover and 12 mm bar, effective depth d
eff
= (500 - 50 - 0.5 · 12) mm = 444 mm
m= fc/fy =0.0556 γ = 0.85 - 0.007 · (fc - 28) = 0.87 take γ = 0.85 ( Clause 8.1.2.2) K
umax
= 0.4 (Clause 8.1.3)
K = 0.34 ·γ · (1 - 0.2 · λ) = 0.34 · 0.85(1 - 0.2 · 0.85) = 0.24 u
R = 0.85 · fc · γ · K · (1 - γ · K /2) = 0.85(25)(0.85)(0.24)(1 - 0.85 · 0.24/2) = 3.891 umax u u N/mm 2 M = φ [R · b · d 2] =0.80 [3.891 N/mm 2 · 5,000 mm · (444 mm)2]10-6 = 3,068 umax umax KNm Mu < Mumax Hence OK
Area of Steel Required Along X Direction (Bottom) Astx = 1,083 mm2 Minimum area of steel Ast min = 0.002 · b · d = 2,664 mm2 Provided area = 2,664 mm2
Along X Direction (Top) Astx = 1,268 mm2 Minimum area of steel Ast min = 0.002 · b · d = 2,664 mm2 Provided area = 2,664 mm2
Verification Manual — 19
Chapter — 1 1.4 General Combined Foundation 2
Along Z Direction (Bottom) Therefore, Astz = 3,096 mm2 Minimum area of steel Ast min = 0.002 · b · d = 4,440 mm2 Provided area = 4,440 mm2 Figure 1-5: Graphs of combined strip footing internal forces
20 — STAAD Foundation Advanced V8i
Section 1 Australian Code (AS3600-2001[AMnd 2004]) 1.4 General Combined Foundation 2
Check for One-Way Shear Developed shear stress V = 299.5(10)3/(3,000 · 444) = 0.225 N/mm2 τcmax = 0.2 · fc = 5 N/mm2 ß1 =1.1(1.6-d/1000) = 1.2716 ß2 = 1 ß3 = 1 τc =ß1.ß2.ß3.(Ast.fc/b.d)1/3 = 0.488 N/mm2 V
umax
= 299.5 KN
Developed shear stress, τv = 299.5(10)3/(3,000 · 444) = 0.225 N/mm 2 τc
max
= 0.2 · fc = 5 N/mm 2
ß1 = 1.1(1.6 - d/1000) = 1.1(1.6 - 444/1,000) = 1.272 ß2 = 1 ß3 = 1 τ = φ · ß1 · ß2 · ß3. · [Ast · fc/(b · d)] 1/3 = 0.7{1.272(1)(1)[2,664 · 25/(3,000 · 444)] 1/3} = 0.328 c N/mm 2 Hence OK
Punching Shear For Column One Punching shear is checked on a perimeter 0.5 · d from the column face. Two way shear = 777.8 KN Pm = 4 · (300 mm + 444 mm) = 2,976 mm τv = Vmax/(Pm · d) = 777.8 KN · 1000/(2,976 mm · 444 mm) = 0.589 N/mm 2 τ = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm 2 c
τv < τc , Hence safe
For Column Two Punching shear is checked on a perimeter 0.5d from the column face. Two way shear= 713.4 KN Pm = 2,976 mm τv = Vmax/(Pm · d) = 713.4 KN · 1000/(2,976 mm · 444 mm) = 0.540 N/mm 2 τ = φ · [0.34 · √(fc)] = 0.7 · [0.34 · √(25)] = 1.19 N/mm 2 c
τv < τc , Hence safe
Verification Manual — 21
Chapter — 1 1.4 General Combined Foundation 2
1.4.4 Comparison Table 1-4: Australian verification example 4 comparison STAAD FounReference Percent DifValue of… dation Result ference Result Bearing Pressure, KN/m2 95.3 95.32 None Governing Moment, KNm
Resisting Moment, KNm
Shear Force (One-Way), KN Shear capacity (One-Way), N/mm2 Shear Force (Two-Way), KN Shear capacity (Two-Way), N/mm2 Resisting Moment for Overturning (Z), KNm Resisting Moment for Overturning (X), KNm
22 — STAAD Foundation Advanced V8i
83.3 172
83.32 167
201
201
489 1,840
512 1,840
1,840
1,840
3,068 299.5 0.328
3,068 299.4 0.328
None None
777.8
777.8
None
713.4 1.19
713.4 1.19
None
3,349
3,349
None
2,010
2,010
None
Negligible
None
Section 2
British Code (BS8110-11997) 2.1 General Isolated Foundation 1 2.1.1 Reference ‘Reinforced Concrete’ by T.J.Macgingley & B.S.Choo, Page 333 and Example: 11.1.
2.1.2 Problem A column 400mm X 400mm carries a dead load of 800 kN and an imposed load of 300 kN. The safe bearing pressure is 200 kN/m2. Design a square base to resist the loads. The concrete is grade 35 and the reinforcement is grade 460.
Verification Manual — 23
Chapter — 2 2.1 General Isolated Foundation 1
2.1.3 Solution Figure 2-1: Bending section considered
Figure 2-2: One way shear section considered
Figure 2-3: Two way shear section considered
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Section 2 British Code (BS8110-1-1997) 2.1 General Isolated Foundation 1
Size of base Self-weight of footing = 2.5 x 2.5 x 0.5 x 25 = 78.125 kN. Therefore, Service load = Dead load + Imposed load + Self weight = (800 + 300 + 78.125) kN = 1178.125 kN. Area required = 1178.125 / 200 m2 = 5.890625 m2. Make the base 2.5 m x 2.5 m.
Moment Steel Ultimate load = (1.4 x 800) + (1.6 x 300) = 1600 kN. Ultimate pressure = 1600 / (2.5 x 2.5) = 256 kNm2 The critical section YY at the column face is shown in Figure 6.1. MYY= 256 x (2.5 / 2 - 0.4 / 2) x 2.5 x 0.525 = 352.8 kNm. Try an overall depth of 500 mm with 20 mm bars. Effective depth = 500 – 40 – 20 – 10 = 430 mm.
Therefore z = 0.95d,
= 1976.31 mm2. Minimum area of steel = 0.0015 x B x d = 0.0012 x 2500 x 430 = 1625 mm2 < AS (Hence Safe) Let us provide 10 nos. 16 mm bars, AS = 2010.62 mm2.
One Way Shear The critical section Y1 Y1 at d = 430 mm from the face of the column is shown in Figure 6.2. Design shear force, VU = 256 x (2.5 /2 – 0.43 – 0.4 / 2) x 2.5 = 396.8 kN Design shear stress, v = 396.9(10)3 / (2500 x 430) = 0.369 N/mm2 Now, vC1 = min(0.8
,5) = 4.7328 N/mm2 > v (Hence Safe)
Verification Manual — 25
Chapter — 2 2.2 General Isolated Foundation 2 = 0.395 N / mm2 > v (Hence Safe) Hence no shear reinforcement is required.
Punching Shear Punching shear is checked on a perimeter 1.5d = 625.5 mm from the column face. The critical perimeter is shown in Figure 6.3. Perimeter = 1690 x 4 = 6760 mm. Shear = 256 x (2.52 – 1.69 2) = 868.8 kN. v = 868 x 103 / (6760 x 430) = 0.3 N / mm2 < VC (Hence Safe). Hence no shear reinforcement is required.
Spacing We provided 10 nos. 16 mm bars, AS = 2010.62 mm2. Spacing = (2500 - 40 x 2 - 16) / (10 -1) = 267.11 mm.
2.1.4 Comparison Table 2-1: British verification example 1 comparison STAAD Foundation Value of Reference Results Percent Difference Result Effective Depth 430 mm 430 mm None Governing Moment 352.8 KN-m 352.8 KN-m None Area of Steel 1976.31 1976.31 None 2 2 Shear Stress (One-Way) 0.369 N/mm 0.369 N/mm None Shear Stress (Two-Way) 0.3 N/mm2 0.3 N/mm2 None
2.2 General Isolated Foundation 2 2.2.1 Reference ‘Reinforced Concrete’ by T.J.Macgingley & B.S.Choo, Page 340 and Example: 11.2.
2.2.2 Problem The characteristic loads for an internal column footing in a building are given in the following table. The proposed dimensions for the column and base are shown in Figure 6.4. The safe bearing pressure of soil is 150 kN / m2. The materials to be used in the foundation are grade 35 concrete and grade 460 reinforcement. Table 2-2: Table BS2.1 - Column loads Vertical Load (kN) Moment (KN m) Dead Load 770 78 Imposed Load 330 34
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Section 2 British Code (BS8110-1-1997) 2.2 General Isolated Foundation 2 Figure 2-4: Plan and Elevation
2.2.3 Solution Self-weight of footing = 0.5 x 3.6 x 2.8 x 24 = 120.96 kN. Total axial load = 770 + 330 + 120.96 = 1220.96 kN. Total moment = 78 + 34 = 112 kN-m. Base area = 2.8 x 3.6 = 10.08 m2. Section modulus = (I / y) = (1/12)BD3/(D/2) = 6.048 m3. Maximum pressure = 1220.96/10.08 + 112/6.048 = 139.65 kN / m2 < 150 kN / m2 (Hence Safe). Factored axial load = (1.4 x 770) + (1.6 x 330) = 1606 kN. Factored moment = (1.4 x 78) + (1.6 x 34) = 163.6 kN-m. Maximum pressure = 1606/10.08 + 163.6/6.048 = 186.38 kN / m2. Minimum pressure = 1606/10.08 - 163.6/6.048 = 132.28 kN / m2.
Calculation of Reinforcement Along Shorter Span (X - X ): 1
1
Average pressure for section X1X1 (as shown in Figure 6.5) = 159.33 kN / m2. Moment (MY) = (159.33 x 1.175 x 3.6) x (1.175 / 2) = 395.955 kN-m. Effective depth (d) = 500 – 40 – 10 = 450 mm.
0.015 < 0.156 (Hence Safe)
Verification Manual — 27
Chapter — 2 2.2 General Isolated Foundation 2
Therefore z = 0.95d,
= 2119.475 mm2. The minimum area of steel = 0.13 x 3600 x 500 / 100 = 2340 mm2 > calculated area of steel. Provide minimum steel. Figure 2-5: Sections considered for bending in both directions
Calculation of Reinforcement Along Longer Span (Y -Y ): 1
Pressure at section Y1 Y1 (as shown in Figure 6.5) = 162.7 kN / m2.
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1
Section 2 British Code (BS8110-1-1997) 2.2 General Isolated Foundation 2 Moment(MX) = (162.7 x 2.8 x 1.575)x(1.575 / 2)+(0.5 x 1.575 x (186.38 – 162.7) x 2.8)x(2 / 3 x 1.575) = 619.862 kN-m. Effective depth (d) = 500 – 40 – 20 –10 = 430 mm.
0.034 < 0.156 (Hence Safe)
= 0.96d Therefore z = 0.95d,
= 3472.334 mm2. The minimum area of steel = 0.13 x 2800 x 500 / 100 = 1820 mm2 < calculated area of steel. (Hence safe)
One Way Shear Along Section Y -Y : 2
2
The critical section Y2 Y2 at d = 430 mm from the face of the column is shown in Figure 6.6. Average pressure for the required section = 177.78 kN / m2. Design shear force, VU = 177.78 x 2.8 x 1.145 = 569.96 kN
Design shear stress, v = Now, vC1 = min(0.8
=473.388 kN / m2 ,5) = 4732.8 kN / m2 > v (Hence Safe)
= 429.6 kN / m2. Let us consider 1.5 times shear enhancement. Vce = 1.5 x 429.6 = 644.4 kN/m2 > v (Hence safe) Hence no shear reinforcement is required.
Verification Manual — 29
Chapter — 2 2.2 General Isolated Foundation 2 Figure 2-6: Sections considered for one-way shear in both directions
Along Section X -X : 2
2
The critical section X2X2 at d = 450 mm from the face of the column is shown in Figure 6.6. Average pressure for the required section = 159.33 kN / m2. Design shear force, VU = 159.33 x 3.6 x 7.25 = 415.85 kN =256.698 kN / m2
Design shear stress, v = Now, vC1 = min(0.8
,5) = 4732.8 kN / m2 > v (Hence Safe)
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Section 2 British Code (BS8110-1-1997) 2.2 General Isolated Foundation 2
= 409.6 kN / m2. Let us consider 1.5 times shear enhancement. Vce = 1.5 x 409.6 = 614.4 kN/m2 > v (Hence safe) Hence no shear reinforcement is required.
Punching Shear Figure 2-7: Section considered for punching shear
The punching shear will be calculated for an area outside the area enclosed by the rectangle at a distance 1.5d from the column face as shown in Figure 6.7. Total pressure under the base = 2.8 x 3.6 x 132.28 + 0.5 x 3.6 x 2.8 x (186.38 – 132.28) = 1606.05 kN. Pressure under enclosed rectangle = (1.74)2 x 146.255 + 0.5 x (1.74)2 x (172.4 – 146.255) = 482.38 kN Punching shear force = 1606.05 – 482.38 = 1123.67 kN. Critical perimeter = 1.74 x 4 = 6.96 m. Punching shear stress = 1123.67 / (6.96 x 0.43) = 375.46 kN / m2.
Verification Manual — 31
Chapter — 2 2.3 General Isolated Foundation 3
2.2.4 Comparison Table 2-3: British verification example 2 comparison STAAD FounReference Value of dation Result Result Effective Depth (X-X) 430 mm 430 mm Effective Depth (Y-Y) 450 mm 450 mm Governing Moment (My) 395.955 KN-m 395.943 KN-m Governing Moment (Mx ) 619.862 KN-m 619.909 kN-m Area of Steel (Along X-X) 2340.00 2340.00 Area of Steel (Along Y-Y) 3472.2334 3472.2334 2 Shear Stress (One-Way) (Y1473.388 kN/m 444.81 kN/m2 Y1) Shear Stress (One-Way) (X1256.698 kN/m2 256.698 kN/m2 X1) Shear Stress (Two-Way) 375.46 kN/m2 375.44 kN/m2
Percent Difference None None None None None None Negligible None None
2.3 General Isolated Foundation 3 2.3.1 Reference 2.3.2 Problem Design an isolated footing with the given data: Load Fy = 1500 KN, fc = 25 MPa, fy = 415 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 120 KN/m2. Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5
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Section 2 British Code (BS8110-1-1997) 2.3 General Isolated Foundation 3 Figure 2-8: Plan and Elevation
2.3.3 Solution Approximate area of footing required = 1500/120 m2 = 12.5 m2 Assuming 3.85 m x 3.85 m x 0.65 m footing dimension, Weight of footing = 3.85 x 3.85 x 0.65 x 25 KN = 240.865 KN Therefore, total load on the footing = (1500+240.865) KN = 1740.865 KN Maximum pressure =1740.865/(3.85x3.85)=KN/ m 2 = 117.45 KN/m 2 1.5 Hence Safe
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Section 2 British Code (BS8110-1-1997) 2.11 General Isolated Foundation with Eccentricity
Along Z- Direction Disturbing force = -200 KN Restoring Force = mu*(Wt of Footing + Fy + Wt of Soil) = 649.685 KN Hence, FacFor Overturning:tor of Safety against Sliding = (649.685/200) =3.2484 > 1.5 Hence Safe
About X- Direction Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) = 98.32– 200* (0 +1) = -298.32 KN-m Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt of Footing) * Width of Footing*0.5 = 3098.425 KN-m Hence, Factor of Safety against Overturning = (3098.425/298.32) =10.386 > 1.5 Hence Safe
About Z- Direction Overturning Moment = Mx + Fz* (Ht of Pedestal + Depth of Footing) =45.89 + 300* (0 +1) = 345.89 KN-m Restoring Moment = Fy * (Width of Footing *0.5 –Ozd)+ (Wt of Soil + Wt of Footing) * Width of Footing*0.5 = 3398.425 KN-m Hence, Factor of Safety against Overturning = (3398.425/345.89) =9.82516 > 1.5 Hence Safe
Base Pressure for Shear and Moment Calculation The pressure at the four corners are given by:σ 1 = (500/ 25) + (6*195.89 /5.03) - (6*148.32 /5.03) = 22.2834KN/m2 σ 2 = (500/25) - (6*195.89 /5.03) - (6*148.32 /5.03) = 3.47792KN/m2 σ 3 =(500/ 25) - (6*195.89 /5.03) + (6*148.32 /5.03) = 17.7167 KN/m2 σ 4 = (500/ 25) + (6*195.89 /5.03) + (6*148.32 /5.03) = 36.52208 KN/m2
Check for Flexure and Calculation for Reinforcement Factored loads and soil reaction: To proportion the footing for strength (depth and required reinforcement) factored loads are used. For this problem, the factors used are all 1.0 Figure 2-22: Bending about major axes
Verification Manual — 91
Chapter — 2 2.11 General Isolated Foundation with Eccentricity
Bending About Z-axis
Bending About X-axis
Critical section for moment is at the face of column
About X- axis Average Base Pressure along one edge =(22.2834+3.47792)/2 =12.8806 KN/m2 Average Base Pressure along other edge =(17.7167+36.5221)/2 = 27.1194 KN/m2 Approximate Base Pressure at the critical section =27.1194- {(27.1194 – 12.8806)/5.0*2.05} =21.2815 KN/ m2 [2.05 =5(5/2+0.3+0.15)] Hence, the moment at the critical section Mu =5.0*{21.2815 *2.05*2.05*0.5+0.5*(27.1194-21.2815)* 2.05*2.05*2/3}= 264.48 KNm Effective depth (d) = 1000 – 50 – 20 = 930 mm
Hence safe Therefore,
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Section 2 British Code (BS8110-1-1997) 2.11 General Isolated Foundation with Eccentricity
The minimum area of steel = 0.13 x 5000 x 1000 / 100 = 6500 mm2 > Calculated area of steel. So, provide minimum steel = 6500 mm2
About Z- axis Average Base Pressure along one edge =(36.5221+22.2834)/2 =29.4027 KN/m2 Average Base Pressure along other edge =(17.7167+3.47792)/2 = 10.5973 KN/m2 Approximate Base Pressure at the critical section =29.4027- {(29.4027-10.5973)/5.0*2.65} =19.4358 KN/ m2 [2.65 =(5/2+0.30.15)] Hence, the moment at the critical section Mu =5.0*{19.4358 *2.65*2.65*0.5+0.5*(29.4027 –19.4358)*2.65*2.65*2/3}= 457.874 KNm Effective depth (d) = 1000 – 50 – 20 = 930 mm
Hence safe Therefore,
The minimum area of steel = 0.13 x 5000 x 1000 / 100 = 6500 mm2 > Calculated area of steel. So, provide minimum steel = 6500 mm2
Check for Shear Assume overall footing thickness = 1.0m and average effective thickness d = 0.92m (36.22 in) Wide-beam action (One-Way Shear) :
Verification Manual — 93
Chapter — 2 2.11 General Isolated Foundation with Eccentricity
Along Z-Z axis Vu = qs
tributary area
Bw = 5.00m = 196.8504 in qs is given by:Average Base Pressure along one edge =(22.2834+3.47792)/2 =12.8806 KN/m2 Average Base Pressure along other edge =(17.7167+36.5221)/2 = 27.1194 KN/m2 Approximate Base Pressure at the critical section =27.1194- {(27.1194 – 12.8806)/5.0*1.13} =23.9014 KN/ m2 [1.13=5 -(5/2 +0.3 +0.92 +0.15)] Hence, the one- way shear at the critical section Vux =5.0*{23.9014*1.13+0.5*(27.1194-23.9014)*1.13}= 144.134 KN Design shear stress, v = 144.134/(5.0 x 0.93) =30.996 kN/ m2 Now, VC1 = min(0.8 √(fcu),5) N/ mm2= 4381.78 kN/ m2 > v (Hence Safe)
= 348.5494 kN/ m2 Let us consider 1.5 times shear enhancement. Vce = 1.5 x 348.5494 = 522.824 kN/m2 > v (Hence safe) Hence no shear reinforcement is required.
