Sample Benchmark Problem Set

In this document many sample benchmark problems are listed with results. Each
problem is tested to ensure that foundation design results are calculated correctly. The
sample problems are chosen from text books, hand calculations or other documents.

Problem 1 – Square Soil Supported Spread

Footing With Moment Governing Reinforcement
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a square soil-supported foundation supporting a
pedestal. In this problem, the moment in the footing governs the footing reinforcement.

Reference: Reinforced Concrete Design – Wang & Salmon (Third Edition) – Eg 20.8

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Bearing pressure 5.0 ksf
2 Maximum shear (Beam shear) 156 kips
3 Two way shear (Punching shear) 595 kips
4 Bending moment 554 kip ft
5 Footing Reinforcement 15 # 8 bars

The input and output represented below consists of the same example run in Mat3D.
The comparison of results is tabulated at the end of the output.
Dimensional Solutions Mat3D Version 4.0.4 Date 3/11/2008
Foundation Name Soil supported spread footing Time 3:54:42 PM
Designed By: Dimensional Solutions Inc. Engineer Checker

Filename: \\Dim733\c$\DSNewDevelopment\Build\Documentation\QA\Mat3D\RCDesign_Wang_Salmon_Eg20-8.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name: RC Design - Wang & Salmon - Third Edition

Project Number: Eg 20.8
Client:
Project Location
Foundation Description SOIL SUPPORTED SPREAD FOOTING

DESIGN CODE ACI 318 - 1999 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 18

Unit Weight (pcf) 150.00 Type Auger Cast

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 40.00 Max Long Bar Size 11

Unit Weight (pcf) 490.00 Min Long Bar Size 7
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 4
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 11
Min Ftg Bar Size 6
Allowable Net Bearing Capacity (psf) 4750.00 Temp & Shrinkage Steel 0.0012
Unit Weight (pcf) 100.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 2.08

Minimum Soil Cover (ft) 0.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 300.00 0.00 0.00 0.00 0.00

2 - Live 160.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 460.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 692.00 0.00 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead + Live 4.91 4.96 0.00 0.00 0.00 0.00

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All

Comb N/S Dir E/W Dir S.R. FS - N/S FS - E/W FS

1 - Dead + Live 100.00 100.00 1.50 100.00 100.00 1.50

 FOOTING DESIGN INFORMATION

X Dim (ft) 10.00

Z Dim (ft) 10.00
Thickness (ft) 2.08

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 E-W

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 N-S

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 17 8 8 1.34 1.23 55.36 E-W

1. 1.4Dead + 1.7Live 15 8 8 1.18 1.17 55.36 N-S

PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 594.69 157.33 186.23

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 2.25 155.70 61.79 93.11

 MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 2.25 155.70 61.79 93.11

PIER/BASE PLATE DESIGN INFORMATION

P1
X Dim (ft) 2.00
Z Dim (ft) 2.00
Height (ft) 0.00
X Offset (ft) 5.00
Z Offset (ft) 5.00
Requested Reinft. Ratio
Provided Reinft. Ratio
Long Bar Size
Bars in X Dir
Bars in Z Dir
Total Long Bars
Tie Bar Size
Total No. of Ties
Major Tie Spacing (in)
Results Comparison

Item No Item Description Result Mat3D Result

1 Bearing pressure 5.0 ksf 4.96 ksf
2 Maximum shear (Beam shear) 156 kips 155.70 kips
3 Two way shear (Punching shear) 595 kips 594.69 kips
4 Bending moment 554 kip ft 553.60 kip ft
5 Footing Reinforcement 15 # 8 bars 17 # 8 bars
Problem 2 – Rectangular Soil Supported Spread
Footing
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a rectangular soil-supported foundation supporting a
pedestal.

Reference: Reinforced Concrete Design – Wang & Salmon (Third Edition) – Eg 20.10

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Bearing pressure 5.5 ksf
2 Maximum shear (Beam shear) – X direction 140.5 kips
3 Two way shear (Punching shear) 454.8 kips
4 Bending moment in X direction 452 kip ft
5 Footing Reinforcement in X direction 14 # 7 bars
6 Bending moment in Z direction 283 kip ft
7 Footing Reinforcement in Z direction 10 # 7 bars

The input and output represented below consists of the same example run in Mat3D.
The comparison of results is tabulated at the end of the output.
Dimensional Solutions Mat3D Version 4.0.4 Date 3/12/2008
Foundation Name Time 11:28:56 AM
Designed By: Dimensional Solutions Inc. Engineer Checker

Filename: C:\DSNewDevelopment\Build\Documentation\QA\Mat3D\RCDesign_Wang_Salmon_Eg20-10.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name: RC Design - Wang & Salmon - Third Edition

Project Number: Eg 20.10
Client:
Project Location
Foundation Description

DESIGN CODE ACI 318 - 1999 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 0

Unit Weight (pcf) 150.00 Type Auger Cast

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 40.00 Max Long Bar Size 11

Unit Weight (pcf) 490.00 Min Long Bar Size 7
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 4
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 11
Min Ftg Bar Size 6
Allowable Net Bearing Capacity (psf) 5300.00 Temp & Shrinkage Steel 0.0020
Unit Weight (pcf) 100.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 2.00

Minimum Soil Cover (ft) 0.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 235.00 0.00 0.00 0.00 0.00

2 - Live 115.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 350.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 524.50 0.00 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead + Live 5.46 5.50 0.00 0.00 0.00 0.00

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All

Comb N/S Dir E/W Dir S.R. FS - N/S FS - E/W FS

1 - Dead + Live 100.00 100.00 1.50 100.00 100.00 1.50

 FOOTING DESIGN INFORMATION

X Dim (ft) 9.67

Z Dim (ft) 7.00
Thickness (ft) 1.83

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 E-W

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 N-S

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 14 7 6 1.2 1.21 64.65 E-W

1. 1.4Dead + 1.7Live 12 7 10 0.75 0.75 29.3 N-S

PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 454.76 175.45 186.23

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 2.59 140.21 92.73 93.11

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 1.25 93.66 44.84 93.11

 PIER/BASE PLATE DESIGN INFORMATION

P1
X Dim (ft) 1.50
Z Dim (ft) 1.50
Height (ft) 0.17
X Offset (ft) 4.84
Z Offset (ft) 3.50
Results Comparison

Item No Item Description Result Mat3D Result

1 Bearing pressure 5.5 ksf 5.46 ksf
2 Maximum shear (Beam shear) – X direction 140.5 kips 140.21 kips
3 Two way shear (Punching shear) 454.8 kips 454.76 kips
4 Bending moment in X direction 452 kip ft 452.55 kip ft
5 Footing Reinforcement in X direction 14 # 7 bars 14 # 7 bars
6 Bending moment in Z direction 283 kip ft 283.33 kip ft
7 Footing Reinforcement in Z direction 10 # 7 bars 12 # 7 bars
Problem 3 – Square Soil Supported Spread
Footing With Temperature and Shrinkage
Reinforcement Governing
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a square soil-supported foundation supporting a
pedestal. In this problem, the moment in the footing does not govern the footing
reinforcement but the temperature and shrinkage steel governs.