Along X-X axis Vu = qs
tributary area
Bw = 5.00m = 196.8504 in qs is given by:Average Base Pressure along one edge =(36.5221+22.2834)/2 =29.4027 KN/m2 Average Base Pressure along other edge
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Section 2 British Code (BS8110-1-1997) 2.11 General Isolated Foundation with Eccentricity
=(17.7167+3.47792)/2 = 10.5973 KN/m2 Approximate Base Pressure at the critical section =29.4027- {(29.4027-10.5973)/5.0*1.73} =22.89603 KN/ m2 [ 1.73=(5/2 +0.3 –0.92 –0.15)] Hence, the Design one-way shear at the critical section Vuz =5.0*{22.89603*1.73+0.5*(29.4027-22.89603)*1.73}= 226.1924 KN Design shear stress, v = 226.1924/(5.0 x 0.93) =48.64353 kN/ m2 Now, vC1 = min(0.8 √(fcu),5) N/ mm2= 4381.78 kN/ m2 > v (Hence Safe)
= 348.5494 kN/ m2 Let us consider 1.5 times shear enhancement. Vce = 1.5 x 348.5494 = 522.824 kN/m2 > v (Hence safe) Hence no shear reinforcement is required.
Verification Manual — 95
Chapter — 2 2.11 General Isolated Foundation with Eccentricity
Two-way action (Punching Shear) Along X-X axis
[3090 mm = 300 + 2x(1.5 x 930)] The punching shear will be calculated for an area outside the area enclosed by the rectangle at a distance 1.5d from the column face as shown in figure. Total pressure under the base = 5.0 x 5.0 x 10.5973 + 0.5 x 5.0 x 5.0 x (29.4027 – 10.5973) = 500.00 kN. Pressure at the critical sections:σa = 29.4027 – ((29.4027-10.5973)/5.0*0.955) = 25.810869 KN/m2 σb = 10.5973 + ((29.4027-10.5973)/5.0*0.955) = 14.189131 KN/m2 Pressure under enclosed rectangle = (3.09)2 x 14.189131 + 0.5 x (3.09)2 x (25.810869 – 14.189131) = 190.962 kN Punching shear force = 500.00-190.962 = 309.038 kN. Critical perimeter = 3.09 x 4 =12.36 m.
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Section 2 British Code (BS8110-1-1997) 2.11 General Isolated Foundation with Eccentricity
Punching shear stress = 309.038/(12.36 x 0.93) = 26.885 kN / m2. Hence, the punching shear stress is less than VC . Hence Safe
Along Z-Z axis
The punching shear will be calculated for an area outside the area enclosed by the rectangle at a distance 1.5d from the column face as shown in figure. Total pressure under the base = 5.0 x 5.0 x 12.8806 + 0.5 x 5.0 x 5.0 x (27.1194 – 12.8806) = 500.00 kN. Pressure at the critical sections:σa = 27.1194 – ((27.1194-12.8806)/5.0*0.955) = 24.3998 KN/m2 σb = 12.8806 + ((27.1194-12.8806)/5.0*0.955) = 15.60021 KN/m2 Punching shear force = 500.00-190.962 = 309.038 kN. Critical perimeter = 3.09 x 4 =12.36 m. Punching shear stress = 309.038/(12.36 x 0.93)= 26.885 kN / m2.
Verification Manual — 97
Chapter — 2 2.11 General Isolated Foundation with Eccentricity Hence, the punching shear stress is less than VC . Hence Safe Hence, the moment at the critical section Mu =5.0*{19.4358 *2.65*2.65*0.5+0.5*(29.4027 –19.4358)*2.65*2.65*2/3}= 457.874 KNm Effective depth (d) = 1000 – 50 – 20 = 930 mm
2.11.4 Comparison Table 2-12: British verification example 13 comparisons STAAD Reference Difference (Reasons Foundation Result there-of) Result* Moment about X 264.48 259.98 Error due to approxKNm KNm imation in base pressure interpolation Moment about Z 457.874 448.24 Error due to approxKNm KNm imation in base pressure interpolation Area of steel about 6500.00 6500.00 Negligible X-X mm2 mm2 Area of steel about 6500.00 6500.00 Negligible 2 2 Z-Z mm mm Shear Stress 48.64 46.66 KN/ Error due to approxKN/ m2 m2 imation in base pressure (One way) along X interpolation Shear Stress 30.996 29.28 KN/ Error due to approxKN/ m2 m2 imation in base pressure (One way) along Z interpolation Shear Force 309.038 305.46 KN Error due to approxKN imation in base pressure (Two way) interpolation Factor of Safety 2.1656 2.167 Negligible against Sliding (X) Factor of Safety 3.2484 3.250 Negligible against Sliding (Z) Factor of Safety 10.386 10.392 Negligible against Overturning (X) Factor of Safety 9.82516 9.830 Negligible against Overturning (Z)
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Section 3
Canadian Code (CSA A23.3-2004) 3.1 CSA General Isolated Foundation 1 3.1.1 Reference 3.1.2 Problem Design of a square Isolated Footing A tied column, 450 mm square, and reinforced with eight No. 35 bars carries an unfactored dead load of 1300 kN and an unfactored live load of 1000 kN. Suitable soil with a factored soil bearing pressure of 300 kN/m2 is available at a depth of 1.5 m . Design a square footing. The compressive strength f’c is 30 MPa for the column and 25 MPa for the footing. All steel has fy=400 MPa. Unit weight of concrete and soil is 24 kN/m2 and 16 kN/m2 respectively.
Verification Manual — 99
Chapter — 3 3.1 CSA General Isolated Foundation 1 Figure 3-1: Plan and Elevation
3.1.3 Solution Trial Footing Size Calculate the initial footing size based on soil bearing capacity. As per CSA A.23.3-04 cls. 8.3 and Annex C. the 2005 National Building Code of Canada load combination factors must be used: Factored Load = 1.25 DL + 1.5 LL = (1.25 X 1300 kN) + (1.5 x 1000 kN) = 3,125 kN Required area of footing: 3125/300 = 10.41 m2 Total Axial load = 3125+Self Weight of footing + weight of soil Self Weight of footing = 3.6 x 3.6 x 0.75 x 24 = 233.28 KN weight of soil=3.6 x 3.6 x 1.5 x 16 = 311.04 KN For square footing, the axial force on the footing is: 3125+233.28+311.04 =3669.32 KN So stress on soil=369.32/(3.6x3.6)=283.12 KN/m2
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Section 3 Canadian Code (CSA A23.3-2004) 3.1 CSA General Isolated Foundation 1
Calculate Factors of Safety In this case, we do not have any sliding and overturning forces. The CSA A23.3-04 recommends for a footing that experiences horizontal shear, the designer must make sure that this shear is transferred to the subgrade utilizing the passive soil resistance and the friction between the subgrade and the footing surface. The passive soil resistance will be ignored in STAAD Foundation to calculate the factor of safety against sliding check. Factor of safety against overturning must be checked as per the NBCC. Anyway, max sliding force equals the axial load x coefficient of friction for coeff. of friction =0.5, Sliding force= 0.5x 3669.32 =1834.66 KN (same for X & Z dir) Max resisting moment against overturning = axial force x Dimension/2= 0.5x 3669.32x3.6 KNm = 6604.78 KNm (Same wrt both x and z axis). Stress on soil from Factored load = 3125/(3.6x3.6)=241.126 KN/m2
Check for One-Way Shear Along X Direction Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (750-50-0.5 x 20) mm = 690 mm Vumax = = 768.22 KN Ø = 0.65, λ = 1 dv = 0.9.deff = 0.9 x 690 = 621 mm bw=3600 mm Now allowable shear Vc =
=1030913 N =1031 KN
V < Vc, Hence Safe
Along Z Direction Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (750-50-0.5 x 20) mm = 690 mm Vumax =
= 768.22 KN
Ø = 0.65, λ = 1 dv = 0.9.deff=0.9 x 690=621 mm
Verification Manual — 101
Chapter — 3 3.1 CSA General Isolated Foundation 1
bw = 3600 mm Now allowable shear Vc =
= 1030913 N = 1031 KN
V < Vc, Hence Safe
Punching Shear Punching shear is checked on a perimeter 0.5d = 345 mm from the column face. Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (750-50-0.5 x 20) mm = 690 mm Area within Critical Perimeter Am = (450+2x0.5x.69)2=1.2996 m2 Vmax = 1.2996)=2811.63 KN
241.126x(3.6x3.6-
Critical perimeter Pm = 2 X ( b + h + 2x d) = 4.56 m τv = Vmax/(Pm · d) = 0.8936 N/mm2 α=4 ß=L/B =4.5/4.5 =1 1.8525 N/mm2 2.5846 N/mm2 1.235 N/mm2 As effective depth>300 mm so the multiplier=1300/(1000+deff)=0.769 So, Vr1= 1.424 N/mm2 =1424 KN/m2 Vr2= 1.987N/mm2 = 1987 KN/m2 Vr3= 0.9497 N/mm2 = 949.7 KN/m2 So min {Vr1, Vr2, Vr3} = 949.7 KN/m2 So allowable shear = Vc = 949.7 KN/m2 V < Vc , Hence safe
Development Length Along Z Axis ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) db k1 = 1 if clear cover is less than 300 mm or else use 0.45
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Section 3 Canadian Code (CSA A23.3-2004) 3.1 CSA General Isolated Foundation 1
k2 = 1 if coated reinforcement is used k2 = 1.2 if epoxy coated reinforcement is used k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3x db k2 = 1.5 if bar spacing is less than 6x db k3 = 1 Normal density concrete k4 = 0.8 for 20M and smaller bar size k4 = 1 for 20M and larger bar size ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (400 MPa)/√(25MPa) x 19.5 mm = 449.28 mm Available Length = (3600-450)/2-50 = 1525 mm Hence OK
Along X Axis ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) db k1 = 1 if clear cover is less than 300 mm or else use 0.45 k2 = 1 if coated reinforcement is used k2 = 1.2 if epoxy coated reinforcement is used k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdb k2 = 1.5 if bar spacing is less than 6 xdb k3 = 1 Normal density concrete k4 = 0.8 for 20M and smaller bar size k4 = 1 for 20M and larger bar size ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (400 MPa)/√(25MPa) x 19.5 mm = 449.28 mm Available Length = (3600-450)/2-50 = 1525 mm Hence OK
Check For Trial Depth Against Moment About X Axis Bending moment at critical section: Mux =
= 1076.66 KN-m
α1 = 0.85-0.0015.f’c=0.8125 Øs=0.85
Verification Manual — 103
Chapter — 3 3.1 CSA General Isolated Foundation 1
= 0.62817 Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (750-50-0.5 x 20) mm = 690 mm So, ρ =0.001892 Hence OK
About Z Axis Bending moment at critical section, Mux =
= 1076.66 KN-m
α1 = 0.85-0.0015.f’c=0.8125 Øs=0.85
= 0.62817 Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (750-50-0.5 x 20) mm = 690 mm So,ρ =0.001892 Hence OK
Area of Steel Required Along X Direction (Bottom) Astx =ρ.B.deff= 4700 m2m Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 6750 mm2 Provided area = 6750 m2m
Along Z Direction (Bottom) Astz = ρ.L.deff= 4700 m2m Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 6750 mm2 Provided area = 6750 m2m
Along X Direction (Top) Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 6750 mm2 Provided area = 6750 m2m
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Section 3 Canadian Code (CSA A23.3-2004) 3.2 CSA General Isolated Foundation 2
(as no uplift is present so min steel is provided)
Along Z Direction (Top) Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 6750 mm2 Provided area = 6750 m2m (as no uplift is present so min steel is provided)
3.1.4 Comparison Table 3-1: CSA verification example 1 comparison STAAD FounReference Percent DifValue of dation Result ference Result Bearing Pressure 286.45 KN/m2 283.5 KN/m2 Negligible Governing Moment 1076.66 KN-m 1076.64 KN- Negligible m 1076.66 KN-m 1076.66 KNm Shear Force(One-Way) 768.22 KN 768.01 KN Negligible Shear Force(Two-Way) Resisting Shear Force (One-Way) Resisting Shear Stress (Two-Way) Resisting force for sliding Resisting Moment for Overturning
768.22 KN 2811.63 KN 1031 KN
768.01 KN 2811.49 KN 1031.14 KN
1031 KN 949.7 KN/m2 1834.66 KN
1031.14 KN 949.86 KN/m2 1837.09 KN
1834.66 KN 6604.78 KNm
1837.09 KN 6613.4 KNm
Negligible None Negligible Negligible Negligible
Ast (B)
6604.78 KNm 6613.4 KNm 6750 mm 6750 mm
None
Ast (T)
6750 mm 6750 mm
6750 mm 6750 mm
None
Ld (rqrd)
6750 mm 449.28 mm
6750 mm 449.28 mm
None
Ld (available)
449.28 mm 1525 mm
449.28 mm 1525 mm
None
1525 mm
1525 mm
3.2 CSA General Isolated Foundation 2 3.2.1 Reference
Verification Manual — 105
Chapter — 3 3.2 CSA General Isolated Foundation 2
3.2.2 Problem Design of a square Isolated Footing A tied column, 500 mm square, and reinforced with eight No. 35 bars carries an unfactored dead load of 900 kN and an unfactored live load of 800 kN. Suitable soil with a factored soil bearing pressure of 300 kN/m2 is available at a depth of 1.5 m . Design a square footing. The compressive strength f’c is 20 MPa for the column and 20 MPa for the footing. All steel has fy=350 MPa. Unit weight of concrete and soil is 24 kN/m2 and 16 kN/m2 respectively. Figure 3-2: Plan and Elevation
3.2.3 Solution Trial Footing Size Initial footing size is based on soil bearing capacity. As per CSA A.23.3-04 cls. 8.3 and Annex C. the 2005 National Building Code of Canada load combination factors must be used: Factored Load = 1.25 DL + 1.5 LL = (1.25 X 900 kN) + (1.5 x 800 kN) = 2,325 kN Required area of footing: 2,325 /300 = 7.75 m2
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Section 3 Canadian Code (CSA A23.3-2004) 3.2 CSA General Isolated Foundation 2
Total Axial load = 2,325 +Self Weight of footing + weight of soil Self Weight of footing = 3 x 3 x 0.6 x 24 = 129.6 KN weight of soil=3 x 3 x 1.5 x 16 = 216 KN For square footing, the axial force on the footing is: 2,325 +129.6 + 216 =2670.6 KN So stress on soil=2670.6 /(3x3)=296.73 KN/m2
Calculate Factors of Safety In this case, we do not have any sliding and overturning forces. The CSA A23.3-04 recommends for a footing that experiences horizontal shear, the designer must make sure that this shear is transferred to the subgrade utilizing the passive soil resistance and the friction between the subgrade and the footing surface. The passive soil resistance will be ignored in STAAD Foundation to calculate the factor of safety against sliding check. Factor of safety against overturning must be checked as per the NBCC. Anyway, max sliding force =axial load x coeff of friction for coeff of friction =0.5, Sliding force= 0.5x 2670.6 =1335.3 KN (same for X & Z dir) Max resisting moment against overturning = axial force x Dimension/2 = 0.5x 2670.6x3 KNm = 4005.45 KNm (Same WRT both x and z axis). Stress on soil from Factored load=2325/(3x3)=258.33 KN/m2
Check for One-Way Shear Along X Direction Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (600-50-0.5 x 20) mm = 540 mm
Vumax =
= 550.24 KN
Ø = 0.65, λ = 1 dv = 0.9.deff = 0.9 x 490 = 441 mm bw = 3000 mm Now allowable shear Vc =
=655986 N =655.99 KN
V < Vc, Hence Safe
Verification Manual — 107
Chapter — 3 3.2 CSA General Isolated Foundation 2
Along Z Direction Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (600-50-0.5 x 20) mm = 540 mm
Vumax =
= 550.24 KN
Ø = 0.65, λ = 1 dv = 0.9.deff = 0.9 x 490 = 441 mm bw = 3000 mm Now allowable shear Vc =
= 655986 N = 655.99 KN
V < Vc, Hence Safe
Punching Shear Punching shear is checked on a perimeter 0.5d = 270 mm from the column face. Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (600-50-0.5 x 20) mm = 540 mm Area within Critical Perimeter Am = (500+2x0.5x.54)2 = 1.0816 m2 Vmax =
258.33 x (3x3-1.0816) = 2045.56 KN
Critical perimeter Pm = 2 x ( b + h + 2x d) = 4.16 m τv = Vmax/(Pm · d) = 0.91 N/mm2 α=4
ß=L/B =5/5 =1
1.657 N/mm2 2.645 N/mm2 1.1046 N/mm2 As effective depth > 300 mm so the multiplier = 1300/(1000+deff) = 0.844 So,
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Section 3 Canadian Code (CSA A23.3-2004) 3.2 CSA General Isolated Foundation 2
Vr1= 1.398 N/mm2 =1398KN/m2 Vr2= 2.232N/mm2 ==2232 KN/m2 Vr3= 0.932 N/mm2 =932 KN/m2 So min{ Vr1,Vr2,Vr3} = 932 KN/m2 So allowable shear = Vc = 932 KN/m2 V < Vc , Hence safe
Development Length Along Z Axis ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) db k1 = 1 if clear cover is less than 300 mm or else use 0.45 k2 = 1 if coated reinforcement is used k2 = 1.2 if epoxy coated reinforcement is used k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdb k2 = 1.5 if bar spacing is less than 6 xdb k3 = 1 Normal density concrete k4 = 0.8 for 20M and smaller bar size k4 = 1 for 20M and larger bar size ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (350 MPa)/√(20MPa) x 19.5 mm = 439.52 mm Available Length = (3000-500)/2-50 = 1200 mm Hence OK
Along X Axis ld = 0.45 k1 x k2 x k3 x k4 fy/√(f'c) db k1 = 1 if clear cover is less than 300 mm or else use 0.45 k2 = 1 if coated reinforcement is used k2 = 1.2 if epoxy coated reinforcement is used k2 = 1.5 if epoxy coated reinforcement is used and clear cover is less than 3xdb k2 = 1.5 if bar spacing is less than 6 xdb k3 = 1 Normal density concrete k4 = 0.8 for 20M and smaller bar size k4 = 1 for 20M and larger bar size ld = 0.45 x 1 x 0.8 x 1 x 0.8 x (350 MPa)/√(20MPa) x 19.5 mm = 439.52 mm Available Length = (3000-500)/2-50 = 1200 mm Hence OK Verification Manual — 109
Chapter — 3 3.2 CSA General Isolated Foundation 2
Check For Trial Depth Against Moment About X Axis Bending moment at critical section Mux =
= 605.46 KN-m
α1 = 0.85-0.0015.f’c=0.82 Øs=0.85
= 0.0346 Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (600-50-0.5 x 20) mm = 540 mm So,ρ =0.002405 Hence OK
About Z Axis Bending moment at critical section Mux =
= 605.46 KN-m
α1 = 0.85-0.0015.f’c=0.82 Øs=0.85
= 0.0346 Assuming 50 mm clear cover and 20 mm bar, effective depth deff = (600-50-0.5 x 20) mm = 540 mm So,ρ =0.002405 Hence OK
Area of Steel Required Along X Direction (Bottom) Astx =ρ.B.deff= 3896 m2m
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Section 3 Canadian Code (CSA A23.3-2004) 3.2 CSA General Isolated Foundation 2
Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 4599.9 mm2 Provided area = 4600 m2m
Along Z Direction (Bottom) Astz = ρ.L.deff= 3896 m2m Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 4599.9 mm2 Provided area = 4600 m2m Use #20 @ 190 c/c
Along X Direction (Top) Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 4599.9 mm2 Provided area = 4600 m2m (as no uplift force is present only min steel is provided) Use #20 @ 190 c/c
Along Z Direction (Top) Minimum area of steel Ast min = (0.2x√f’c /fy)xB.D= 4599.9 mm2 Provided area = 4600 m2m (as no uplift force is present only min steel is provided) Use #20 @ 190 c/c
Verification Manual — 111
Chapter — 3 3.3 CSA General Isolated Foundation 3
3.2.4 Comparison Table 3-2: CSA verification example 2 comparison STAAD Percent Value of Reference Result Foundation Difference Result 2 Bearing Pressure 296.73 KN/m 296.07 Negligible KN/m2 Governing Moment 605.46 KN-m 605.46 KN- None m 605.46 KN-m 605.46 KNm Shear Force(One550.24 KN 550.06 KN Negligible Way) 550.24 KN 550.06 KN Shear Force(Two2045.56 KN 2045.45 KN Negligible Way) Resisting force for 1335.3KN 1335.3KN 1332.3 KN Negligible sliding 1332.3 KN Resisting Moment 4005.45 KNm 3996.827 Negligible for Overturning 4005.45 KNm KNm
Ast (B)
#20@190 c/c #20@190 c/c
Ast (T)
#20@190 c/c #20@190 c/c
3996.827 KNm #20@190 c/c #20@190 c/c #20@190 c/c
Ld (rqrd)
439.52 mm
#20@190 c/c 439.52 mm
Ld (available)
439.52 mm 1200 mm
439.52 mm 1200 mm
1200 mm
1200 mm
None
None
None None
3.3 CSA General Isolated Foundation 3 3.3.1 Reference 3.3.2 Problem Design an isolated footing with the given data: Load Fy = 1200 KN, fc = 30 MPa, fy = 400 MPa, Column Dimension = 300 mm x 300 mm, and Bearing Capacity of Soil = 90KN/m2.
112 — STAAD Foundation Advanced V8i
Section 3 Canadian Code (CSA A23.3-2004) 3.3 CSA General Isolated Foundation 3 Coefficient of friction =0.5, FOS against sliding =1.5, FOS against overturning =1.5. Height of soil above footing=450 mm, GWT is 300 mm from GL. Surcharge= 10 KN/m2 Figure 3-3: Plan and Elevation
3.3.3 Solution Approximate area of footing required = 1200/90 m2 = 13.33 m2 Assuming 4.3 m x 4.3 m x 0.500 m footing dimension, Weight of footing = 4.3 x 4.3 x 0.500 x 25 KN = 231.125 KN Weight of above soil = 4.3 x 4.3 x 0.450 x 18 KN = 149.77 KN Reduction of Weight due to buoyancy = 4.3x4.3 x (0.500+0.450-0.300) x 9.81 KN = 117.9 KN Load due to surcharge = 4.3x4.3 x 10 KN =184.9 KN
Therefore, total load on the footing = (1200+231.125 +149.77 +184.9 -117.9) KN = 1647.895 KN Maximum pressure = 1647.895 /(4.3x4.3) = 89.12 KN/m2 89.12 KN/ m2 =0.67 (Clause No 10.1.7) Øc = 0.6 (clause 8.4.2) Øs = 0.85 (clause 8.4.3) Solving the equation ρ (steel area ratio = 0.165 % Therefore, Astx = ρ.b,d= 1450 m2m Minimum area of steel Astmin = 0.2/100 x B x D = 2280 mm2 Provided area = 2280 mm2
Along Z Direction Calculate Kr (neutral axis/depth ratio) for Actual Bending Moment
Solving the previously stated equation ρ (steel area ratio = 0.165 % Therefore, Astx = ρ.b,d= 1450 m2m Minimum area of steel Astmin = 0.2/100 x B x D = 2280 mm2 Provided area = 2280 mm2
Verification Manual — 121
Chapter — 3 3.4 CSA General Combined Foundation s1
Check for Development Length Ld (required)=1.15.k1.k2.k3.k4.fy/((dcs+Kr) ).Ab/√(f' )= 380.7 mm c
(CSA A23-3-04 Clause No 12.2.2 & 12.2.3) Ld (available)Along X=(Length-pedestal length) 1/2 –Cover=775 mm Ld (required)250) Provided area = 5323 m2m
Check for One-Way Shear Along X Direction
Percentage of steel pt = = 0.236 Average Base Pressure along one edge = (133.69 + 154.73)x0.5 = 144.21 KN/m2 Average Base Pressure along other edge = (133.69 + 154.73)x0.5 = 144.21 KN/m2 Approximate Base Pressure at the left critical section = 144.21 + (144.21 144.21) x 2667/3950 = 144.21 KN/m2 Approximate Base Pressure at the right critical section = 144.21 + (144.21 144.21) x 2667/3950 = 144.21 KN/m2 Hence, the SF at critical section F = (144.21 + 144.21) x0.5 x 1.283 x 3.95 = 730.84 KN So max SF along X axis Fux = 731 KN Developed shear stress τv = 731 x 1000 / (3950 x 542) = 0.341 N/mm2
Verification Manual — 155
Chapter — 4 4.7 IS General Isolated Foundation 7
Now allowable stress= 0.348 N/mm2 τv < τc, Hence Safe
Along Z Direction
Percentage of steel pt = = 0.2486 Average Base Pressure along one edge = (133.69 + 133.69)x0.5 = 133.69 KN/m2 Average Base Pressure along other edge = (154.73 + 154.73)x0.5 = 154.73 KN/m2 Approximate Base Pressure at the left critical section = 154.73 + (133.69 154.73) x 2667/3950 = 144.21 KN/m2 Approximate Base Pressure at the right critical section = 154.73 + (133.69 154.73) x 1283/3950 = 144.21 KN/m2 Hence, the SF at critical section (left) F = (133.69 + 140.53) x0.5 x 1.283 x 3.95 = 694.84 KN Hence, the SF at critical section (right) F = (15473 + 147.90) x0.5 x 1.283 x 3.95 = 766.83 KN So max SF along X axis Fux = 731 KN
156 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.7 IS General Isolated Foundation 7
So max SF=767 KN Developed shear stress τv = 767 x 1000 / (3950 x 542) = 0.358 N/mm2 Now allowable stress= 0.359 N/mm2 τv < τc Hence Safe
Punching Shear Punching shear is checked on a perimeter 0.5d = 271 mm from the column face. Area within Critical Perimeter Am = 0.709 m2 Vmax =
2148 KN
Critical perimeter Pm = 2 X ( b + h + 6 x d) = 3368 mm τv = Vmax/(Pm · d) = 1.177 N/mm2 ß=L/B =3.95/3.95 =1 k=0.5 +ß=1.5 , k250) Provided area = 1029 m2m
Along X Direction (Top) From IS -456-2000 Annex G, G-1, b: Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck) So solving equation for Ast, Astx = 192 m2m Minimum area of steel Ast min = 0.0012 x B x D = 972 mm2 ( as fy>250) Provided area = 972 m2m
Along Z Direction (Bottom) From IS -456-2000 Annex G, G-1, b: Mu =0.87.fy.Ast.d.(1-Ast.fy/b.d.fck) So solving equation for Ast,
Verification Manual — 161
Chapter — 4 4.8 IS Toolkit Combined 1
Astz = 627 m2m Minimum area of steel Ast min = 0.0012 x B x D = 4140 mm2 ( as fy>250) Provided area = 4140 m2m Figure 4-13: Dimension, Moment, and Shear and diagrams
Check for One-Way Shear
Percentage of steel pt = Vumax = 168.2 KN
162 — STAAD Foundation Advanced V8i
= 0.133
Section 4 Indian Code (IS 456 -2000) 4.8 IS Toolkit Combined 1
Developed shear stress V = 168.2 x 1000 / (1350 x 544)= 0.229 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Punching Shear For Column 1 Punching shear is checked on a perimeter 0.5d = 272 mm from the column face. 2 way shear= 489.89 KN τv = Vmax/(Pm · d) = 489.89 x 1000/(300 x 2 + 300 x 2 + 544 x 4) x 544 = 0.2668 N/mm2 ß=L/B = 5.75/1.35 = 4.26 k=0.5 +ß=5.26 , k250) Provided area = 3600 mm2
Verification Manual — 167
Chapter — 4 4.9 IS Toolkit Combined Foundation 2
Check for One-Way Shear
Percentage of steel pt = Vumax = 169.3 KN
= 0.133
Developed shear stress τv = 169.3 x 1000 / (1650 x 544) = 0.1886 N/mm2 Now allowable stress= 0.29 N/mm2 τv < τc, Hence Safe
Punching Shear For Column One Punching shear is checked on a perimeter 0.5d = 272 mm from the column face. 2 way shear= 434.3 KN τv = Vmax/(Pm · d) = 434.3 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544 = 0.2356 N/mm2 ß=L/B =5.75/1.35 =4.26 k=0.5 +ß=5.26 , k250) Provided area = 3888 mm2 Figure 4-17: Shear Force and Bending Moment diagrams
Check for One-Way Shear Percentage of steel pt = Vumax = 223.95 KN
= 0.133
Developed shear stress V = 223.95 x 1000 / (1650 x 544) = 0.249 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
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Section 4 Indian Code (IS 456 -2000) 4.10 IS Toolkit Combined Foundation 3
Punching Shear For Column 1 Punching shear is checked on a perimeter 0.5d = 272 mm from the column face. 2 way shear= 630.07 KN τv = Vmax/(Pm · d) = 630.07 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544 = 0.343 N/mm2 ß=L/B =5.4/1.65 =3.27 k=0.5 +ß=4.27 , k250) Provided area = 4320 mm2
Check for One-Way Shear Percentage of steel pt = 0.133 Vumax = 248.613 KN Developed shear stress V = 0.261 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Punching Shear For Column One Punching shear is checked on a perimeter 0.5d = 272 mm from the column face. 2 way shear= 449.289 KN τv = Vmax/(Pm · d) = 449.289 x 1000 / (300 x 2 + 300 x 2 + 544 x 4) x 544 = 0.245 N/mm2 ß=L/B =6/1.75 =3.43 k=0.5 +ß=4.43 , k 250) Provided area = 2,098 mm2
Calculation of Shear
Parallel to X Axis For shear wrt X1X1 Contribution from pile 1 = pile 2 = 320.95 x 0.67 = 215.03 KN So Total V X1X1 = 430 KN For shear wrt X2X2
186 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.12 IS Pilecap 1
Contribution from pile 3 = pile 4 = 320.95 x 0.67 = 215.03 KN So Total V X2X2 = 430 KN So Maximum V parallel to X direction = 430 KN
Parallel to Z Axis For shear wrt Z1Z1 Contribution from pile 1 = pile 4 = 320.95 x 0.67 = 215.03 KN So Total V Z1Z1 = 430 KN For shear wrt Z2Z2 Contribution from pile 2 = pile 3 = 320.95 x 0.67 = 215.03 KN So Total V Z2Z2 = 430 KN So Max V parallel to Z direction = 430 KN
Check for One-Way Shear Along X Direction Percentage of steel pt = 100·Ast/(B·de) = 0.136 Vumax = 430 KN Developed shear stress V = 430 x 1,000 / 1,900 x 814 = 0.278 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Along Z Direction Percentage of steel pt = 100·Ast/(B·de) = 0.136 Vumax = 430 KN Developed shear stress V = 430 x 1,000 / 1,900 x 814 = 0.278 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Verification Manual — 187
Chapter — 4 4.12 IS Pilecap 1
Punching Shear
Punching shear is checked on a perimeter 0.5d = 407 mm from the column face. Contribution from pile 1 = from pile 2 = from pile 3 = from pile 4 = 276.4 KN So total punching shear Vmax= 1,105.7 KN Pm = 4 x (250 + 814/2 + 814/2) = 4,256 mm τv = Vmax/(Pm · d) = 0.319 N/mm2 ß = L/B =1,900/1,900 = 1 k = 0.5 + ß = 1.5 , k ≤ 1 Hence, k = 1 Now allowable stress= τc = k(0.25)√fck = 1.25 N/mm2 τv < τc , Hence safe
188 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.13 IS Pilecap 2
4.12.4 Comparison Table 4-13: IS verification example 12 comparison STAAD FounReference Percent DifValue of dation Result ference Result Pile Reaction, Service 220.95 220.5 None (KN) Pile Reaction, Ultimate 320.95 320.5 None (KN) Governing Moment, Mx 304.9 304.5 None (KNm) Governing Moment, Mz 304.9 304.5 None (KNm) Shear Force, One-Way, 430 429.5 None X (KN) Shear Force, One-Way, 430 429.5 None Z (KN) Shear Force, Two-Way 1,105.7 1,104.3 None (KN)
4.13 IS Pilecap 2 4.13.1 Reference 4.13.2 Problem Design pilecap foundation with the given data: Load Fy = 1,100 KN, Mx= 50 KNm, Fz= 50 KN,fc = 25 MPa, fy = 415 MPa, Column Dimension = 250 mm x 250 mm. Pedestal ht= 500 mm Diameter of pile= 400 mm. Vertical capacity =300 KN, Horizontal capacity = 100 KN Uplift capacity = 80 KN Pedestal dimensions: 250 mm x 250 mm
Verification Manual — 189
Chapter — 4 4.13 IS Pilecap 2 Figure 4-21: Plan, Elevation, and Pedestal dimensions
4.13.3 Solution depth of pilecap is equal to 1.5x the pile diameter, D = 600 mm Take D = 1,255 mm c/c pile distance = 3x pile diameter =1,200 mm. Edge distance =350 mm Assuming five pile combination, Coordinates of piles considering pedestal at 0, 0, 0
190 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.13 IS Pilecap 2 Table 4-14: Pile Coordinates in Plan Pile X Coordinate Z Coordinate No (mm) (mm) 1 -849 -849 2 -849 849 3 0 0 4 849 -849 5 849 -849 pilecap dimension is 2,400 mm x 2,400 mm x 1,255 mm Weight of footing = 2.4 x 2.4 x 1.255 x 25 KN = 180.72 KN Weight of pedestal = 0.25 x 0.25 x 0.5 x 25 KN = 0.78 KN Therefore, total load on the pilecap = (1,100 + 180.72 + 0.78) KN = 1,281.5 KN So Pile reaction from axial load= 1,281.5 /5= 256.3 KN Moment from lateral load = (1.255 + 0.5) x 50= 87.75 KNm Moment Mx ( from input) = 50 KNm So Total moment = 137.75 KNm Using Rivet theory: Reaction from moment= ±137.75(0.849)/[4(0.849 2)] = ±40.56 KNm So Reaction at Pile 2= reaction at pile 5 = 256.3 + 40.56 = 296.86 KN Reaction at Pile 1= reaction at pile 4 = 256.3 - 40.56 = 215.74 KN Reaction at Pile 3= 256.3 KN So Critical vertical reaction= 297 KN< 300 KN Lateral reaction = 50/5 = 10 KN < 50 KN, Hence OK As there is no net uplift load, so each pile is safe in uplift capacity.