Reference: Hand Calculation

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Bearing pressure 4.69 ksf
2 Maximum shear (Beam shear) 200.98 kips
3 Two way shear (Punching shear) 802.22 kips
4 Bending moment 82.63 kip ft / ft
5 Footing Reinforcement 26 # 6 bars

The following pages show the hand calculations of the foundation design with the results
indicated in the table above followed by the input and output of the same example run in
Mat3D. The comparison of results is tabulated at the end of the output.
 Dimensional Solutions, Inc.
Advanced Software For Foundation Design

Mat Foundation Design - Soil Supported

INPUTS

Loads
Dead Load OWT 400.00 kips
Live Load LwT 275.00 kips
Dead Shear BWT 0.00 kips
Live Shear LsT 0.00

Footing and Pedestal Geometry

Few = 13

Pew = 2

Pns = 2 Fns = 13

Depth of footing below grade FBG 5.00 ft

Footing EW Dimension FEW 13.00 ft
Footing NS Dimension FNS 13.00 ft
Footing thickness FTH 3.00 ft
Pier EW Dimension PEW 2.00 ft
Pier NS Dimension PNS 2.00 ft
Pier ht above grade PHT 4.00 ft
Pier EW offset from footing C.L. PEWO 0.00 ft
Pier NS offset from footing C.L PNSO 0.00 ft
Effective depth FEffD 2.67 ft
Soil depth Sd 2.00 ft

Material Properties
Concrete compressive strength Fc' 3000.00 psi
Concrete unit wt γc 150.00 pcf
Reinforcing yield strength Fy 60.00 ksi
Reinforcing steel unit wt γR 490.00 pcf
Allowable net bearing pressure NBP 4000.00 psf
Soil unit wt γs 115.00 pcf

Applied Loads LF Axial Shear NS Mom EW

Dead 1.2 400.00 0.00 0.00
Live 1.6 275.00 0.00 0.00

RESULTS

Bearing Pressure Calculation

Footing weight = Fwt =Few*Fns*FThk*Yc/1000 76.05 kips
Soil weight = Swt =((Few*Fns)-(Pew*Pns))*(FBG-Fth)*Ys/1000 37.95 kips
Pier weight = Pwt =Pew*Pns*(PHt+(FBG-Fth))*Yc/1000 3.60 kips

Total Selfweight Twt =Fwt + Swt + Pwt 117.60 kips

Applied load Oa =Owt+Lwt 675.00 kips

Total load TL =Twt + Oa 792.60 kips

Mom at footing base Mb =Frs*(FBG+PHt) 0.00 kip ft

eccentricity Ecc =Mb/TL 0.00 ft

Bearing pressure BP =(TL/(Few*Fns))*(1+6*Ecc/Few) 4.69 ksf

Gross pressure GP =NBP/1000+(FBG*Ys/1000) 4.58 ksf

Footing Fails in Bearing Pressure

Max Ult Bearing Pressure
Ultimate loads
Axial Load Pult =LF*(Owt + Lwt) 920 kips
Shear Load Sult =LF*Frs 0 kips
Selfweight SWult =LF*Twt 141.12 kips
Total Ult load TLult =Pult+SWult 1061.12 kips

Ult Mom at footing base Mult =Sult*(FBG+PHt) 0.00 kip ft

eccentricity Eult =Mult/TLult 0.00 ft

Max Ult bearing pressure BPUmax =(TLult/(Few*Fns))*(1+6*Eult/Few) 6.28 ksf

Min Ult bearing pressure BPUmin =(TLult/(Few*Fns))*(1-6*Eult/Few) 6.28 ksf

Punching Shear Calculation

Shear perimeter Peri =2*(Pew+FEffD)+2*(Pns+FEffD) 18.68 ft
Vertical load at base of pier Pub =(Pult+Pwt)+wt of footing area within shear planes 939.15 kips
Punching shear area Apu,shr =(Pew+FEffD)*(Pns+FEffD) 21.81 sq ft
Soil resistance Rsoil =(BPUmax+BPUmin)/2*Apu,shr 136.93 kips
Punching shear Pshear =(Pub-Rsoil) 802.22 kips
Punching shear stress Pstress =Pshear/1000*(Peri*FEffD*144) 111.70 psi
Shear Reduction Factor Øc 0.75
Beta Factor ß 1.00
Allowable punching shear Pall,str =Ø*(2+4/ß*sqr(fc')) 164.32 psi

Punching Shear OK

Beam Shear Calculation in N-S Direction

Critical section for beam shear Bc =(Fns/2+Pns/2+FEffD) 10.17 ft
Bearing Pressure at critical section BPc =Bc/Fns*(BPUmax-BPUmin) 6.28 ksf
Shear force outside critical section Ap =(BPc+BPUmax)/2*Few*(Fns-Bc) 231.00 kips
Shear force due to soil/footing wt Ssf =(Sd*Ys/1000)+(Fth*Yc/1000)*Few*(Fns-Bc) 30.02 kips
Max shear at crit section Smax =Ap-Ssf 200.98 kips
Shear stress BSstr =Smax/(Few*FEffD*144) 40.21 psi
Shear reduction Factor Øc 0.75
Allowable shear stress Ball,str =Øc*2*sqr(fc') 82.16 psi

Beam Shear OK
Moment Calculation
Critical section for moment Mc =(Fns/2+Pns/2) 7.50 ft
Bearing Pressure at crit section BPmc =Mc/Fns*(BPUmax-BPUmin) 6.28 ksf
Centroid of pressure diagram Cp 2.75 ft
Ult moment - crit section Mult =(BPUmax+BPmc)/2*(Fns-Mc)*Cp*Few 1234.57 kip ft
Ult moment - Soil and footing Mult,s 160.45 kip ft
Net Ult moment Mult,Net 1074.13 kip ft
Ult moment per unit length Mult,L =Mult/Few 82.63 kip ft/ft
Area of steel required for moment As,m =Mult/(phi*au*d) 0.65 sq in/ft
Temp and shrinkage steel area Ats =0.0018*Fth*12*12 0.78 sq in/ft