Factored Design Load factor for self wt is taken =1 Load factor for axial load is taken 1.5 So, Axial Load on pilecap = 1.5(1,100) + 1(180.72) + 1(0.78) = 1,831.5 KN Moment on pilecap = 1.5(137.75) = 206.62 KNm Load on each pile from axial reaction = 1,831.5/5 = 366.3 KN Reaction from moment= ±206.62(0.849)/[4(0.849 2)] = ±60.84 KNm So Reaction at Pile 2= reaction at pile 5 = 366.3 + 60.84 = 427.14 KN Reaction at Pile 1= reaction at pile 4 = 366.3 - 60.84 = 305.46 KN
Verification Manual — 191
Chapter — 4 4.13 IS Pilecap 2
Reaction at Pile 3= 366.3 KN
Calculation of Moment Moment is calculated at face of column
About Z Axis For moment wrt X1X1 Contribution from pile 1 = 305.46 x 0.724 = 221.15 KNm Contribution from pile 2 = 427.14 x 0.724 = 309.25KNm Contribution from pile 3 = 1.7 KNm So Total Mz X1X1 = 532.1 KNm For moment wrt X2X2 Contribution from pile 4 = 305.46 x 0.724 = 221.15 KNm Contribution from pile 5 = 427.14 x 0.724 = 309.25KNm Contribution from pile 3 = 1.7 KNm So Total Mz X2X2 = 532.1 KNm So Max value of Mz = 532.1 KNm
About X Axis For moment wrt Z1Z1
192 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.13 IS Pilecap 2
Contribution from pile 1 = 305.46 x 0.724 = 221.15 KNm Contribution from pile 4 = 305.46 x 0.724 = 221.15 KNm Contribution from pile 3 = 1.7 KNm So Total Mx Z1Z1 = 444 KNm For moment wrt Z2Z2 Contribution from pile 2 = 427.14 x 0.724 = 309.25 KNm Contribution from pile 5 = 427.14 x 0.724 = 309.25 KNm Contribution from pile 3 = 1.7 KNm So Total Mx Z2Z2 = 620.2 KNm So Max value of MX = 620.2 KNm
Check For Trial Depth Moment About Z Axis Bending moment at critical section Muz = 532.1 KN-m Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth deff = 1,149 mm K = 700/(1,100 + 0.87x fy ) = 0.479107 Ru = 0.36 (fck) Kumax (1-0.42Kumax) = 3.4442 N/mm2 B =2,400 mm, deff = 1,149 mm Resisting Moment =Ru. B deff2 = 10,913 KNm Hence OK
Moment About X Axis Bending moment at critical section Mux = 620.2 KN-m Assuming 50 mm clear cover, 50 mm pile in pilecap & and 12 mm bar, effective depth deff = 1,149 mm K = 700/(1,100 + 0.87x fy ) = 0.479107 Ru = 0.36 (fck) Kumax (1-0.42Kumax) = 3.4442 N/mm2 B = 2,400 mm, deff = 1,149 mm Resisting Moment =Ru. B deff2 = 10,913 KNm Hence OK
Verification Manual — 193
Chapter — 4 4.13 IS Pilecap 2
Area of Steel Required Along X Direction From IS -456-2000 Annex G, G-1, b: 1 − A stf y Mu = 0.87fyA st d bd f ck
So solving equation for Ast, Astx = 1,510 mm2 Minimum area of steel Ast min = 0.0012 x B x D = 3,614 mm2 ( as fy > 250) Provided area = 3,614 mm2
Along Z Direction From IS -456-2000 Annex G, G-1, b: 1 − A stf y Mu = 0.87fyA st d bd f ck
So solving equation for Ast, AstZ = 1,293 mm2 Minimum area of steel Ast min = 0.0012 x B x D = 3,614 mm2 ( as fy > 250) Provided area = 3,614 mm2
Calculation of Shear According to Amendment 1shear is checked on a perimeter 0.5d =574.5 mm from the column face.
194 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.13 IS Pilecap 2
Parallel to X Axis
For shear wrt X1X1 Contribution from pile 1 = 305.46 x 0.873 = 266.67 KN Contribution from pile 2 = 427.14 x 0.873 = 372.89 KN So Total V X1X1 = 639.56 KN For shear wrt X2X2 Contribution from pile 4 = 305.46 x 0.873 = 266.67 KN Contribution from pile 5 = 427.14 x 0.873 = 372.89 KN So Total V X2X2 = 639.56 KN So Max V parallel to X direction = 639.56 KN
Parallel to Z Axis For shear wrt Z1Z1 Contribution from pile 1 = 305.46 x 0.873 = 266.67 KN Contribution from pile 4 = 305.46 x 0.873 = 266.67 KN Contribution from pile 3 = 0 KN So Total V Z1Z1 = 533.34 KN For shear wrt Z2Z2 Contribution from pile 2 = 427.14 x 0.873 = 372.89 KN Contribution from pile 5 = 427.14 x 0.873 = 372.89 KN Contribution from pile 3 = 0 KN
Verification Manual — 195
Chapter — 4 4.13 IS Pilecap 2 So Total V Z2Z2 = 745.7 KN So Max V parallel to Z direction = 745.7 KN
Check for One-Way Shear Along X Direction Percentage of steel pt = 100·Ast/(B·de) = 0.131 Vumax = 639.56 KN Developed shear stress V = 639.56 x 103 / (2,400 x 1,149) = 0.232 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Along Z Direction Percentage of steel pt = 100·Ast/(B·de) = 0.131 Vumax = 745.75 KN Developed shear stress V = 745.75 x 103 / (2,400 x 1,149) = 0.27 N/mm2 Now allowable stress= 0.29 N/mm2 V < τc, Hence Safe
Punching Shear
Punching shear is checked on a perimeter 0.5d = 574.5 mm from the column face. Contribution from pile 1 = from pile 4 = 300.6 KN Contribution from pile 2 = from pile 5 = 420.3 KN Contribution from pile 3 = 0 KN So total punching shear Vmax= 1,441.8 KN Pm = 4x(250 + 574.5 + 574.5) = 5,596 mm
196 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.14 IS Mat Combined Foundation 1
τv = Vmax/(Pm · d) = 0.224 N/mm2 ß = L/B = 2,400/2,400 = s1 k = 0.5 +ß = 1.5 , k ≤ 1 Hence, k = 1 Now allowable stress= τc =k(0.25)√fck = 1.25 N/mm2 τv < τc , Hence safe
4.13.4 Comparison Table 4-15: IS verification example 13 comparison STAAD FounReference Percent DifValue of dation Result ference Result Pile Reaction, Service 215.74 215.62 Negligible (KN) 296.86 296.788
Pile Reaction, Ultimate (KN)
Governing Moment (KNm) Shear Force, One-Way (KN) Shear Force, Two-Way (KN)
256.3
256.203
215.74
215.617
296.86 305.46
296.788 305.32
427.14
427.081
366.3
366.203
305.46
305.324
427.14 532
427.081 531
Negligible
620 640
619.5 641
Negligible
746 1441.8
747 1435.7
Negligible
Negligible
4.14 IS Mat Combined Foundation 1 4.14.1 Reference ‘Reinforced Concrete Design’ by Pillai & Menon, Page 652, Example 14.7.
4.14.2 Problem Design a combined footing for two columns with the given data: C1 (400 mm x 400 mm) with 4-25 Ø bars and C2 (500 mm x 500mm) with 4-28 Ø bars supporting axial loads P1 = 900 KN and P2 = 1600 KN respectively (under service dead and live loads). The column C1 is an exterior column whose exterior face is flush with the property line. The center-tocentre distance between C1 and C2 is 4.5 meters. The allowable soil pressure at the base of
Verification Manual — 197
Chapter — 4 4.14 IS Mat Combined Foundation 1 the footing, 1.5 m below ground level, is 240 KN/m2. Assume a steel of grade Fe 415 in the columns as well as the footing, and a concrete grade of M 20 in the footing. Figure 4-22: Footing Plan
Figure 4-23: >Loads on Footing
4.14.3 Solution Dimension of Mat (Based on the bearing Capacity given): Length = 6.16 m Width = 2 m Depth = 0.95 m
Calculation for base-pressure Self-weight of mat = 6.16 x 2 x 0.95 x 25 KN = 292.6 KN Total load on the mat = (1600+900+200.2) KN = 2792.6 KN Base pressure = 279.6 / (6.16 x 2) KN/m2 = 226.67 KN/m2 < 240 KN/m2 (Hence Safe) Ultimate load for C 1 = Pu1 = 1.5 x 900 = 1350 KN Ultimate load for C 2 = Pu2 = 1.5 x 1600 = 2400 KN
198 — STAAD Foundation Advanced V8i
Section 4 Indian Code (IS 456 -2000) 4.14 IS Mat Combined Foundation 1
Then uniformly distributed upward load = (Pu1+Pu2)/6.16 KN/m = 608.8 KN/m Developed shear stress,
v
= 0.533 N/mm2
0.2 m) 1 1 3.000 m 3.000 m 1.000 m 0.500 m Table 9-2: Reinforcement details Base Number 1
Base Reinforcement Bottom Reinf. Bottom Reinf. Main Stirrups (Mz) (Mx) Bars # 10 @ 60 mm c / # 10 @ 60 mm c / N / A N/A c c Foundation Reinforcement
Verification Manual — 437
Chapter — 9 9.1 Cone Footing Design
9.1.1 Problem Characteristics of Concrete and Steel Heavy concrete units: 18.000 kN/m3 Compressive strength of concrete: 11.900 N/mm2 Reinforcement strength: 210.000 N/mm2 Minimum bar size: # 6 Maximum bar size: # 50 Minimum bar spacing: 50.00 mm Maximum bar spacing: 500.00 mm Clear Cover Reinforcement layer thickness (F, CL): 50.00 mm
Soil Characteristics Unit Weight: 18.00 kN/m3 Foundation bearing capacity: 180.00 kPa Surcharge: 0.00 kN/m2 Height of soil above footing: 2000.00 mm
Geometry Information Initial size of base Thickness (Ft) : 1000.00 mm Length - X (Fl) : 3000.00 mm Width - Z (Fw) : 3000.00 mm Edge height of the cone footing (St) : 500.00 mm
Column Dimension Column Shape: Rectangular Column length - X (Pl) : 600.00 mm Column width - Z (Pw) : 600.00 mm
Column Cap Column cap length - X : N/A Column cap width - Z : N/A
438 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.1 Cone Footing Design
9.1.2 Solution Table 9-3: Loads for foundation base size estimation -For foundation base (1) Condition Vertical Shear X Shear Z Moment X Moment Z No. Force (KN) (KN) (KN) (kN·m) (kN·m) 101 1000.000 0.000 0.000 99.998 99.998 Table 9-4: Loads for Punching shear check and reinforcements- For foundation base (1) Vertical Force Shear X Shear Z Moment X Moment Z LC (KN) (KN) (KN) (kN·m) (kN·m) 102 1000.000 0.000 0.000 99.998 99.998
Basic dimensions Initial size (Lo) = 3.00 m Initial size (Wo) = 3.00 m Net buoyancy = -0.00 kN Adhesion = 0.00 kN The minimum required base area, Amin = P / fa = 7.356 m2 The initial design area , Ao = Lo·Wo = 9.00 m2
Final design size Length (L2) = 3.00 m No. of control condition: # 101 Width (W2) = 3.00 m No. of control condition: # 101 Area (A2) = 9.00 m2 Figure 9-1: Four corners of the calculated stress
Verification Manual — 439
Chapter — 9 9.1 Cone Footing Design
Load Case 101 101 101 101
Pressure at Corner1 (q1) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner2 (q2) (KN/m2) 102.6667 102.6667 102.6667 102.6667
Pressure at Corner3 (q3) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner4 (q4) (KN/m2) 191.5556 191.5556 191.5556 191.5556
Zero-pressure area (Au) (m2) 0.00 0.00 0.00 0.00
If Au equals zero, that means it is small eccentricity, and do not need to adjust the pressure. Otherwise, the pressure needs to be adjusted. The negative pressure should always set as 0. Keep adjusting if necessary. Four corners of the stress adjusted data (if any). Pressure at No. Load Corner1 (q1) Condition (KN/m2) 101 147.1111 101 147.1111 101 147.1111 101 147.1111
Pressure at Corner2 (q2) (KN/m2) 102.6667 102.6667 102.6667 102.6667
Pressure at Corner3 (q3) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner4 (q4) (KN/m2) 191.5556 191.5556 191.5556 191.5556
If necessary, the bottom will be adjusted accordingly based on size. Zero-pressure area ( if any ) Control the condition number = N / A Foundation area = 9.00 m2 Zero-pressure area = 0.00 m2 Zero-pressure area percentage = 0.00%
9.1.3 Check Overturning and Sliding Stability Figure 9-2: Elevation of stability forces
440 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.1 Cone Footing Design Table 9-5: Factor of safety Sliding Factor of Safety Overturning Factor of Safety Load Case No. X Dir. Z Dir. X Dir. Z Dir. 101 N/A N/A 19.763 19.763
Critical load cases and governing factor of safety of overturning Along the X Direction Critical sliding load case along the X direction: 101 Governing sliding force : 0.000 kN Resisting Force for Sliding: 658.760 kN Minimum sliding coefficient under critical load case: 0.000 Critical Overturning load case along X direction: 101 Critical overturning moment: 99.998 kN·m Resisting moment for Overturning: 1976.244 kN·m Minimum overturning coefficient under critical load case: 19.763
Along the Z Direction Critical sliding load case along the Z direction : 101 Governing sliding force : 0.000 kN Resisting Force for Sliding: 658.760 kN Minimum sliding coefficient under critical load case: 0.000 Critical Overturning load case along Z direction : 101 Critical overturning moment: 99.998 kN·m Resisting Moment for Overturning: 1976.244 kN·m Minimum overturning coefficient under critical load case: 19.763
9.1.4 Check Shear Following formulae are used per GB50007 - 2002 code for design of building foundations. F ≤ 0.7·β f a h (Ref. clause 8.2.7 - 1) l
a
m
hp t m 0
= (A + a ) / 2 (Ref. clause 8.2.7 - 2) t
b
F = P ·A (Ref. clause 8.2.7 - 3) l
j
l
Punching One-way Check Positive X Side Control condition = # 102
Verification Manual — 441
Chapter — 9 9.1 Cone Footing Design Punching shear F = P ·A = 88.889·724774.976 = 64.424 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Negative X Side Control condition = # 102 Punching shear F = P ·A = 133.333·724774.976 = 96.637 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Positive Z Side Control condition = # 102 Punching shear F = P ·A = 133.333·724774.976 = 96.637 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7·0.917·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Negative Z Side Control condition = # 102 Punching shear F = P ·A = 88.889·724774.976 = 64.424 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7·0.92·1.270·(0.600 +2.470) / 2·0.935 = 1169.589 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Two-way punching test (four sides) Control condition = # 102 442 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.1 Cone Footing Design Punching shear F = P ·A = 111.111·2899099.905 = 322.122 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7·0.917·1.270·(2.400 +9.880) / 2·0.935 = 4678.355 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
9.1.5 Reinforcement Reinforcement Along the X Direction Figure 9-3: Reinforcement parallel to the X-direction
A simplified formula for reinforcement is used per GB50010 – 2002. No control condition = # 102 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Cross-sectional area about X-axis, A cross = 2,425,000.005 Minimum reinforcement area Astmin = Ρmin·A cross- = 0.15 · 2,425,000.005 = 3,637.500 Calculate moment MI = (A1) 2 [(2·l + a ')·(pmax + p - 2·G / A) + (pmax - p)·l] / 12 = 1,200.0002·[(2·3,000.000 +600.000) (0.169 +0.152 - 2·324,000.000/9,000,000.000) + (0.169 0.152)·3,000.000] / 12 = 20,3519,997.379 kN·m Calculate area required A = M / (0.9·h ·f ) = 20,3519,997.379 / (0.9·935.000·210.000) = 1,139.498 st
I
0 y
Select rebar size, db = 10.000 Minimum allowable reinforcement spacing, Smin = 50.000 mm Verification Manual — 443
Chapter — 9 9.1 Cone Footing Design Maximum allowable reinforcement spacing, Smax = 500.000 mm With actual spacing, S = 60.000 mm Actual area, Ast (Actual) = 3637.500 mm2 Smin ≤ S ≤ Smax Selected Reinforcement satisfy the requirements. Astmin ≤ Ast, with real Selected Reinforcement satisfy the requirements.