Reinft - Use 26 # 6 at 6" o.c. each way - bottom level

Dimensional Solutions Mat3D Version 4.0.4 Date 3/12/2008
Foundation Name Time 11:54:25 AM
Designed By: Engineer Checker

Filename: C:\DSNewDevelopment\Build\Documentation\QA\Mat3D\Mat_Soil_Eng.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name:
Project Number:
Client:
Project Location
Foundation Description

DESIGN CODE ACI 318 - 2002 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 0

Unit Weight (pcf) 150.00 Type Auger Cast

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 60.00 Max Long Bar Size 10

Unit Weight (pcf) 490.00 Min Long Bar Size 3
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 4
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 18
Min Ftg Bar Size 3
Allowable Net Bearing Capacity (psf) 4000.00 Temp & Shrinkage Steel 0.0018
Unit Weight (pcf) 115.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 5.00

Minimum Soil Cover (ft) 2.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 400.00 0.00 0.00 0.00 0.00

2 - Live 275.00 0.00 0.00 0.00 0.00
3 - Wind 0.00 0.00 0.00 0.00 0.00
4 - Earthquake 0.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 675.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.2Dead + 1.6Live 920.00 0.00 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment Rem

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead + Live 4.69 4.58 0.00 0.00 0.00 0.00 Cap Exc.

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All Remarks

Comb N/S Dir E/W Dir S.R. FS - N/S FS - E/W FS

1 - Dead + Live 100.00 100.00 1.50 100.00 100.00 1.50

 FOOTING DESIGN INFORMATION

X Dim (ft) 13.00

Z Dim (ft) 13.00
Thickness (ft) 3.00

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.2Dead + 1.6Live 0 0 0 0 0 0 E-W

1. 1.2Dead + 1.6Live 0 0 0 0 0 0 N-S

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.2Dead + 1.6Live 26 6 6 0.88 0.79 82.72 E-W

1. 1.2Dead + 1.6Live 26 6 6 0.88 0.78 82.72 N-S

PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.2Dead + 1.6Live 804.25 112.20 164.32

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.2Dead + 1.6Live 2.83 201.45 40.36 82.16

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.2Dead + 1.6Live 2.83 201.45 40.36 82.16

Results Comparison

Item No Item Description Result Mat3D Result

1 Bearing pressure 4.69 ksf 4.69 ksf
2 Maximum shear (Beam shear) 200.98 kips 201.45 kips
3 Two way shear (Punching shear) 802.22 kips 804.25 kips
4 Bending moment 82.63 kip ft / ft 82.72 kip ft
5 Footing Reinforcement 26 # 6 bars 26 # 6 bars
Problem 4 – Rectangular Soil Supported
Combined Footing Subjected To Axial Load

The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a rectangular soil-supported combined foundation
supporting two pedestals and subjected to axial load only.

Reference: Reinforced Concrete Design – Wang & Salmon (Third Edition) – Eg 20.13

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Bearing pressure 5.0 ksf
2 Point of Max Shear from left edge of footing 16.51 ft
3 Maximum shear at point of max shear – X dir 329 kips
4 Two way shear (Punching shear) – Col A 453 kips
5 Two way shear (Punching shear) – Col B 523 kips
6 Max Positive Bending moment location 19.99 ft
7 Max Positive Bending moment in X direction 80 kip ft
8 Positive moment Footing Reinforcement in X direction # 7 bars @ 8 in spacing
9 Point of max shear along X direction 10.15 ft
10 Max Negative moment in X direction 2025 kip ft
11 Negative moment Reinforcement in X direction # 11 bars @ 4.5 in
spacing

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
Dimensional Solutions Mat3D Version 4.0.4 Date 3/12/2008
Foundation Name Time 5:45:20 PM
Designed By: Engineer Checker

Filename: C:\DSNewDevelopment\Build\Documentation\QA\Mat3D\Mat_Soil_Eng_Combined.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name:
Project Number:
Client:
Project Location
Foundation Description

DESIGN CODE ACI 318 - 2005 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 0

Unit Weight (pcf) 150.00 Type Auger Cast

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 40.00 Max Long Bar Size 8

Unit Weight (pcf) 490.00 Min Long Bar Size 4
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 6
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 18
Min Ftg Bar Size 5
Allowable Net Bearing Capacity (psf) 4625.00 Temp & Shrinkage Steel 0.0018
Unit Weight (pcf) 100.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 2.33

Minimum Soil Cover (ft) 0.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 210.00 0.00 0.00 0.00 0.00

2 - Live 140.00 0.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 240.00 0.00 0.00 0.00 0.00

2 - Live 160.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 350.00 0.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 400.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 532.00 0.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 608.00 0.00 0.00 0.00 0.00

 BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment Rem

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead + Live 4.98 4.86 0.00 0.02 16.75 0.00 Cap Exc.

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All Remarks

Comb N/S Dir E/W Dir S.R. FS - N/S FS - E/W FS

1 - Dead + Live 100.00 100.00 1.50 100.00 100.00 1.50

FOOTING DESIGN INFORMATION

X Dim (ft) 21.75

Z Dim (ft) 7.50
Thickness (ft) 2.33

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 22 11 4 4.58 4.2 -269.8 E-W

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 N-S

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 15 5 6 0.61 0.6 10.7 E-W

1. 1.4Dead + 1.7Live 43 5 6 0.61 0.6 31.66 N-S
 PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 453.98 163.18 164.32

P2

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 523.77 130.65 164.32

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 16.52 334.90 155.05 82.16 Shear Exc

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 6.49 -153.52 24.51 82.16

PIER/BASE PLATE DESIGN INFORMATION

P1 P2
X Dim (ft) 1.33 1.48
Z Dim (ft) 1.83 1.48
Height (ft) 0.00 0.00
X Offset (ft) 1.25 19.26
Z Offset (ft) 3.75 3.75
Requested Reinft. Ratio
Results Comparison

Item
Item Description Result Mat3D Results
No
1 Bearing pressure 5.0 ksf 4.98 ksf
2 Point of Max Shear from left edge of footing 16.51 ft 16.52 ft
3 Maximum shear at point of max shear – X dir 329 kips 334.9 kips
4 Two way shear (Punching shear) – Col A 453 kips 453.98 kips
5 Two way shear (Punching shear) – Col B 523 kips 523.77 kips
6 Max Positive Bending moment location 19.99 ft 19.99 ft
7 Max Positive Bending moment in X direction 80 kip ft 80.25 kip ft
8 Positive moment Footing Reinforcement in X # 7 bars @ 8 in #5 bars @ 6 in
direction spacing spacing
9 Point of max shear along X direction 10.15 ft 10.12 ft
10 Max Negative moment in X direction 2025 kip ft 2023.5 kip ft
11 Negative moment Reinforcement in X # 11 bars @ 4.5 # 11 bars @ 4.0
direction in spacing in spacing
Problem 5 - Rectangular Soil Supported
Combined Footing Subjected To Axial Load And
Shear
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a rectangular soil-supported combined foundation
supporting two pedestals and subjected to axial load and shear.