Reinforcement Along the Z Direction Figure 9-4: Reinforcement parallel to the Z-direction
A simplified formula for reinforcement is used per GB50010 – 2002. No control condition = # 102 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Cross-sectional area about Z-axis, A cross = 2425000.005 Minimum reinforcement area Astmin = Ρmin·A cross = 0.15%·2425000.005 = 3637.500 Calculate moment MI = (A1) 2 [(2·l + a ')·(pmax + p - 2·G / A) + (pmax - p)·l] / 12 = 1200.0002·[(2·3000.000 +600.000) (0.169 +0.152 - 2·324000.000/9000000.000) + (0.169 0.152)·3000.000] / 12 = 203519997.379 kN·m Calculate area required Ast = MI / (0.9·h0·fy) = 203519997.379 / (0.9·935.000·210.000) = 1151.685 Select rebar size, db = 10.000 Minimum allowable reinforcement spacing, Smin = 50.000 mm 444 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.2 PKPM Isolated Footing Design Maximum allowable reinforcement spacing, Smax = 500.000 mm With actual spacing, S = 60.000 mm Actual area, Ast (Actual) = 3637.500 mm2 Smin ≤ S ≤ Smax Reinforced selected to meet the requirements . Astmin ≤ Ast, with real Reinforcement meet the requirements Reinforcements should be placed at the base bottom.
9.2 PKPM Isolated Footing Design 9.2.1 Problem Elevation and Plan
Foundation type: cast-in-site cone footing Initial iteration base dimensions: Length = 3000 mm Width = 3000 mm
Verification Manual — 445
Chapter — 9 9.2 PKPM Isolated Footing Design
Height = 500 mm Second iteration Length = 700 mm Width = 700 mm Height = 500 mm Bottom elevation of the basis: -2.0 m Shifts of the base: S Direction: 0 mm B direction: 0 mm Reinforcement at the bottom of the base: Y direction : 10 @ 200 X direction : 10 @ 200 Weight of the foundation and soil:: 18.0 kPa
Column section information High column section: 600 mm Column section width: 600 mm Eccentric x : 0 mm Eccentric y : 0 mm Column angle: 0°
Loading information Basic values of vertical load: Nk = 1000 kN Basic value of the moment along X dir.: Mx = 100 kN·M Basic value of the moment along Y dir.: My = 100 kN·M
9.2.2 Solution Check Shear Following formula Per GB5007 - 2002 code for design of building foundation: F ≤ 0.7·β f a h (Ref. clause 8.2.7 - 1) l
a
m
hp t m 0
= (A + a ) / 2 (Ref. clause 8.2.7 - 2) t
b
F = P ·A (Ref. clause 8.2.7 - 3) l
j
l
Resisting Shear force calculation: X + direction , height H = 1000 F = P ·A = 133.33·0.69 = 91.67 l
j
l
F ≤ 0.7·β f (A + a )·h /2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN l
hp t
t
b
0
Punching Shear check is satisfied in this direction. X- direction , height H = 1000
446 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.2 PKPM Isolated Footing Design
F = P ·A = 92.59·0.69 = 63.66 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN hp t
t
b
o
Punching Shear check is satisfied in this direction. Y + direction , height H = 1000 F = P ·A = 92.59·0.69 = 63.66 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN hp t
t
b
o
Punching Shear check is satisfied in this direction. Y- direction , height H = 1000 F = P ·A = 133.33·0.69 = 91.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.60 +2.50)·0.95 / 2 = 1288.19 KN hp t
t
b
o
Punching Shear check is satisfied in this direction.
Check Shear Edges H = 1000. Fl = N - pk·(bc +2·h0)·(hc +2·h0) = 1000.00 - 111.1·(600.0 + 2·950.0)·(600.0 +2·950.0)·1e-6 = 305.56 Kn Fr = 0.7·β ·f ·a ·h = 0.7·0.98·1270.9·(600.0 + 600.0 + 2·950.0)·950.0·1e-6 = 5152.76 Kn hp t m
0
Punching Shear check at edges is satisfied. X + direction , height H = 1000 mm F = P ·A = 133.33·0.56 = 74.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN hp t
t
b
o
Punching Shear check at edges is satisfied. X- direction , height H = 1000 mm F = P ·A = 91.85·0.56 = 51.44 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN hp t
t
b
o
Punching Shear check at edges is satisfied. Y + direction , height H = 1000 mm F = P ·A = 91.85·0.56 = 51.44 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN hp t
t
b
o
Punching Shear check at edges is satisfied. Y- direction , height H = 1000 mm F = P ·A = 133.33·0.56 = 74.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7·0.98·1270.94·(0.70 + 2.60)·0.95 / 2 = 1371.30 KN hp t
t
b
o
Punching Shear check at edges is satisfied.
Verification Manual — 447
Chapter — 9 9.2 PKPM Isolated Footing Design
Bending Reinforcement The following formula are used Per GB5007 - 2002 code for design of building foundation: M = (1/12)a 2·[(2·l + a')(P 1
jmax
+ P ) + (P j
jmax
+ P )·l ] j
Moment calculations x direction, h0 = 940 mm M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52 kN·m M =(1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 = 148.48 kN·m y direction , h0 = 940 mm M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 = 148.48 kN·m M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52 kN·m x direction , h0 = 940 mm M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52 kN·m M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 = 148.48 kN·m y direction , h0 = 940 mm M = (1.20)2·[(2·3.00 + 0.60)·(88888.89 + 106666.66) + (88888.89 - 106666.66)·3.00] / 12 = 148.48 kN·m M = (1.20)2·[(2·3.00 + 0.60)·(133333.33 + 115555.55) + (133333.33 - 115555.55)·3.00] / 12 = 203.52 kN·m Reinforcement calculation: M = 203.520 1
A
Gx
= M / (0.9·h ·f ) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm 2 1
0 y
M = 203.520 2
A
Gy
= M / (0.9·h ·f ) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm 2 2
0 y
M = 203.520 1
A
Gx
= M / (0.9·h ·f ) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm 2 1
0 y
M = 203.520 2
A
Gy
= M / (0.9·h ·f ) = 203520.016 / (0.9·0.940·210.) = 1145.559 mm 2 2
0 y
The area of steel at X direction: 1145.559 The area of steel at Y direction: 1145.559 The initial area of steel along X direction is satisfied.
448 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.3 Stepped Foundation Design The initial area of steel along Y direction is satisfied. The area of steel required: AgX: 10 @ 200 AgY: 10 @ 200
9.3 Stepped Foundation Design
-
Table 9-6: Overview of the stepped foundation design Basic Geometry Dimension (Base Level) Group Length X Dir. Width Z Dir. Height Number Order (M) (M) (M) 1 Total 3.000 m 3.000 m 1.200 m Article 3.000 m 3.000 m 0.400 m (1)Order Article (2)order 2.000 m 2.000 m 0.400 m
-
-
Node Number 1 -
Article (3)order 1.000 m
1.000 m
0.400 m
Table 9-7: Reinforcement details Node Number 1
Base Reinforcement Bottom Reinf. Bottom Reinf. Main Stirrups (Mz) (Mx) Bars # 10 @ 60 mm c / # 10 @ 60 mm c / N / A N/A c c Foundation Reinforcement
9.3.1 Problem Basic Geometry Height of the base - (Ft): 1200.00 mm Length of the base - X (Fl): 3000.00 mm Width of the base - Z (Fw): 3000.00 mm
Column Dimension Column Shape : Rectangular Length of the Column section - X (Pl): 600.00 mm Width of the column section - Z (Pw): 600.00 mm
Base Base length - X: N / A Base width - Z: N / A
Verification Manual — 449
Chapter — 9 9.3 Stepped Foundation Design
Concrete and Steel Parameters Concrete density: 18.000 kN/m3 Concrete strength: 11.900 N/mm2 Reinforcement strength: 210.000 N/mm2 Minimum bar Size: # 6 Maximum bar size: # 40 Minimum bar spacing : 50.00 mm Maximum bar spacing : 500.00 mm Clear cover (F, CL): 50.00 mm
Soil Properties Soil type: Drained Density: 18.00 kN/m3 Foundation bearing capacity : 180.00 kPa Surcharge: 0.00 kN/m2 Embedment depth of foundation: 2,000.00 mm Adhesion: 0.00 kN/m2
Factor of Safety for sliding and overturning Basal friction coefficient: 0.50 Safety factor of sliding: 1.50 Safety factor of overturning: 1.50 Table 9-8: Critical loads for base size estimation - standard combination Condition Vertical Shear X Shear Z Moment X Moment Z No. Force (KN) (KN) (KN) (kN·m) (kN·m) 101 1000.000 0.000 0.000 99.998 99.998 Table 9-9: Loads for foundation design- the basic combination Vertical Force Shear X Shear Z Moment X Moment Z LC (KN) (KN) (KN) (kN·m) (kN·m) 102 1000.000 0.000 0.000 99.998 99.998
9.3.2 Solution Foundation Dimensions The initial length (Lo) = 76.20 m The initial width (Wo) = 76.20 m Buoyancy = -0.00 KN 450 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.3 Stepped Foundation Design Adhesion = 0.00 kN Minimum area of steel required Bearing pressure, Amin = P / qmax = 7.356 m2 Initial foundation area , Ao = Lo x Wo = 5806.44 m2
Final Design Sizes Length of the Base (L2) = 3.00 m Number of load case: # 101 Width of the base (W2) = 3.00 m Number of load case: # 101 Height of the base (D2) = 1.20 m Number of load case: # 101 Area (A2) = 9.00 m2
Corner Stresses Initial pressure at four corners ( before adjustment ) Figure 9-5: Four corners of the calculated stress
Load Case 101 101 101 101
Pressure at Corner1 (q1) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner2 (q2) (KN/m2) 102.6667 102.6667 102.6667 102.6667
Pressure at Corner3 (q3) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner4 (q4) (KN/m2) 191.5556 191.5556 191.5556 191.5556
Zero-pressure area (Au) (m2) 0.00 0.00 0.00 0.00
If Au equals zero, that means it is small eccentricity, and do not need to adjust the pressure. Otherwise, the pressure needs to be adjusted. The negative pressure should always set as 0. Keep adjusting if necessary.
Verification Manual — 451
Chapter — 9 9.3 Stepped Foundation Design
four corners of the stress of adjustment ( if necessary ) No. Load Condition 101 101 101 101
Pressure at Corner1 (q1) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner2 (q2) (KN/m2) 102.6667 102.6667 102.6667 102.6667
Pressure at Corner3 (q3) (KN/m2) 147.1111 147.1111 147.1111 147.1111
Pressure at Corner4 (q4) (KN/m2) 191.5556 191.5556 191.5556 191.5556
If necessary, the bottom will be adjusted accordingly based on size.
Details of the Zero-pressure zone ( if any ) Design condition number = N / A Area of Foundation Base = 9.00 sq.m Zero-pressure area = 0.00 sq.m Zero-pressure area percentage = 0.00%
Check overturning and sliding stability Factor of Safety table Table 9-10: Safety factors Sliding Factor of Safety Overturning Factor of Safety Load Case No. X Dir. Z Dir. X Dir. Z Dir. 101 N/A N/A 19.782 19.782
Critical loads and governing factor of safety of overturning and sliding Along the X Direction Critical sliding load case along X direction: 101 Governing sliding force: 0.000 kN Resisting Force for Sliding: 659.408 kN Minimum sliding coefficient under critical load case: 0.000 Critical Overturning load case along X direction: 101 Critical overturning moment: 99.998 kN·m Resisting moment for Overturning: 1978.188 kN·m Minimum overturning coefficient under critical load case 19.782
452 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.3 Stepped Foundation Design
Along the Z Direction Critical sliding load case along Z direction: 101 Critical sliding force: 0.000 Resisting Force for Sliding: 659.408 kN Minimum sliding coefficient under critical load case: 0.000 Critical Overturning load case along Z direction: 101 Critical overturning moment: 99.998 kN·m Resisting Moment for Overturning: 1978.188 kN·m Minimum overturning coefficient under critical load case: 19.782
9.3.3 Check Shear The following formulae are used per GB50007 - 2002 code for design of building foundations. F ≤ 0.7·β f a h (Ref. clause 8.2.7 - 1) l
a
m
hp t m 0
= (A + a ) / 2 (Ref. clause 8.2.7 - 2) t
b
F = P ·A (Ref. clause 8.2.7 - 3) l
j
l
Punching One-way Check Positive X Direction Control condition = # 102 Punching shear F = P ·A = 88.889·190774.972 = 16.958 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 0.933 · 1.270 · (0.600 + 2.870) / 2 · 1.135 = 1633.932 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Negative X Direction Control condition = # 102 Punching shear F = P ·A = 133.333 · 190774.972 = 25.437 kN l
j
l
Punching shear capacity F = 0.7·β f a h =0.7 · 0.933 · 1.270 ·(0.600 +2.870) / 2 · 1.135 = 1633.932 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe Verification Manual — 453
Chapter — 9 9.3 Stepped Foundation Design
Positive Z Direction Control condition = # 102 Punching shear F = P ·A = 133.333 · 190774.972 = 25.437 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 0.933 · 1.270 · (0.600 +2.870) / 2 · 1.135 = 1633.932 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Negative Z Direction Control condition = # 102 Punching shear F = P ·A = 88.889 · 190774.972 = 16.958 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 0.933 · 1.270 · (0.600 +2.870) / 2 · 1.135 = 1633.932 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
Two-way punching test (four sides) Control condition = # 102 Punching shear F = P ·A = 111.111 · 763099.890 = 84.789 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 0.933 · 1.270 · (2.400 +11.480) / 2 · 1.135 = 6535.727 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, Safe
454 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.3 Stepped Foundation Design
9.3.4 Reinforcement Calculations Along the X Axis Figure 9-6: Reinforcement parallel to the X-direction
A simplified formula for reinforcement is used per GB50010 – 2002. Critical load case number = # 102 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Cross-sectional area about X-axis, A cross = 2400000.000 Minimum reinforcement area Astmin = 0.15(A cross)- = 0.15(2,400,000.000) = 3600.000 Calculate moment MI = (A1) 2 [(2·l + a ') · (pmax + p-2·G / A) + (pmax - p)·l] / 12 = 1,200.0002 · [(2 · 3,000.000 + 600.000) (0.169 + 0.152 - 2 · 324,000.000/9,000,000.000) + (0.169 - 0.152) · 3000.000] / 12 = 203,519,997.379 kN·m Calculate the area required A = M / (0.9·h ·f ) = 203,519,997.379 / (0.9 · 1,135.000 · 210.000) = 1, 069.687 st
I
0 y
Select Rebar size, db = 10.000 Minimum allowable reinforcement spacing, Smin = 50.000 mm Maximum allowable reinforcement spacing, Smax = 500.000 mm Actual spacing, S = 60.000 mm Actual area, Ast (Actual) = 3,600.000 mm2 Smin ≤ S ≤ Smax Selected Reinforcements satisfy the requirements.
Verification Manual — 455
Chapter — 9 9.3 Stepped Foundation Design
Astmin ≤ Ast, with real Selected Reinforcements satisfy the requirements.
Along the Z Axis Figure 9-7: Reinforcement parallel to the Z-direction
A simplified formula for reinforcement is used per GB50010 – 2002. Critical load case number = # 102 Minimal reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Cross-sectional area about Z-axis, A cross = 2400000.000 Minimum reinforcement area Astmin = Ρmin · A cross- = 0.15% · 2400000.000 = 3600.000 Calculate moment MI = (A1) 2 [(2·l + a ') · (pmax + p-2·G / A) + (pmax - p)·l] / 12 = 1,200.0002 · [(2 · 3,000.000 + 600.000) (0.169 + 0.152 - 2 · 324,000.000/9,000,000.000) + (0.169 - 0.152) · 3000.000] / 12 = 203,519,997.379 kN·m Calculate the area required A = M / (0.9·h ·f ) = 203,519,997.379 / (0.9 · 1,135.000 · 210.000) = 1,084.241 st
I
0 y
Reinforced selected size, db = 10.000 Minimum allowable reinforcement spacing, Smin = 50.000 mm Maximum allowable reinforcement spacing, Smax = 500.000 mm With actual spacing, S = 60.000 mm Actual area, Ast (Actual) = 3600.000 mm2 Smin ≤ S ≤ Smax Selected Reinforcements satisfy the requirements. 456 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.4 PKPM Stepped Footing Design
Astmin ≤ Ast, with real Selected Reinforcements satisfy the requirements. Reinforcements should be placed at the base bottom.
9.4 PKPM Stepped Footing Design 9.4.1 Problem Foundation type : Cast-in-place, stepped footing Initial Single base dimensions: Length = 3,000 mm Width = 3,000 mm Height = 400 mm Second Length = 2,000 mm Width = 2,000 mm Height = 400 mm Third Length = 1,000 mm Width = 1,000 mm Height = 400 mm Bottom elevation of the base: -2.0 m Shift the basis of the heart: S Direction : 0 mm B direction : 0 mm Bottom Reinforcement: Y direction : 10 @ 200 X direction : 10 @ 200 Unit self weight of the soil and footing: 18.0 kPa Column section information: Height of the column section: 600 mm Width of the Column section: 600 mm Eccentricity x : 0 mm Eccentricity y : 0 mm Column angle: 0 °
Loading information The basic values of vertical load: Nk = 1,000 kN X direction of the basic value of the moment: Mx = 100 kN·m Y direction of the basic value of the moment: My = 100 kN·m Verification Manual — 457
Chapter — 9 9.4 PKPM Stepped Footing Design Elevation and plan
9.4.2 Solution Check Shear The following formulae are used per GB5007 - 2002 code of design of building foundations: F ≤ 0.7·β f a h (Ref. clause 8.2.7 - 1) l
a
m
hp t m 0
= (A + a ) / 2 (Ref. clause 8.2.7 - 2) t
b
F = P ·A (Ref. clause 8.2.7 - 3) l
j
l
Calculate resisting Shear force: X + direction , height H = 1000 F = P ·A = 133.33·0.69 = 91.67 l
j
l
F ≤ 0.7·β f (A + a )·h /2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN l
hp t
t
b
0
Punching shear check is satisfied along this direction X- direction , height H = 1200 F = P ·A = 89.63 · 0.15 = 13.22 l
j
l
458 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.4 PKPM Stepped Footing Design
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y + direction , height H = 1200 F = P ·A = 89.63 · 0.15 = 13.22 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y- direction , height H = 1200 F = P ·A = 133.33 · 0.15 = 19.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 0.97 · 1270.94 · (0.60 +2.90) · 1.15 / 2 = 1,730.76 KN hp t
t
b
o
Punching shear check is satisfied along this direction
Check Shear Edges H = 1200. Fl = N-pk · (bc +2 · h0) · (hc +2 · h0) = 1000.00-111.1 · (600.0 +2 ******)*( 600.0 +2 ******)* 1e-6 = 65.56 Kn F = 0.7·β f a h = 0.7 · 0.97 · 1270.9 · (600.0 +600.0 +2 ******)******* 1e-6 = 6923.04 Kn l
hp t m 0
Sides punching checking meet X + direction , height H = 800 mm F = P ·A = 133.33 · 0.69 = 91.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN hp t
t
b
o
Punching shear check is satisfied along this direction X- direction , height H = 800 mm F = P ·A = 92.59 · 0.69 = 63.66 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y + direction , height H = 800 mm F = P ·A = 92.59 · 0.69 = 63.66 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y- direction , height H = 800 mm F = P ·A = 133.33 · 0.69 = 91.67 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (1.00 +2.50) · 0.75 / 2 = 1167.68 KN hp t
t
b
o
Punching shear check is satisfied along this direction X + direction , height H = 400 mm F = P ·A = 91.11 · 0.43 = 38.95 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN hp t
t
b
o
Verification Manual — 459
Chapter — 9 9.4 PKPM Stepped Footing Design Punching shear check is satisfied along this direction X- direction , height H = 400 mm F = P ·A = 133.33 · 0.43 = 57.00 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y + direction , height H = 400 mm F = P ·A = 91.11 · 0.43 = 38.95 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN hp t
t
b
o
Punching shear check is satisfied along this direction Y- direction , height H = 400 mm F = P ·A = 133.33 · 0.43 = 57.00 l
j
l
0.7·β ·f ·(a + a )·h / 2 = 0.7 · 1.00 · 1270.94 · (2.00 +2.70) · 0.35 / 2 = 731.75 KN hp t
t
b
o
Punching shear check is satisfied along this direction
Bending Reinforcement The following formula is used per GB50007 - 2002 code for design of building foundations: M = (1/12)a 2·[(2·l + a')(P 1
jmax
+ P ) + (P j
jmax
+ P )·l ] j
Moment calculations x direction , h0 = 340 mm M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (133,333.33 + 125,925.92) + (133,333.33 - 125,925.92) · 3.00] / 12 = 36.11 kN·m M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (88,888.89 + 96,296.30) + (88,888.89 - 96,296.30) · 3.00] / 12 = 25.00 kN·m y direction , h0 = 340 mm M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (88,888.89 + 96,296.30) + (88,888.89 - 96,296.30) · 3.00] / 12 = 25.00 kN·m M = 0.50 · 0.50 [(2 · 3.00 +0.60) · (133,333.33 + 125,925.92) + (133,333.33 - 125,925.92) · 3.00] / 12 = 36.11 kN·m x direction , h0 = 740 mm M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (133,333.33 + 118,518.52) + (133,333.33 - 118,518.52) · 3.00] / 12 = 142.22 kN·m M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (88,888.89 + 103,703.70) + (88,888.89 - 103,703.70) · 3.00] / 12 = 102.22 kN·m y direction , h0 = 740 mm M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (88,888.89 + 103,703.70) + (88,888.89 - 103,703.70) · 3.00] / 12 = 102.22 kN·m
460 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.5 Combined Foundation
M = 1.00 · 1.00 [(2 · 3.00 +0.60) · (133,333.33 + 118,518.52) + (133,333.33 - 118,518.52) · 3.00] / 12 = 142.22 kN·m x direction , h0 = 1140 mm M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (133,333.33 + 115,555.55) + (133,333.33 - 115,555.55) · 3.00] / 12 = 203.52 kN·m M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (88,888.89 + 106,666.66) + (88,888.89 - 106,666.66) · 3.00] / 12 = 148.48 kN·m y direction , h0 = 1140 mm M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (88,888.89 + 106,666.66) + (88,888.89 - 106,666.66) · 3.00] / 12 = 148.48 kN·m M = 1.20 · 1.20 [(2 · 3.00 +0.60) · (133,333.33 + 115,555.55) + (133,333.33 - 115,555.55) · 3.00] / 12 = 203.52 kN·m Reinforcement calculation: M = 36.111 1
A
Gx
= M / (0.9·h ·f ) = 36,111.113 / (0.9 · 0.340 · 210.) = 561.953 mm 2 1
0 y
M = 36.111 2
A
Gy
= M / (0.9·h ·f ) = 36,111.113 / (0.9 · 0.340 · 210.) = 561.953 mm 2 2
0 y
M = 142.222 1
A
Gx
= M / (0.9·h ·f ) = 142,222.219 / (0.9 · 0.740 · 210.) = 1,016.890 mm 2 1
0 y
M = 142.222 2
A
Gy
= M / (0.9·h ·f ) = 142,222.219 / (0.9 · 0.740 · 210.) = 1,016.890 mm 2 2
0 y
M = 203.520 1
A
Gx
= M / (0.9·h ·f ) = 203,520.016 / (0.9 · 1.140 · 210.) = 944.584 mm 2 1
0 y
M = 203.520 2
A
Gy
= M / (0.9·h ·f ) = 203,520.016 / (0.9 · 1.140 · 210.) = 944.584 mm 2 2
0 y
The area of steel at X direction: 1,016.890 The area of steel at Y direction: 1,016.890 The original area of steel at X direction is satisfied. The original area of steel at Y direction is satisfied. Calculated the areas of steel are: AgX: 10 @ 200 AgY: 10 @ 200
9.5 Combined Foundation Per Chinese standard GB50007-2002.
Verification Manual — 461
Chapter — 9 9.5 Combined Foundation
Base Number 1
Table 9-11: Overview of the design results Left CanRight CanLength Width Height tilever (M) tilever (M) (M) (M) (M) 0.150 2.150 8.300 3.100 0.700
Table 9-12: Foundation reinforcement details Top LonBottom LonTop Trans- Bottom TransBase gitudinal Rein- gitudinal Rein- verse Reinverse ReinNumber forcement forcement forcement forcement 1 #12 @ 55 mm #12 @ 105 mm #12 @ 105 mm #12 @ 105 mm c/c c/c c/c c/c Elevation and plan
462 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.5 Combined Foundation
9.5.1 Problem Basic Geometry Column 1 Column dimensions Column Shape : Rectangle Length of the column - X (Pl): 0.30 m Width of the column - Z (Pw): 0.30 m No Column caps
Column 2 Column section size Column Shape : Rectangle Length of the Column - X (Pl): 0.30 m Width of the Column - Z (Pw): 0.40 m No Column cap Left overhanging length : 0.15 m Right cantilevered length : 2.15 m Whether the length of the left cantilever needs design ( or enter a fixed value )? Yes Whether the length of the right cantilever needs design ( or enter a fixed value )? Yes The initial input length (Lo) of the foundation: 1500.00 mm The initial input width (Wo) of the foundation: 3.10 m The initial input of height (Do) of the foundation: 700.00 mm
Clear Cover and Soil Properties The thickness of the clear cover for cap : 50.00 mm The thickness of the clear cover for foundation : 50.00 mm Density of the Soil: 25.00 kN/m3 Foundation bearing capacity : 200.00 kN/m2 Additional ground pressure : 0.00 kip/in2 Weight of soil about foundation : 1500.00 mm Groundwater depth : -0.00 KN
Concrete and Steel Properties Concrete density: 25.000 kN/m3
Verification Manual — 463
Chapter — 9 9.5 Combined Foundation Compressive strength of concrete : 11.900 N/mm2 Reinforcement strength : 210.000 N/mm2 Minimum bar Size : 12.0 mm Maximum bar size : 50.0 mm Minimum bar spacing : 50.00 mm Maximum bar spacing : 400.00 mm
9.5.2 Solution Buoyancy generated on the ground = -0.00 kN Minimum area of steel required Amin = Pc / qmax: 13.80 m 2 Specify the initial cross-sectional area Ao = L x W: 25.73 m 2 Final provided foundation dimensions: Length of base , L: 8.30 m Width of base, W: 3.10 m Height of base, Do: 0.70 m Area of base, A: 25.73 m2 Left Cantilever length , Llo: 0.15 m Right Cantilever length , Lro: 2.15 m Table 9-13: Load cases for base dimensions estimation - standard combination Condition Column Axial Shear Shear Moment Moment No. No. Force (KN) X (KN) Z (KN) X (kN·m) Z (kN·m) 1 1 105076.125 0.000 0.000 0.000 0.000 1 2 210152.249 0.000 0.000 0.000 0.000 Table 9-14: Load cases for foundation design - basic combinationn Condition Column Axial Shear Shear Moment Moment No. No. Force (KN) X (KN) Z (KN) X (kN·m) Z (kN·m) 1 1 105076.125 0.000 0.000 0.000 0.000 1 2 210152.249 0.000 0.000 0.000 0.000 Four corners of the calculated stress Load Case 1 1 1 1
Pressure at Corner1 (q1) (KN/m2) 107.2940 107.2940 107.2940 107.2940
464 — STAAD Foundation Advanced V8i
Pressure at Corner2 (q2) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Pressure at Corner3 (q3) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Pressure at Corner4 (q4) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Zero-pressure area (Au) (m2) 0.00 0.00 0.00 0.00
Section 9 Chinese Code (GB50007-2002) 9.5 Combined Foundation If Au equals zero, that means it is small eccentricity, and do not need to adjust the pressure. Otherwise, the pressure needs to be adjusted. The negative pressure should always set as zero. Keep adjusting if necessary. Adjusted pressure at corners (if necessary) Pressure at Condition Corner1 (q1) No. (KN/m2) 1 107.2940 1 107.2940 1 107.2940 1 107.2940
Pressure at Corner2 (q2) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Pressure at Corner3 (q3) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Pressure at Corner4 (q4) (KN/m2) 107.2940 107.2940 107.2940 107.2940
Overturning Stability Test Moment Moment Resistance Resistance Overturning Overturning StaX Z Moment X Moment Z Stability bility Factor Z (kN·m) (kN·m) (kN·m) (kN·m) Factor X 0.000 0.000 4273.272 11441.341 N / A 633,778,703.608
Condition No. 1
9.5.3 Check Shear The following formulae are used per GB50007 - 2002 code for design of building foundations. Formula is as follows : F ≤ 0.7·β f a h (Ref. clause 8.2.7 - 1) l
a
m
hp t m 0
= (A + a ) / 2 (Ref. clause 8.2.7 - 2) t
b
F = P ·A (Ref. clause 8.2.7 - 3) l
j
l
One-way Punching Shear Check Column 1, +X Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 5,097,642.75 = 356.62 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 1, -X Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 0.00 = 0.0 kN l
j
l
Verification Manual — 465
Chapter — 9 9.5 Combined Foundation Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 1, +Z Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 1,010,688.00 = 70.70 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 1, -Z Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 1,010,688.00 = 70.70 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.56) / 2 · 0.64 = 523.64 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 2, +X Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 3,725,275.99 = 260.61 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.66) / 2 · 0.64 = 579.83 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 2, -X Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 7,548,609.37 = 528.08 kN l
j
l
466 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.5 Combined Foundation Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.30 · 1.66) / 2 · 0.64 = 579.83 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 2, +Z Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 163,8475.99 = 114.62 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.40 · 1.56) / 2 · 0.64 = 551.73 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 2, -Z Direction Control condition = # 1 Punching shear F = P ·A = 69.96 · 163,8475.99 = 114.62 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (0.40 · 1.56) / 2 · 0.64 = 551.73 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 1, Four Edges Control condition = # 1 Punching shear F = P ·A = 139.91 · 3,559,509.38 = 498.03 kN l
j
l
Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (1.20 · 4.99) / 2 · 0.64 = 1,739.48 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
Column 2, Four Edges Control condition = # 1 Punching shear F = P ·A = 139.91 · 7,275,418.66 = 1,017.94 kN l
j
l
Verification Manual — 467
Chapter — 9 9.5 Combined Foundation Punching shear capacity F = 0.7·β f a h = 0.7 · 1.00 · 1270.00 · (1.20 · 6.46) / 2 · 0.64 = 2,206.94 kN u
hp t m 0
F < 0.7·β f a h l
hp t m 0
Hence, safe.