Reference: Hand Calculation

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Bearing pressure 5.12 ksf
2 Point of Max Shear from left edge of footing 3.92 ft
3 Maximum shear at point of max shear – X dir 332.4 kips
4 Two way shear (Punching shear) – Col A 456.28 kips
5 Two way shear (Punching shear) – Col B 521.20 kips
6 Max Positive Bending moment location 19.99 ft
7 Max Positive Bending moment in X direction 83 kip ft
8 Positive moment Footing Reinforcement in X # 5 bars @ 6 in spacing
direction
9 Point of max shear along X direction 10.27 ft
10 Max Negative moment in X direction 1934.51 kip ft
11 Negative moment Reinforcement in X direction # 14 bars @ 6 in spacing

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
Dimensional Solutions Mat3D Version 4.0.4 Date 3/12/2008
Foundation Name Time 6:35:02 PM
Designed By: Engineer Checker

Filename: C:\DSNewDevelopment\Build\Documentation\QA\Mat3D\Mat_Soil_Eng_Combined_Shear.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name:
Project Number:
Client:
Project Location
Foundation Description

DESIGN CODE ACI 318 - 2005 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 0

Unit Weight (pcf) 150.00 Type Auger Cast

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 40.00 Max Long Bar Size 8

Unit Weight (pcf) 490.00 Min Long Bar Size 4
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 6
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 18
Min Ftg Bar Size 5
Allowable Net Bearing Capacity (psf) 4625.00 Temp & Shrinkage Steel 0.0018
Unit Weight (pcf) 100.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 2.33

Minimum Soil Cover (ft) 0.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 210.00 50.00 0.00 0.00 0.00

2 - Live 140.00 0.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 240.00 0.00 0.00 0.00 0.00

2 - Live 160.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 350.00 50.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead + Live 400.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 532.00 70.00 0.00 0.00 0.00

P2

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead + 1.7Live 608.00 0.00 0.00 0.00 0.00

 BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment Rem

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead + Live 5.12 4.86 0.00 0.12 99.75 0.00 Cap Exc.

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All Remarks

Comb N/S Dir E/W Dir S.R. FS - N/S FS - E/W FS

1 - Dead + Live 100.00 75.48 1.50 100.00 2.02 1.50

FOOTING DESIGN INFORMATION

X Dim (ft) 21.75

Z Dim (ft) 7.50
Thickness (ft) 2.33

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 15 14 6 4.5 4.05 -257.95 E-W

1. 1.4Dead + 1.7Live 0 0 0 0 0 0 N-S

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(in) (sq in/ft) (sq in/ft) (kip ft/ft)

1. 1.4Dead + 1.7Live 15 5 6 0.61 0.6 11.1 E-W

1. 1.4Dead + 1.7Live 43 5 6 0.61 0.6 31.66 N-S
 PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 456.23 163.99 164.32

P2

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kips) (psi) (psi)

1. 1.4Dead + 1.7Live 523.37 130.55 164.32

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 3.92 -332.40 153.89 82.16 Shear Exc

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(ft) (kips) (psi) (psi)

1 - 1.4Dead + 1.7Live 6.49 -153.52 24.51 82.16

PIER/BASE PLATE DESIGN INFORMATION

P1 P2
X Dim (ft) 1.33 1.48
Z Dim (ft) 1.83 1.48
Height (ft) 0.00 0.00
X Offset (ft) 1.25 19.26
Z Offset (ft) 3.75 3.75
Results Comparison

Item
Item Description Result Mat3D Result
No
1 Bearing pressure 5.12 ksf 5.12 ksf
2 Point of Max Shear from left edge of 3.92 ft 3.92 ft
footing
3 Maximum shear at point of max shear 332.4 kips 332.4 kips
– X dir
4 Two way shear (Punching shear) – 456.28 kips 456.23 kips
Col A
5 Two way shear (Punching shear) – 521.20 kips 523.37 kips
Col B
6 Max Positive Bending moment 19.99 ft 19.99 ft
location
7 Max Positive Bending moment in X 83 kip ft 83.25 kip ft
direction
8 Positive moment Footing # 5 bars @ 6 in # 5 bars @ 6 in
Reinforcement in X direction spacing spacing
9 Point of max shear along X direction 10.27 ft 10.27 ft
10 Max Negative moment in X direction 1934.51 kip ft 1934.63 kip ft
11 Negative moment Reinforcement in X # 14 bars @ 6 in # 14 bars @ 6 in
direction spacing spacing
Problem 8 – Rectangular Soil Supported Mat With
Heavy Eccentric Load
The purpose of this problem is to ensure that Mat3D computes the soil bearing
correctly for a rectangular soil-supported spread foundation subjected to a heavy
eccentric load. The load is eccentric with respect to both X and Z axis.

Reference: Research Article:

How to Calculate Footing Soil Bearing by Computer by Eli Czerniak – Eg 2, Pg 75

Input Specifics:

Axial Load = 100 kips

Eccentricity of the resultant load in X direction = 3.75 ft
Eccentricity of the resultant load in Z direction = 3.25 ft

The soil bearing results using this example should be as follows

Item No Item Description Result

1 Max bearing pressure 5.0 ksf
2 Min bearing pressure 0.0 ksf
3 Compression length on X axis 15.0 ft
4 Compression length on Z axis 8.0 ft
5 Area in compression 60.0 sq ft
6 Percent of gross area in compression 38.095%

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
Dimensional Solutions Mat3D Version 4.0.4 Date 3/15/2008
Foundation Name Time 12:02:31 PM
Designed By: Engineer Checker

Filename: C:\DSNewDevelopment\Build\Documentation\QA\Mat3D\Mat_Soil_Spread_EccentricLoad2.m3d

DETAIL REPORT

PROJECT INFORMATION

Project Name: How to Calculate Footing Soil Bearing by Computer by Eli Czerniak
Project Number: Eg 2
Client:
Project Location
Foundation Description