9.5.4 Reinforcement Design Top Longitudinal Reinforcement A simplified formula for reinforcement is used in accordance with GB50010-2002. No control condition = # 1 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Minimum area of steel, Astmin = 3,255.000 mm2 The area of steel required Ast = MI / (0.9 · h0 · fy) = 740,000,006.857 / (0.9 · 6,44.000 · 210.000) = 6,079.727 mm 2 Selected rebar size,db = 12.000 mm Minimum allowable reinforcement spacing, Smin = 50.00 mm Maximum allowable reinforcement spacing, Smax = 400.00 mm Actual spacing, S = 55.00 mm Actual area of steel required, Ast (Actual) = 6220.353 mm2 Smin ≤ S ≤ Smax Selected Reinforcements satisfy the requirements. Astmin ≤ Ast, with actual Selected Reinforcements satisfy the requirements.
Bottom Longitudinal Reinforcement A simplified formula for reinforcement is used in accordance with GB50010-2002. No control condition = # 1 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Minimum area of steel, Astmin = 3,255.000 mm2 The area of steel required Ast = MI / (0.9 · h0 · fy) = -479,467,391.579 / (0.9 · 644.000 · 210.000) = -3,939.231 mm 2 Selected rebar size,db = 12.000 mm Minimum allowable reinforcement spacing, Smin = 50.00 mm Maximum allowable reinforcement spacing, Smax = 400.00 mm Actual spacing, S = 105.00 mm Actual area of steel required, Ast (Actual) = 3279.823 mm2 Smin ≤ S ≤ Smax 468 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.5 Combined Foundation Selected Reinforcements satisfy the requirements. Astmin ≤ Ast, with actual Selected Reinforcements satisfy the requirements.
Top Transverse Reinforcement A simplified formula for reinforcement is used in accordance with GB50010-2002. No control condition = # 1 Minimum reinforcement ratio [per Cl. 9.5.2], min = 0.15% Minimum area of steel, Astmin = 8715.000 mm2 The area of steel required Ast = MI / (0.9 · h0 · fy) = 0.000 / (0.9 · 644.000 · 210.000) = 0.000 mm 2 Selected rebar size,db = 12.000 mm Minimum allowable reinforcement spacing, Smin = 50.00 mm Maximum allowable reinforcement spacing, Smax = 400.00 mm Actual spacing, S = 105.00 mm Actual area of steel required, Ast (Actual) = 8821.592 mm2 Smin ≤ S ≤ Smax Selected Reinforcements satisfy the requirements. Astmin ≤ Ast, with actual Selected Reinforcements satisfy the requirements.
Bottom Transverse Reinforcement A simplified formula for reinforcement is used in accordance with GB50010-2002. No control condition = # 1 Minimum reinforcement ratio [per Cl. 9.5.2], ρmin = 0.15% Minimum area of steel, Astmin = 8,715.000 mm2 The area of steel required Ast = MI / (0.9 · h0 · fy) = 569,032,250.186 / (0.9 · 644.000 · 210.000) = 4,675.082 mm 2 Selected rebar size,db = 12.000 mm Minimum allowable reinforcement spacing, Smin = 50.00 mm Maximum allowable reinforcement spacin, Smax = 400.00 mm Actual spacing, S = 105.00 mm Actual area of steel required, Ast (Actual) = 8,821.592 mm2 Smin ≤ S ≤ Smax Selected Reinforcements satisfy the requirements. Astmin ≤ Ast, with actual
Verification Manual — 469
Chapter — 9 9.6 Pile Foundation Design Selected Reinforcements satisfy the requirements.
9.6 Pile Foundation Design A typical pile foundation design example is provided here to verify the pile foundation design per Chinese codes in the program. The Chinese codes implemented are " GB500072002 code for design of building foundations "," GB50009-2001 Load code for design of building structures "," GB50010-2002 Code for design of Concrete Structures "," Technical Code for Building Pile Foundations”
9.6.1 Problem Basic conditions Rectangular column foundation. Length of the column is 0.5000 m and the width of the column is 0.5000 m. The height of the base is 0.5000 m , the length of the base is 0.8 m, and the width of the base is 0.8. Loads: vertical load is 1500 kN and the basic combination distribution factor is 1.4 ( 1500 X 1.4 will involve in all members and reinforcements design).
Basic design parameters Concrete strength: 25 N/mm2 Concrete density: 25 kN/m3 Steel yield strength: 210 N/mm2 Clear cover thickness on sides: 50 mm Clear cover thickness on bottom: 50 mm Depth of pile cap: 75 mm The initial depth of pile cap: 300 mm Minimum bar diameter: 10 Maximum bar diameter: 45
Pile Parameters Pile layout: 3 row x 3 row = total 9 piles, spacing 1.5 m , center to edge of pile cap edge 0.5 m , pile diameter and 0.5 m , thus base of the cap is 4 m in length and 4 m in width. Pile bearing capacity: lateral capacity is 100 kN , vertical capacity is 500 kN , uplift capacity is 300 kN (both single pile). So the reactions of the pile can be calculated as: Table 9-15: Pile capacities under load case no. 101 Vertical Uplift Lateral -180.888 0.000 0.000 -180.888 0.000 0.000 -180.888 0.000 0.000 -180.888 0.000 0.000
470 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.6 Pile Foundation Design
Vertical -180.888 -180.888 -180.888 -180.888 -180.888
Uplift 0.000 0.000 0.000 0.000 0.000
Lateral 0.000 0.000 0.000 0.000 0.000
Table 9-16: Pile capacities under load case no. 102 Vertical Uplift Lateral -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000 -247.555 0.000 0.000
9.6.2 Solution Pile layout Column Dimension Column Shape : Rectangular Column length - X (Pl): 0.500 m Column width - Z (Pw): 0.500 m
Base A base ? Yes Base Shape : Rectangular Base height (Ph): 0.500 m Base length - X (Pl): 0.800 m Base width - Z (Pw): 0.800 m
Cap geometry Pile length P CL = 4.000 m Cap width P CW = 4.000 m Initial cap height t I = 0.300 m
Verification Manual — 471
Chapter — 9 9.6 Pile Foundation Design
Pile geometry Pile spacing, P s = 1.500 m Distance from the edge of the Pile cap to the center of pile, e = 0.500 m Pile diameter, d P = 0.500 m
Bearing capacity of pile Vertical bearing capacity of P P = 500.000 kN Lateral bearing capacity of P L = 100.000 kN Pullout capacity of P L = 300.000 kN
Material Properties Concrete f ' c = 25,000.004 kN/m2 Concrete f ' t = 1,890.000 kN/m2 Steel f y = 210,000.035 kN/m2
Concrete clear cover Concrete clear cover on the bottom, CC B = 0.050 m Concrete clear cover on the sides, CC S = 0.050 m Depth of pile cap depth, PC P = 0.075 m Load Case 101 102
Table 9-17: Load about the pile cap Fx Fz Mx (kNMy (kNFy (kN) (kN) (kN) m) m) 0.000 0.000 0.000 0.000 1500.00 0.000 0.000 0.000 0.000 2100.00
Mz (kNm) 0.000 0.000
Pile Design Calculations The total number of piles N = 9 Coordinates of Piles Pile No. 1 2 3 4
Reactions
X (m)
Y (m)
-1.500 -1.500 -1.500 0.000
-1.500 0.000 1.500 -1.500
472 — STAAD Foundation Advanced V8i
Vertical (kN) -247.555 -247.555 -247.555 -247.555
Lateral (kN) 0.000 0.000 0.000 0.000
Uplift (kN) 0.000 0.000 0.000 0.000
Section 9 Chinese Code (GB50007-2002) 9.6 Pile Foundation Design
Coordinates of Piles Pile No. 5 6 7 8 9
Reactions
X (m)
Y (m)
0.000 0.000 1.500 1.500 1.500
0.000 1.500 -1.500 0.000 1.500
Vertical (kN) -247.555 -247.555 -247.555 -247.555 -247.555
Lateral (kN) 0.000 0.000 0.000 0.000 0.000
Uplift (kN) 0.000 0.000 0.000 0.000 0.000
Check Depth of Pile Cap One Way Punching Shear Along Length Critical Load Case #102 Influential factor of sectional height β
hs
= (800/h )1/4 = (800/0)1/4 = 1.000 0
Shear Span-to-Depth Ratios λ = a /h = 1.050/0.300 = 3.000 x
x
0
Punching Shear Factor of Pile Cap α = 1.75/(λ + 1) = 1.75/(3.000 + 1) = 0.438 x
Shear Capacity of Pile Cap dV = β c
hs
·α·f ·b t
0·
h = 1.000 · 0.438 · 1,890.000 · 4.000 · 0.300 = 992.250 kN 0
Maximum Shear Design Value, V = 742.665 kN V < dVc Hence, Safe
One Way Punching Shear Along Width Critical Load Case #102 Influential factor of sectional height β
hs
= (800/h )1/4 = (800/0)1/4 = 1.000 0
Shear Span-to-Depth Ratios λ = a /h = 1.050/0.300 = 3.000 y
y
0
Punching Shear Factor of Pile Cap α = 1.75/(λ + 1) = 1.75/(3.000 + 1) = 0.438 y
Shear Capacity of Pile Cap dV = β c
hs
·α·f ·b t
0·
h = 1.000 · 0.438 · 1,890.000 · 4.000 · 0.300 = 992.250 kN 0
Maximum Shear Design Value, V = 742.665 kN V < dVc Verification Manual — 473
Chapter — 9 9.6 Pile Foundation Design Hence, Safe
Punching Shear Check for Column Critical Load Case #102 Shear Span-to-Depth Ratios λ
0x
= a /h = (1.050/0.300) = 1.000 0x
0
Shear Span-to-Depth Ratios λ
0y
= a /h = (1.050/0.300) = 1.000 0y
0
Influential factor of sectional height β
0x
= 0.84/(λ
0x
+ 0.2) = 0.84/(1.000 + 0.2) = 0.700
Influential factor of sectional height β
0y
= 0.84/(λ
0y
+ 0.2) = 0.84/(1.000 + 0.2) = 0.700
Shear Capacity of Pile Cap dV = 2 · [β · (b + a ) + β · (h + a )] · β · f · h = 2 · [0.700 · (0.500 + 1.050) + c 0x c 0y 0y c 0x hp t 0 0.700 · (0.500 + 1.050)] · 1.000 · 1,890.000 · 0.300 = 2460.780 kN Maximum Punching Shear Design Value Fl = 1980.440kN F < dV l
c
Hence, Safe
Punching Shear Check for Corner Column Critical Load Case #102 Shear Span-to-Depth Ratios λ = a /h = (0.300/0.300) = 1.000 1x
1x
0
Shear Span-to-Depth Ratios λ = a /h = (0.300/.0.300) = 1.000 1y
1y
0
Shear Span-to-Depth Ratios β = 0.56/(λ + 0.2) = 0.56/(1.000 + 0.2) = 0.467 1x
1x
Shear Span-to-Depth Ratios β = 0.56/(λ + 0.2) = 0.56/(1.000 + 0.2) = 0.467 1y
1y
Shear Capacity of Pile Cap dV = [β · (c + a /2) + β · (c + a /2)] · β · f · h = [0.467 · (0.700 + 0.300/2) + 0.467 c 1x 2 1y 1y 1 1x hp t 0 · (0.700 + 0.300/2)] · 1.000 · 1,890.000 · 0.300 = 449.820 kN Maximum Punching Shear Design Value Nl = 247.555kN N < dV l
c
Hence, Safe
474 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.6 Pile Foundation Design
Reinforcement Calculations Use the same reinforcement along both top and bottom.
Along X Direction Critical Load Case #102 Critical Moment M = ∑N x = 816.931 kN·m y
i i
Area of Steel Required A = M /(0.9 · f · h ) = 816.931/(0.9 · 210,000.035 · 0.300 = 14,407 mm 2 sy
y
y
0
Minimum Area of Steel Required A
s,min
= 0.15 · B · H = 0.15 · 4,000 · 300 = 1,800 mm 2
Bar Diameter, ds = 20 mm Bar Space, S = 80 mm Min Bar Space, Smin = 50 mm Max Bar Space, Smax = 500 mm Actual Bar Area required, As,actual = 49 · π · 10 · 10 = 15,393 mm2 S VDJ1=
500.00 (* 1.35)
KN Top
h0= 350.
αy= 900.
λy=2.571
VPL = βhs*1.75/(λ+1.0)*b0*h0*ft
Verification Manual — 481
Chapter — 9 9.6 Pile Foundation Design
=1.000*1.75/(2.571+1.0)*4000.* 350.*1.8881*1.e-3 =
1295.2KN
VCJ2= 1295.24KN > VDJ2=
500.00 (* 1.35)
KN
8、Steel Area Calculation DMX1 =
742.500
AGX = DMX1/(0.9*h0*fy)/YS = 350.0*210.0)/4.0= 2806.123mm*mm/M DMX2 =
742.500/(0.9*
742.500
AGX = DMX2/(0.9*h0*fy)/YS = 350.0*210.0)/4.0= 2806.123mm*mm/M DMY1 =
742.500/(0.9*
742.500
AGY = DMY1/(0.9*h0*fy)/XS = 350.0*210.0)/4.0= 2806.123mm*mm/M DMY2 =
742.500/(0.9*
742.500
AGY = DMY2/(0.9*h0*fy)/XS = 350.0*210.0)/4.0= 2806.123mm*mm/M ASX=2806.1mm*mm/M
742.500/(0.9*
ASY=2806.1mm*mm/M
The Area of Steel at x direction is satisfied, hence, safe. The Area of Steel at y direction is satisfied, hence, safe. Actual Areas of Steel required： AGx: 16@100 Com No
ASX
AGy: 16@100 ASY
H(1)
H(2) 1
2806.1
2806.1
400.0
2
2455.4
2455.4
450.0
3
2182.5
2182.5
500.0
4
1964.3
1964.3
550.0
482 — STAAD Foundation Advanced V8i
Section 9 Chinese Code (GB50007-2002) 9.6 Pile Foundation Design
5
1785.7
1785.7
600.0
6
1636.9
1636.9
650.0
7
1511.0
1511.0
700.0
9.6.3 Comparison Table 9-18: Chinese verification example 6 comparison STAAD FounReference Value of dation Result Result 2 Bearing Pressure 108.94 KN/m 108.63 KN/m2 Resisting force for sliding (x) 313.74 KN 312.867 KN Resisting Moment for Overturning 752.98 KNm 750.87 KNm (z) Resisting force for sliding (z) 313.74 KN 312.867 KN Resisting Moment for Overturning 752.98 KNm 750.87 KNm (x)
Percent Difference Negligible Negligible Negligible Negligible Negligible
Verification Manual — 483
Chapter 9 9.6 Pile Foundation Design
484 — (Undefined variable: Primary.ProductName)
Section 10
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Verification Manual — 485
Chapter 10
486 — (Undefined variable: Primary.ProductName)
Drilled Pier
357 E
Eccentricity
88 G
GB50007-2002
437 I
Indian Code
125
IS 456
125 P
Pile Cap
Index
Chinese Code
470
Plant Foundation
385
U
A ACI 318
201, 321
AS3600
3
Australian
3
General Combined Footing General Isolated Footing
United States Code
201
V Vertical Vessel Foundation 1
385
14, 16 3, 6
B British Combined Foundation Isolated Foundation
71, 77
23, 26, 32, 38, 44, 53, 62, 88
Mat Combined Foundation
83
British Code
23
BS8110
23 C
Canadian Code
99
Chinese Code
437
CSA A23.3
99 D
Deadman Anchors
321
Verification Manual — 487
List of Figures & Tables Figures Figure 1-1: Australian code General isolated foundation
4
Figure 1-2: Plan and Elevation
6
Figure 1-3: Plan and Elevation
15
Figure 1-4: Plan and Elevation
17
Figure 1-5: Graphs of combined strip footing internal forces
20
Figure 2-1: Bending section considered
24
Figure 2-2: One way shear section considered
24
Figure 2-3: Two way shear section considered
24
Figure 2-4: Plan and Elevation
27
Figure 2-5: Sections considered for bending in both directions
28
Figure 2-6: Sections considered for one-way shear in both directions
30
Figure 2-7: Section considered for punching shear
31
Figure 2-8: Plan and Elevation
33
Figure 2-9: Section considered for bending about the Z axis
47
Figure 2-10: Section considered for bending about the Z axis
48
Figure 2-11: Section considered for one-way shear along X direction
50
Figure 2-12: Section considered for one-way shear along z direction
51
Figure 2-13: Section considered for punching shear
52
Figure 2-14: Plan and Elevation
63
Figure 2-15: Section considered for punching shear
69
Verification Manual — 489
Chapter — 12 Figures
Figure 2-16: Plan and Elevation
72
Figure 2-17: Shear force and Bending Moment diagrams
76
Figure 2-18: Plan and Elevation
78
Figure 2-19: Shear force and Bending Moment diagrams
82
Figure 2-20: Plan and Elevation
84
Figure 2-21: Plan and Elevation
89
Figure 2-22: Bending about major axes
91
Figure 3-1: Plan and Elevation
100
Figure 3-2: Plan and Elevation
106
Figure 3-3: Plan and Elevation
113
Figure 3-4: Elevation and Plan, with dimension and loads
116
Figure 3-5: Bending sections considered
117
Figure 3-6: Shear sections considered
119
Figure 3-7: Two-way shear sections considered
120
Figure 3-8: Plan and Elevation
123
Figure 4-1: Plan and Elevation
126
Figure 4-2: Plan of Reinforcement
128
Figure 4-3: Cross Section showing Reinforcement
129
Figure 4-4: Plan and Elevation
130
Figure 4-5: Elevation and Plan showing reinforcement design
132
Figure 4-6: Plan and Elevation
134
Figure 4-7: Plan and Elevation
139
Figure 4-8: Plan and Elevation
141
Figure 4-9: Plan and Elevation
146
Figure 4-10: Plan and Elevation
151
Figure 4-11: Final Plan Dimensions
158
Figure 4-12: Plan and Elevation
159
Figure 4-13: Dimension, Moment, and Shear and diagrams
162
Figure 4-14: Plan and Elevation
165
Figure 4-15: Shear Force and Bending Moment diagrams
169
Figure 4-16: Plan and Elevation
171
Figure 4-17: Shear Force and Bending Moment diagrams
174
Figure 4-18: Plan and Elevation
177
Figure 4-19: Shear Force and Bending Moment diagrams
181
Figure 4-20: Plan and Elevation
183
490 — STAAD Foundation Advanced V8i
List of Figures & Tables Figures
Figure 4-21: Plan, Elevation, and Pedestal dimensions
190
Figure 4-22: Footing Plan
198
Figure 4-23: >Loads on Footing
198
Figure 4-24: Shear Force (kN, top) and Bending Moment (kNm, bottom) diagrams
200
Figure 5-1: Elevation and loads
202
Figure 5-2: Considered sections for two-way (bo) and beam (bw) action
203
Figure 5-3: Critical section for moment (long projection)
204
Figure 5-4: Elevation and Plan
207
Figure 5-5: Elevation and Plan
211
Figure 5-6: Elevation and Plan
216
Figure 5-7: Section considered for two-way shear
218
Figure 5-8: Elevation and Plan
221
Figure 5-9: Elevation and Plan
230
Figure 5-10: Elevation and Plan
234
Figure 5-11: Corner pressure values on plan for punching shear
236
Figure 5-12: One-way shear pressure values along x-direction
237
Figure 5-13: One-way shear pressure values along z-direction
238
Figure 5-14: Bending pressure about Z axis
239
Figure 5-15: Bending pressure about X axis
239
Figure 5-16: Elevation and Plan
241
Figure 5-17: Shear Force and Bending Moment diagrams
243
Figure 5-18: Elevation and Plan
247
Figure 5-19: Shear Force and Bending Moment diagrams
252
Figure 5-20: Elevation and Plan
254
Figure 5-21: Shear Force and Bending Moment diagrams
255
Figure 5-22: Elevation and Plan
259
Figure 5-23: Shear Force and Bending Moment diagrams
261
Figure 5-24: Elevation and Plan
265
Figure 5-25: Section considered for punching shear
267
Figure 5-26: Elevation and Plan
272
Figure 5-27: Section considered for two-way shear
274
Figure 5-28: Section considered for one-way shear
276
Figure 5-29: Section considered for bending
278
Figure 5-30: Elevation and Plan
281
Figure 5-31: Section considered for punching shear
282 Verification Manual — 491
Chapter — 12 Figures
Figure 5-32: Section considered for one-way shear
283
Figure 5-33: Section considered for moment
285
Figure 5-34: Elevation and Plan
288
Figure 5-35: Section considered for punching shear
290
Figure 5-36: Section considered for one-way shear
291
Figure 5-37: Section considered for moment
293
Figure 5-38: Elevation and dimensions
296
Figure 5-39: Forces on foundation
298
Figure 5-40: Shear and Bending diagrams
298
Figure 5-41: Plan and Elevation
303
Figure 5-42: Critical section for punching shear is at d/2
305
Figure 5-43: Critical section for moment is at the face of column
307
Figure 5-44: Plan and Elevation
313
Figure 5-45: Critical section for punching shear at d/2
315
Figure 6-1: Deadman Anchor Guy Tension Block section
324
Figure 6-2: Dispersion of soil against vertical uplift diagram
325
Figure 6-3: Dispersion line diagram
326
Figure 6-4: Top rebar force diagram
328
Figure 6-5: Bending moment diagram - top
328
Figure 6-6: Bending moment diagram - front face
329
Figure 6-7: Deadman Anchor Guy Tension Block section
331
Figure 6-8: Dispersion of soil against vertical uplift
333
Figure 6-9: Top rebar force diagram
336
Figure 6-10: Bending moment diagram - top
336
Figure 6-11: Bending moment diagram - front face
337
Figure 6-12: Deadman Anchor Guy Tension Block section
341
Figure 6-13: Dispersion of soil against vertical uplift diagram
342
Figure 6-14: Dispersion line diagram
344
Figure 6-15: Top rebar force diagram
345
Figure 6-16: Bending moment diagram - top
346
Figure 6-17: Bending moment diagram - front face
346
Figure 6-18: Deadman Anchor Guy Tension Block section
348
Figure 6-19: Dispersion of soil against vertical uplift diagram
350
Figure 6-20: Top rebar force diagram
353
Figure 6-21: Bending moment diagram - top
353
492 — STAAD Foundation Advanced V8i
List of Figures & Tables Tables
Figure 6-22: Bending moment diagram - front face
354
Figure 7-1: Pier Elevation
358
Figure 7-2: Pier Elevation
363
Figure 7-3: Pier Elevation
368
Figure 7-4: Pier Elevation
372
Figure 7-5: Pier Elevation
377
Figure 7-6: Pier Elevation
381
Figure 8-1: Tank and foundation elevation
386
Figure 8-2: Anchor bolt plan
386
Figure 8-3: One-way shear dimensions
392
Figure 8-4: Two-way shear check
392
Figure 8-5: Tank and foundation elevation
395
Figure 8-6: Anchor bolt plan
395
Figure 8-7: One-way shear dimensions
401
Figure 8-8: Two-way shear check
401
Figure 8-9: Tank and foundation elevation
404
Figure 8-10: Anchor bolt plan
404
Figure 8-11: One-way shear dimensions
410
Figure 8-12: Two-way shear check
410
Figure 9-1: Four corners of the calculated stress
439
Figure 9-2: Elevation of stability forces
440
Figure 9-3: Reinforcement parallel to the X-direction
443
Figure 9-4: Reinforcement parallel to the Z-direction
444
Figure 9-5: Four corners of the calculated stress
451
Figure 9-6: Reinforcement parallel to the X-direction
455
Figure 9-7: Reinforcement parallel to the Z-direction
456
Tables Table 1-1: Australian verification example 1 comparison
5
Table 1-2: Australian verification example 2 comparison
14
Table 1-3: Australian verification example 3 comparison
16
Table 1-4: Australian verification example 4 comparison
22
Table 2-1: British verification example 1 comparison
26
Table 2-2: Table BS2.1 - Column loads
26
Table 2-3: British verification example 2 comparison
32 Verification Manual — 493
Chapter — 12 Tables
Table 2-4: British verification example 3 comparison
38
Table 2-5: British verification example 4 comparison
44
Table 2-6: British verification example 5 comparison
53
Table 2-7: British verification example 6 comparison
62
Table 2-8: British verification example 7 comparison
71
Table 2-9: British verification example 8 comparison
77
Table 2-10: British verification example 9 comparison
83
Table 2-11: British verification example 10 comparison
88
Table 2-12: British verification example 13 comparisons
98
Table 3-1: CSA verification example 1 comparison
105
Table 3-2: CSA verification example 2 comparison
112
Table 3-3: CSA verification example 3 comparison
115
Table 3-4: CSA verification example 5 comparison
122
Table 3-5: CSA verification example 5 comparison
124
Table 4-1: IS verification example 1 comparison
129
Table 4-2: IS verification example 2 comparison
133
Table 4-3: IS verification example 3 comparison
138
Table 4-4: IS verification example 4 comparison
140
Table 4-5: IS verification example 5 comparison
145
Table 4-6: IS verification example 6 comparison
150
Table 4-7: IS verification example 7 comparison
158
Table 4-8: IS verification example 8 comparison
164
Table 4-9: IS verification example 9 comparison
170
Table 4-10: IS verification example 10 comparison
176
Table 4-11: IS verification example 11 comparison
182
Table 4-12: Pile Locations in Plan
183
Table 4-13: IS verification example 12 comparison
189
Table 4-14: Pile Coordinates in Plan
191
Table 4-15: IS verification example 13 comparison
197
Table 4-16: IS verification example 14 comparison
200
Table 5-1: US verification example 1 comparison
206
Table 5-2: US verification example 2 comparison
210
Table 5-3: US verification example 3 comparison
215
Table 5-4: US verification example 4 comparison
220
Table 5-5: US verification example 5 comparison
229
494 — STAAD Foundation Advanced V8i
List of Figures & Tables Tables
Table 5-6: US verification example 6 comparison
233
Table 5-7: US Verification problem 9 comparison
240
Table 5-8: US verification example 7 comparison
246
Table 5-9: US verification example 8 comparison
253
Table 5-10: US verification example 7 comparison
258
Table 5-11: US verification example 7 comparison
264
Table 5-12: Pile Coordinates in Plan
266
Table 5-13: US verification example 10 comparison
271
Table 5-14: Pile Coordinates in Plan
273
Table 5-15: US verification example 11 comparison
280
Table 5-16: Pile Coordinates in Plan
281
Table 5-17: US verification example 11 comparison
287
Table 5-18: Pile Coordinates in Plan
289
Table 5-19: US verification example 13 comparison
295
Table 5-20: US verification example 12 comparison
302
Table 5-21: US verification example 14 comparison
311
Table 5-22: US verification example 15 comparison
320
Table 6-1: Soil Test Report Summary
322
Table 6-2: Deadman Anchor (US) verification example 1 comparison
330
Table 6-3: Soil test report summary
331
Table 6-4: Soil layers
334
Table 6-5: Deadman Anchor (US) verification example 2 comparison
338
Table 6-6: Soil test report summary
339
Table 6-7: Soil layers
342
Table 6-8: Deadman Anchor (US) verification example 3 comparison
347
Table 6-9: Soil layers
348
Table 6-10: Deadman Anchor (US) verification example 4 comparison
355
Table 7-1: Drilled Pier (API) verification example 1 comparison
361
Table 7-2: Drilled Pier (API) verification example 2 comparison
366
Table 7-3: Drilled Pier (FHWA) verification example 3 comparison
371
Table 7-4: Drilled Pier (FHWA) verification example 4 comparison
375
Table 7-5: Drilled Pier (Vesic) verification example 5 comparison
380
Table 7-6: Drilled Pier (Vesic) verification example 6 comparison
384
Table 8-1: Primary load description
387
Table 8-2: Wind loads
388
Verification Manual — 495
Chapter — 12 Tables
Table 8-3: Applied Load Combinations - Allowable Stress Level
389
Table 8-4: Applied Load Combinations - Strength Level
389
Table 8-5: Applied Load at Top of Pedestal - Allowable Stress Level
389
Table 8-6: Applied Load at Top of Pedestal - Strength Level
390
Table 8-7: Stability Ratio
391
Table 8-8: Soil Bearing Check
391
Table 8-9: Vertical Vessel verification example 1 comparison
394
Table 8-10: Primary load description
396
Table 8-11: Wind loads
397
Table 8-12: Applied Load Combination - Allowable Stress Level
398
Table 8-13: Applied Load Combination - Strength Level
398
Table 8-14: Applied Load at Top of Pedestal - Allowable Stress Level
398
Table 8-15: Applied Load at Top of Pedestal - Strength Level
399
Table 8-16: Stability Ratio
400
Table 8-17: Vertical Vessel verification example 2 comparison
403
Table 8-18: Primary load description
405
Table 8-19: Wind loads
406
Table 8-20: Applied Load Combination - Allowable Stress Level
407
Table 8-21: Applied Load Combination - Strength Level
407
Table 8-22: Applied Load at Top of Pedestal - Allowable Stress Level
407
Table 8-23: Applied Load at Top of Pedestal - Strength Level
408
Table 8-24: Stability Ratio
409
Table 8-25: Soil Bearing Check
409
Table 8-26: Vertical Vessel verification example 3 comparison
412
Table 8-27: Vertical Vessel verification example 4 comparison
413
Table 8-28: Vertical Vessel verification example 5 comparison
414
Table 8-29: Vertical Vessel verification example 6 comparison
415
Table 8-30: Vertical Vessel verification example 7 comparison
416
Table 8-31: Vertical Vessel verification example 8 comparison
418
Table 8-32: Vertical Vessel verification example 9 comparison
419
Table 8-33: Vertical Vessel verification example 10 comparison
420
Table 8-34: Vertical Vessel verification example 11 comparison
421
Table 8-35: Vertical Vessel verification example 12 comparison
422
Table 8-36: Vertical Vessel verification example 13 comparison
423
Table 8-37: Vertical Vessel verification example 14 comparison
424
496 — STAAD Foundation Advanced V8i
List of Figures & Tables Tables
Table 8-38: Vertical Vessel verification example 15 comparison
426
Table 8-39: Vertical Vessel verification example 16 comparison
427
Table 8-40: Service level load combinations per PIP
429
Table 8-41: Strength level load combinations per PIP
429
Table 8-42: Service level loads applied at the top of the top of the fixed pier
430
Table 8-43: Strength level loads applied at the top of the top of the fixed pier
430
Table 8-44: Service level load combinations per PIP
433
Table 8-45: Strength level load combinations per PIP
433
Table 8-46: Service level loads applied at the top of the top of the fixed pier
434
Table 8-47: Strength level loads applied at the top of the top of the fixed pier
434
Table 9-1: Overview of cone footing design results
437
Table 9-2: Reinforcement details
437
Table 9-3: Loads for foundation base size estimation -For foundation base (1)
439
Table 9-4: Loads for Punching shear check and reinforcements- For foundation base (1)
439
Table 9-5: Factor of safety
441
Table 9-6: Overview of the stepped foundation design
449
Table 9-7: Reinforcement details
449
Table 9-8: Critical loads for base size estimation - standard combination
450
Table 9-9: Loads for foundation design- the basic combination
450
Table 9-10: Safety factors
452
Table 9-11: Overview of the design results
462
Table 9-12: Foundation reinforcement details
462
Table 9-13: Load cases for base dimensions estimation - standard combination
464
Table 9-14: Load cases for foundation design - basic combinationn
464
Table 9-15: Pile capacities under load case no. 101
470
Table 9-16: Pile capacities under load case no. 102
471
Table 9-17: Load about the pile cap
472
Table 9-18: Chinese verification example 6 comparison
483
Verification Manual — 497
Chapter 12 Tables
498 — (Undefined variable: Primary.ProductName)
Bentley Systems, Incorporated 685 Stockton Drive, Exton, PA 19341 USA +1 (800) 236-8539 www.bentley.com
Verification Manual — 499