DESIGN CODE ACI 318 - 2005 INPUT UNITS English OUTPUT UNITS English

CONCRETE PARAMETERS: PILE PARAMETERS:

Compressive Strength (psi) 3000.00 Diameter (in) 12

Unit Weight (pcf) 150.00 Type Drilled Shaft

REINFORCING STEEL PARAMETERS: REBAR PARAMETERS:

Yield Strength (ksi) 40.00 Max Long Bar Size 8

Unit Weight (pcf) 490.00 Min Long Bar Size 4
Modulus of Elasticity (ksi) 29000.00 Max Tie Bar Size 6
Min Tie Bar Size 3
SOIL PARAMETERS: Max Ftg Bar Size 18
Min Ftg Bar Size 5
Allowable Net Bearing Capacity (psf) 5000.00 Temp & Shrinkage Steel 0.0018
Unit Weight (pcf) 100.00 Ratio

MINIMUM FOUNDATION CRITERIA:

Depth of Footing Below Grade (ft) 1.00

Minimum Soil Cover (ft) 0.00
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 76.37 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - Dead 76.37 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kips) (kips) (kip ft) (kips) (kip ft)

1 - 1.4Dead 106.92 0.00 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment

Comb Pressure Pressure N/S Dir E/W Dir N/S axis E/W axis
(ksf) (ksf) (ft) (ft) (kip-ft) (kip-ft)

1 - Dead 5.00 5.10 3.25 3.76 375.59 324.57

No. Load Combination Max Min EW Comp NS Comp Area in % in

Bearing Bearing Len Len Comp Comp
kips/sq ft kips/sq ft ft ft sq ft

1 Dead 4.998 0 14.976 8.016 60.026 38.112

Results Comparison

Item No Item Description Result Mat3D Result

1 Max bearing pressure 5.0 ksf 5.0 ksf
2 Min bearing pressure 0.0 ksf 0.0 ksf
3 Compression length on X axis 15.0 ft 14.976 ft
4 Compression length on Z axis 8.0 ft 8.016 ft
5 Area in compression 60.0 sq ft 60.026 sq ft
6 Percent of gross area in compression 38.095% 38.112%
Problem 9 – Square Soil Supported Mat With Axial
Load – IS 456 2000
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a square soil-supported foundation supporting a base
plate using IS 456 2000 concrete design code. In this problem, the moment in the
footing governs the footing reinforcement.

Reference: Limit State Design of Reinforced Concrete – P.C. Varghese – (Second

Edition), Eg 22.2 (pg 494)

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Max net bearing pressure 200.0 kN/m2
2 Two way shear (Punching shear) 1890.0 kN
3 Bending moment 540.0 kN m
4 Footing Reinforcement 10 – 20 mm bars

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
Dim ensional Solutions Mat3D Version 5.8.1 Date 12/7/2011
Foundation Nam e Design of Square Footing Ex 22.2 - by P.C. Varghes Tim e 11:00:06 AM
Designed By: Engineer Checker

Filenam e:

DETAIL REPORT

PROJECT INFORMATION

Project Nam e:
Project Num ber:
Client:
Project Location
Foundation Description DESIGN OF SQUARE FOOTING EX 22.2 - BY P.C. VARGHES

DESIGN CODE IS 456 : 2000 INPUT UNITS SI OUTPUT UNITS SI

CONCRETE PARAMETERS: REINFORCING STEEL PARAMETERS:

Compressive Strength (N/sq mm) 20 Yield Strength (N/sq mm) 415

Unit Weight (kN/cu m) 25 Unit Weight (kN/cu m) 78
Pier Concrete Cover - X Dir (mm) 50 Modulus of Elasticity (kN/sq mm) 200
Pier Concrete Cover - Z Dir (mm) 50 Pier Min Rebar Spacing (mm) 75
Footing Side Concrete Cover - X Dir (mm) 50 Footing Min Rebar Spacing (mm) 125
Footing Side Concrete Cover - Z Dir (mm) 50 Footing Max Rebar Spacing (mm) 300
Footing Top Concrete Cover (mm) 50
Footing Bottom Concrete Cover - X Dir (mm) 75

SOIL PARAMETERS: REBAR PARAMETERS:

Unit Weight (kN/cu m) 18 Max Long Bar Size 25

Allow able Net Bearing Capacity (kN/sq m) 200 Min Long Bar Size 16
Bearing Capacity Method Linear Soil Pressure Max Tie Bar Size 20
Soil Type Granular Min Tie Bar Size 10
Passive Pressure Coefficient Kp 0 Max Ftg Bar Size 28
Soil To Concrete Friction f 0.4 Min Ftg Bar Size 20
Allow able Increase in Soil Pressure due to Short Term Loads (%) Temp & Shrinkage Steel Ratio 0.0018
Wind 50 Earthquake 0 Test 0
Min Stability Ratio 1.5
Safety Factor against Lateral Forces 1.5

MINIMUM FOUNDATION CRITERIA: BUOYANCY CRITERIA:

Depth of Footing Below Grade (mm) 615 Consider Buoyancy: No

Minimum Soil Cover (mm) 0 Consider soil for buoyancy: No
Grade Elevation (mm) 0 Water table below grade (mm) 0
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kN) (kN) (kN m) (kN) (kN m)

1 - Dead 1000.00 0.00 0.00 0.00 0.00

2 - Live 400.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - Dead + Live 1400.00 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - 1.5Dead + 1.5Live 2100.00 0.00 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment Rem

Comb Pressure Pressure Z Dir X Dir Z axis X axis
(kN/sq m) (kN/sq m) (cm) (cm) (kN-m) (kN-m)

1 - Dead + Live 194.07 211.07 0.00 0.00 0.00 0.00

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All Remarks

Comb Z Dir X Dir S.R. FS - Z FS - X FS

1 - Dead + Live 100.00 100.00 1.50 100.00 100.00 1.50

 FOOTING DESIGN INFORMATION

X Dim (mm) 2800.00

Z Dim (mm) 2800.00
Thickness (mm) 620.00

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.5Dead + 1.5Live 0 0 0 0 0 0 X
1. 1.5Dead + 1.5Live 0 0 0 0 0 0 Z

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.5Dead + 1.5Live 10 20 300 11.22 10.99 193 X

1. 1.5Dead + 1.5Live 10 20 300 11.22 10.94 193 Z

PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kN) (N/sq mm) (N/sq mm)

1. 1.5Dead + 1.5Live 1873.29 0.98 1.12

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (N/sq mm) (N/sq mm)

1 - 1.5Dead + 1.5Live 0.68 510.00 0.35 0.34 Shear Exc

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (N/sq mm) (N/sq mm)

1 - 1.5Dead + 1.5Live 0.68 510.00 0.35 0.34 Shear Exc

 PIER/BASE PLATE DESIGN INFORMATION

P1
X Dim (mm) 400.00
Z Dim (mm) 400.00
Height above grade (mm) 0.00
X Offset (mm) 1400.00
Z Offset (mm) 1400.00
Requested Reinft. Ratio
Provided Reinft. Ratio
Long Bar Size (mm)
Bars in X Dir
Bars in Z Dir
Total Long Bars
Tie Bar Size (mm)
Total No. of Ties
Major Tie Spacing (mm)
Results Comparison

Item No Item Description Result Mat3D Result

1 Max net bearing pressure 200.0 kN/m2 200.0 kN/m2
2 Two way shear (Punching shear) 1890.0 kN 1874 kN
3 Bending moment 540.0 kN m 540.4 kN m
4 Footing Reinforcement 10 – 20 mm bars 10 – 20 mm bars
Problem 10 – Rectangular Pile Supported Mat
using – IS 456 2000
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a rectangular pile-supported foundation supporting a
base plate using IS 456 2000 concrete design code. In this problem, the moment in the
footing governs the footing reinforcement.

Reference: Limit State Design of Reinforced Concrete – P.C. Varghese – (Second

Edition), Eg 22.10 (pg 509)

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Load on pile 488 kN
2 Allowable beam shear stress 0.88 kN/m2

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
Dim ensional Solutions Mat3D Version 5.8.1 Date 12/8/2011
Foundation Nam e Varghese Rectangular Footing - Pile Supported - Ex Tim e 12:09:23 PM
Designed By: Engineer Checker

Filenam e: Varghese-Ex_22.10_Rectangular Footing Pile.m 3d

DETAIL REPORT

PROJECT INFORMATION

Project Nam e:
Project Num ber:
Client:
Project Location Rectangular Pile Supported Foundation
Foundation Description VARGHESE RECTANGULAR FOOTING - PILE SUPPORTED - EX

DESIGN CODE IS 456 : 2000 INPUT UNITS SI OUTPUT UNITS SI

CONCRETE PARAMETERS: REINFORCING STEEL PARAMETERS:

Compressive Strength (N/sq mm) 25 Yield Strength (N/sq mm) 415

Unit Weight (kN/cu m) 24 Unit Weight (kN/cu m) 78
Pier Concrete Cover - X Dir (mm) 50 Modulus of Elasticity (kN/sq mm) 200
Pier Concrete Cover - Z Dir (mm) 50 Pier Min Rebar Spacing (mm) 100
Footing Side Concrete Cover - X Dir (mm) 50 Footing Min Rebar Spacing (mm) 100
Footing Side Concrete Cover - Z Dir (mm) 50 Footing Max Rebar Spacing (mm) 450
Footing Top Concrete Cover (mm) 50
Footing Bottom Concrete Cover - X Dir (mm) 15

SOIL PARAMETERS: REBAR PARAMETERS:

Unit Weight (kN/cu m) 20 Max Long Bar Size 20

Min Long Bar Size 10
PILE PARAMETERS: Max Tie Bar Size 12
Diameter (mm) 350 Min Tie Bar Size 10
Type Auger Cast Max Ftg Bar Size 20
Embedment (mm) 10 Min Ftg Bar Size 10
Edge Distance (mm) 275 Temp & Shrinkage Steel Ratio 0.0013
Min Spacing (mm) 1100
Max Spacing (mm) 2500

MINIMUM FOUNDATION CRITERIA: BUOYANCY CRITERIA:

Depth of Footing Below Grade (mm) 800 Consider Buoyancy: No

Minimum Soil Cover (mm) 0 Consider soil for buoyancy: No
Grade Elevation (mm) 0 Water table below grade (mm) 0
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kN) (kN) (kN m) (kN) (kN m)

1 - Dead 1867.00 0.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - 1.5Dead 2800.50 0.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - 1.5Dead 2800.50 0.00 0.00 0.00 0.00

PILE CAPACITIES

Load Max All Max All Max All Rem

Comb Comp Comp Uplift. Uplift Shear Shear
(kN) (kN) (kN) (kN) (kN) (kN)

1 - 1.5Dead 488.53 500.00 0.00 255.00 0.00 44.00

FOOTING DESIGN INFORMATION

X Dim (mm) 2750.00

Z Dim (mm) 1650.00
Thickness (mm) 800.00

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.5Dead 0 0 0 0 0 0 X
1. 1.5Dead 0 0 0 0 0 0 Z

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.5Dead 16 20 100 30.46 19.01 499 X

1. 1.5Dead 23 20 120 26.28 15.32 168 Z
 PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kN) (N/sq mm) (N/sq mm)

1. 1.5Dead 2800.50 0.78 1.25

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (N/sq mm) (N/sq mm)

1 - 1.5Dead 0.78 -940.23 0.76 0.87

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (N/sq mm) (N/sq mm)

1 - 1.5Dead 0.23 17.82 0.01 2.88

PIER/BASE PLATE DESIGN INFORMATION

P1
X Dim (mm) 450.00
Z Dim (mm) 450.00
Height above grade (mm) 0.00
X Offset (mm) 1375.00
Z Offset (mm) 825.00
Requested Reinft. Ratio
Provided Reinft. Ratio
Long Bar Size (mm)
Bars in X Dir
Bars in Z Dir
Total Long Bars
Tie Bar Size (mm)
Total No. of Ties
Major Tie Spacing (mm)
Results Comparison

Item No Item Description Result Mat3D Result

1 Load on pile 488 kN 488.53 kN
2 Allowable beam shear stress 0.88 kN/m2 0.87 kN/m2
Problem 11 – Square Soil Supported Mat With
Axial & Shear Load – ACI 318 (SI Units)
The purpose of this problem is to ensure that Mat3D computes various foundation
design parameters correctly for a square soil-supported foundation supporting a base
plate using SI Units and ACI 318 concrete design code. In this problem, the foundation
is subjected to both axial and shear load.

Reference: Hand Calculation

Foundation Design results using this example should be as follows:

Item No Item Description Result

1 Max actual gross bearing pressure 143.75 kN/m2
2 Actual gross bearing pressure 227.50 kN/m2
3 Punching shear perimeter 4.84 m
4 Two way shear (Punching shear) 685.19 kN
5 Actual punching shear stress 232.08 kN/sq m
6 Allowable punching shear stress 1318.14 kN/sq m
7 Beam shear critical section from left footing edge 2.66 m
8 Max beam shear at critical section 360.65 kN
9 Actual beam shear stress at critical section 168.92 kN/sq m
10 Allowable beam shear at critical section 659.07 kN/sq m
11 Net ultimate moment per unit length 126 kN m/m
12 Reinforcement area required 12.60 sq cm/m
13 Rebar configuration 16 – 20 mm bars

The following pages show the input and output of the same design run in Mat3D. The
comparison of results is tabulated at the end of the output.
 Dimensional Solutions, Inc.
Advanced Softw are For Foundation Design

Miscellaneous Foundation Design - Soil Supported

INPUTS

Loads
Dead Load OWT 386.00 kN
Wind Load Lwt 192.00 kN
Dead Shear BWT 0.00 kN
Wind Shear Ls T 124.00 kN

Footing and Pedestal Geometry

Few = 3.500

Pew = 0.600

Pns = 0.600 Fns = 3.500

Depth of footing below grade FBG 2.50 m

Footing EW Dimension FEW 3.50 m
Footing NS Dimension FNS 3.50 m
Footing thickness FTH 0.70 m
Pier EW Dimension PEW 0.60 m
Pier NS Dimension PNS 0.60 m
Pier ht above grade PHT 0.30 m
Pier EW offset from footing C.L. PEWO 0.00 m
Pier NS offset from footing C.L PNSO 0.00 m
Effective depth FEffD 0.61 m
Soil depth Sd 1.80 m

Material Properties
Concrete compressive strength Fc' 28.00N/sqmm
Concrete unit wt γc 24.00 kN/cum
Reinforcing yield strength Fy 420.00N/sqmm
Reinforcing steel unit wt γR 78.50 kN/cum
Allowable net bearing pressure NBP 185.00 kN/sqm
Soil unit wt γs 17.00 kN/cum

Applied Loads LF Axial Shear NS Mom EW

Dead 1.2 386.00 0.00 0.00
Live 1.6 192.00 124.00 0.00

RESULTS

Bearing Pressure Calculation

Footing weight = Fwt =Few*Fns*FThk*Yc 205.80 kN
Soil weight = Swt =((Few*Fns)-(Pew*Pns))*(FBG-Fth)*Ys 363.83 kN
Pier weight = Pwt =Pew*Pns*(PHt+(FBG-Fth))*Yc 18.14 kN

Total Selfweight Twt =Fwt + Swt + Pwt 587.78 kN

Applied load Oa =Owt+Lwt 578.00 kN

Total load TL =Twt + Oa 1165.78 kN

Mom at footing base Mb =Frs*(FBG+PHt) 347.20 kNm

eccentricity Ecc =Mb/TL 0.30 m

Bearing pressure BP =(TL/(Few*Fns))*(1+6*Ecc/Few) 143.75 ksf

Gross pressure GP =NBP+(FBG*Ys) 227.50 ksf

Footing OK in Bearing
Max Ult Bearing Pressure
Ultimate loads
Axial Load Pult =LF*(Owt + Lwt) 770.4 kN
Shear Load Sult =LF*Frs 198.4 kN
Selfweight SWult =LF*Twt 705.33 kN
Total Ult load TLult =Pult+SWult 1475.73 kN

Ult Mom at footing base Mult =Sult*(FBG+PHt) 555.52 kNm

eccentricity Eult =Mult/TLult 0.38 m

Max Ult bearing pressure BPUmax =(TLult/(Few*Fns))*(1+6*Eult/Few) 198.21 kN/sqm

Min Ult bearing pressure BPUmin =(TLult/(Few*Fns))*(1-6*Eult/Few) 42.73 kN/sqm

Punching Shear Calculation

Shear perimeter Peri =2*(Pew+FEffD)+2*(Pns+FEffD) 4.84 m
Vertical load at base of pier Pub =(Pult+Pwt)+wt of footing area within shear planes 861.57 kN
Punching shear area Apu,shr =(Pew+FEffD)*(Pns+FEffD) 1.46 sq m
Left punching plane from left edge Pleft =0.5*(Few-Pew)-FeffD/2 1.15 m
Ult pressure at left punching plane Ppunch,left 93.59 kN/sqm
Right punching plane from left edge Pright '=0.5*(Few+Pew)+FeffD/2 2.36 m
Ult pressure at right punching plane Ppunch,right 147.34 kN/sqm
Soil resistance Rsoil =(Ppunch,left+Ppunch,right)/2*Apu,shr 176.38 kN
Punching shear Pshear =(Pub-Rsoil) 685.19 kN
Punching shear stress Pstress =Pshear*(Peri*FEffD) 232.08 kN/sqm
Shear Reduction Factor Øc 0.75
Beta Factor ß 1.00
Allowable punching shear Pall,str =Ø*(2+4/ß*sqr(fc')) 1318.14 kN/sqm

Punching Shear OK
Beam Shear Calculation in E-W Direction
Critical section for beam shear Bc =(Fns/2+Pns/2+FEffD) 2.66 m
Bearing Pressure at critical section BPc =Bc/Fns*(BPUmax-BPUmin)+BPUmin 160.89 kN/sqm
Shear force outside critical section Ap =(BPc+BPUmax)/2*Few*(Fns-Bc) 527.88 kN
Shear force due to soil/footing wt Ssf =(Sd*Ys)+(Fth*Yc)*Few*(Fns-Bc) 167.23 kN
Max shear at crit section Smax =Ap-Ssf 360.65 kN
Shear stress BSstr =Smax/(Few*FEffD) 168.92 kN/sqm
Shear reduction Factor Øc 0.75
Allowable shear stress Ball,str =Øc*2*sqr(fc') 659.07 kN/sqm

Beam Shear OK

Moment Calculation
Critical section for moment Mc =(Fns/2+Pns/2) 2.05 m
Critical section from right face 1.45 m
Bearing Pressure at crit section BPmc =Mc/Fns*(BPUmax-BPUmin) 133.79 kN/sqm
Centroid of pressure diagram Cp 0.68 m
Ult moment - crit section Mult =(BPUmax+BPmc)/2*(Fns-Mc)*Cp*Few 650.28 kNm
Ult moment - Soil and footing Mult,s 209.28 kNm
Net Ult moment Mult,Net 441.00 kNm
Ult moment per unit length Mult,L =Mult/Few 126.00 kNm/m
Area of steel required for moment As,m =Mult/(phi*au*d) 7.33sq cm/m
Temp and shrinkage steel area Ats =0.0018*Fth*100*100 12.60sq cm/m

Reinft - Use 16 - 20 mm bars at 225 mm o.c. each way - bottom level

Dim ensional Solutions Mat3D Version 5.8.1 Date 12/10/2011
Foundation Nam e Soil Supported Foundation With Shear Tim e 12:14:30 PM
Designed By: Engineer Checker

Filenam e: Spread_Footing_SI_Soil_X_Shear.m 3d

DETAIL REPORT

PROJECT INFORMATION

Project Nam e:
Project Num ber:
Client:
Project Location
Foundation Description SOIL SUPPORTED FOUNDATION WITH SHEAR

DESIGN CODE ACI 318 - 2008 INPUT UNITS SI OUTPUT UNITS SI

CONCRETE PARAMETERS: REINFORCING STEEL PARAMETERS:

Compressive Strength (N/sq mm) 28 Yield Strength (N/sq mm) 420

Unit Weight (kN/cu m) 24 Unit Weight (kN/cu m) 78.5
Pier Concrete Cover - X Dir (mm) 50 Modulus of Elasticity (kN/sq mm) 200
Pier Concrete Cover - Z Dir (mm) 50 Pier Min Rebar Spacing (mm) 100
Footing Side Concrete Cover - X Dir (mm) 50 Footing Min Rebar Spacing (mm) 100
Footing Side Concrete Cover - Z Dir (mm) 50 Footing Max Rebar Spacing (mm) 450
Footing Top Concrete Cover (mm) 50
Footing Bottom Concrete Cover - X Dir (mm) 64

SOIL PARAMETERS: REBAR PARAMETERS:

Unit Weight (kN/cu m) 17 Max Long Bar Size 20

Allow able Net Bearing Capacity (kN/sq m) 185 Min Long Bar Size 10
Bearing Capacity Method Linear Soil Pressure Max Tie Bar Size 12
Soil Type Cohesive Min Tie Bar Size 10
Ultimate Cohesion c 50 Max Ftg Bar Size 25
Ultimate Adhesion Ad 50 Min Ftg Bar Size 20
Allow able Increase in Soil Pressure due to Short Term Loads (%) Temp & Shrinkage Steel Ratio 0.0018
Wind 0 Earthquake 0 Test 0
Min Stability Ratio 1.5
Safety Factor against Lateral Forces 1.5

MINIMUM FOUNDATION CRITERIA: BUOYANCY CRITERIA:

Depth of Footing Below Grade (mm) 2500 Consider Buoyancy: No

Minimum Soil Cover (mm) 0 Consider soil for buoyancy: No
Grade Elevation (mm) 0 Water table below grade (mm) 0
 APPLIED LOADS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Case (kN) (kN) (kN m) (kN) (kN m)

1 - Dead 386.00 0.00 0.00 0.00 0.00

2 - Wind 192.00 124.00 0.00 0.00 0.00

UNFACTORED (ALLOWABLE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - Dead + Wind 578.00 124.00 0.00 0.00 0.00

FACTORED (ULTIMATE) LOAD COMBINATIONS

P1

Load Axial Shear X Mom Z Shear Z Mom X

Comb (kN) (kN) (kN m) (kN) (kN m)

1 - 1.2Dead + 1.6Wind 770.40 198.40 0.00 0.00 0.00

BEARING CAPACITY - LINEAR SOIL PRESSURE METHOD

Load Max All Ecc Ecc Moment Moment Rem

Comb Pressure Pressure Z Dir X Dir Z axis X axis
(kN/sq m) (kN/sq m) (cm) (cm) (kN-m) (kN-m)

1 - Dead + Wind 143.79 227.43 0.00 29.79 347.13 0.00

STABILITY RATIO / SLIDING SAFETY FACTOR

Load S.R. S.R. All Sliding Sliding All Remarks

Comb Z Dir X Dir S.R. FS - Z FS - X FS

1 - Dead + Wind 100.00 5.87 1.50 100.00 7.63 1.50

 FOOTING DESIGN INFORMATION

X Dim (mm) 3500.00

Z Dim (mm) 3500.00
Thickness (mm) 700.00

Top Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.2Dead + 1.6Wind 0 0 0 0 0 0 X
1. 1.2Dead + 1.6Wind 0 0 0 0 0 0 Z

Bottom Steel

Governing No of Bar Bar Area Area Moment Direction

Combination Bars Size Spac Prov Req
(mm) (mm) (sq cm/m) (sq cm/m) (kN m/m)

1. 1.2Dead + 1.6Wind 16 20 225 14.37 12.6 127 X

1. 1.2Dead + 1.6Wind 16 20 225 14.37 12.6 68 Z

PUNCHING SHEAR

P1

Control Net Ult Punch. All Rem

Comb Load Stress Stress
(kN) (kN/sq m) (kN/sq m)

1. 1.2Dead + 1.6Wind 685.92 232.59 1318.14

MAXIMUM SHEAR - X DIRECTION

Load Left Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (kN/sq m) (kN/sq m)

1 - 1.2Dead + 1.6Wind 2.66 -363.93 170.61 659.07

MAXIMUM SHEAR - Z DIRECTION

Load Bottom Max Shear All Rem

Comb Dist Shear Stress Stress
(m) (kN) (kN/sq m) (kN/sq m)

1 - 1.2Dead + 1.6Wind 2.66 -190.18 89.16 659.07

Results Comparison

Item No Item Description Result Mat3D Result

1 Max actual gross bearing pressure 143.75 kN/m2 143.79 kN/m2
2 Actual gross bearing pressure 227.50 kN/m2 227.43 kN/m2
3 Punching shear perimeter 4.84 m 4.84 m
4 Two way shear (Punching shear) 685.19 kN 685.92 kN
5 Actual punching shear stress 232.08 kN/sq m 232.59 kN/sq m
6 Allowable punching shear stress 1318.14 kN/sq m 1318.14 kN/sq m
7 Beam shear critical section from left 2.66 m 2.66 m
footing edge
8 Max beam shear at critical section 360.65 kN 363.93 kN
9 Actual beam shear stress at critical 168.92 kN/sq m 170.61 kN/sq m
section
10 Allowable beam shear at critical 659.07 kN/sq m 659.07 kN/sq m
section
11 Net ultimate moment per unit length 126 kN m/m 127 kN m/m
12 Reinforcement area required 12.60 sq cm/m 12.60 sq cm/m
13 Rebar configuration 16 – 20 mm bars 16 – 20 mm bars