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Project 2

SShyam Datta22 Sept 2022

Isolated Footing Design (IS 456-2000)

Footing No. Group ID Foundation Geometry
- - Length Width Thickness
1 1 2.40m 2.40m 0.70m

Footing No. Footing Reinforcement Pedestal Reinforcement
- Bottom Reinforcement(Mz) Bottom Reinforcement(Mx) Top Reinforcement(Mz) Top Reinforcement(Mx) Main Steel Trans Steel
1 Ø16 @ 250 mm c/c Ø16 @ 250 mm c/c N/A N/A 14 - Ø12 Ø8 mm @ 175 mm

Isolated Footing 1








0.3 m1 m0.7 m0.5 mElevation
1.2 m1.2 m2.4 m2.4 m0.61 mXZPlan

Input Values

Footing Geometry

Design Type : Calculate Dimension with user specified minimums as starting value
Minimum Footing Length - X(Fl) : 2000.00 mm
Minimum Footing Width - Z (Fw) : 2000.00 mm
Minimum Footing Thickness(Ft) : 700.00 mm
Eccentricity along X (Oxd) : 0.00 mm
Eccentricity along Z (Ozd) : 0.00 mm

Column Dimensions

Column Shape : Circular
Column Dia : 0.47 m

Pedestal

Include Pedestal : Yes
Pedestal Shape : Circular
Pedestal Height (Ph) : 0.30 m
Pedestal Dia : 0.61 m

Design Parameters

Concrete and Rebar Properties

Unit Weight of Concrete : 24.00 kN/m3
Strength of Concrete : 40.00 N/mm2
Yield Strength of Steel : 500.00 N/mm2
Minimum Bar Size : Ø16
Maximum Bar Size : Ø32
Pedestal Minimum Bar Size : Ø8
Pedestal Maximum Bar Size : Ø40
Minimum Bar Spacing : 100.00 mm
Maximum Bar Spacing : 450.00 mm
Pedestal Clear Cover (P, CL) : 50.00 mm
Footing Clear Cover (F, CL) : 50.00 mm

Soil Properties

Unit Weight : 17.60 kN/m3
Base Value of Soil Bearing Capacity : 120.00 kPa
Multiplying factor for soil bearing capacity for ultimate loads : 1.70
Soil Bearing Capacity Type : Gross Bearing Capacity
Soil Surcharge : 0.00 kN/m2
Height of Soil above Footing : 500.00 mm
Type of Depth : Fixed Top
Minimum Percentage of Slab area in Contact for Service Loads : 0.00
Minimum Percentage of Slab area in Contact for Ultimate Loads : 0.00

Sliding and Overturning

Coefficient of Friction : 0.50
Factor of Safety Against Sliding : 1.50
Factor of Safety Against Overturning : 1.50

Global Settings

Top Reinforcement Option : Calculate only when foundation is subjected to uplift forces
Concrete Design Option : Net Pressure(Gross Pressure - Self Weight Pressure)
------------------------------------------------------

Design Calculations

Load Combinations

Load Combination/s- Service Stress Level
Load Combination Number Load Combination Title Load Case Multiplier (a) Soil Bearing Factor (b) Self Weight Factor (c) Code
a - Value specified in the Load Multiplier table
b - Value specified in the Pile/Soil Bearing Capacity Factors table
c - Value specified in the Apply Self Weight and Dead Weight Factor table
1 EQX+ 1.00 1.00 1.00 -
2 EQZ+ 1.00 1.00 1.00 -
5 WL(0+CPI) 1.00 1.00 1.00 -
6 WL(0-CPI) 1.00 1.00 1.00 -
7 WL(90+CPI) 1.00 1.00 1.00 -
8 WL(90-CPI) 1.00 1.00 1.00 -
4 LL 1.00 1.00 1.00 -
3 DL 1.00 1.00 1.00 -
Load Combination/s- Strength Level
Load Combination Number Load Combination Title Load Case Multiplier (a) Soil Bearing Factor (b) Self Weight Factor (c) Code
a - Value specified in the Load Multiplier table
b - Value specified in the Pile/Soil Bearing Capacity Factors table
c - Value specified in the Apply Self Weight and Dead Weight Factor table
1 EQX+ 1.00 1.00 1.00 -
2 EQZ+ 1.00 1.00 1.00 -
5 WL(0+CPI) 1.00 1.00 1.00 -
6 WL(0-CPI) 1.00 1.00 1.00 -
7 WL(90+CPI) 1.00 1.00 1.00 -
8 WL(90-CPI) 1.00 1.00 1.00 -
4 LL 1.00 1.00 1.00 -
3 DL 1.00 1.00 1.00 -

Applied Loads on Top of Pedestal

Before consideration of self weight and load multiplier table

Moments are About the center of Column / Pedestal (does not include moments caused by lateral loads)
For the loads shown in this table, the sign convention is the same as that for JOINT LOADS in STAAD.Pro when global Y is the vertical axis.

Applied Loads for Column - Service Stress Level
Load Case Fx
(kN) 		Fy
(kN)
Downwards is negative Upwards is positive		 Fz
(kN) 		Mx
(kNm) 		Mz
(kNm)
1 1.76 4.06 0.04 0.00 0.00
2 0.01 14.94 12.52 0.00 0.00
5 7.55 16.06 -1.59 0.00 0.00
6 16.96 22.56 0.91 0.00 0.00
7 19.52 62.07 18.03 0.00 0.00
8 0.08 -41.84 -1.85 0.00 0.00
4 -0.27 -7.04 -0.00 0.00 0.00
3 -0.14 -13.65 -0.00 0.00 0.00
Applied Loads for Column - Strength Level
Load Case Fx
(kN) 		Fy
(kN)
Downwards is negative Upwards is positive		 Fz
(kN) 		Mx
(kNm) 		Mz
(kNm)
1 1.76 4.06 0.04 0.00 0.00
2 0.01 14.94 12.52 0.00 0.00
5 7.55 16.06 -1.59 0.00 0.00
6 16.96 22.56 0.91 0.00 0.00
7 19.52 62.07 18.03 0.00 0.00
8 0.08 -41.84 -1.85 0.00 0.00
4 -0.27 -7.04 -0.00 0.00 0.00
3 -0.14 -13.65 -0.00 0.00 0.00
------------------------------------------------------
Footing Size
Initial Length (Lo) = 2.00 m
Initial Width (Wo) = 2.00 m
Area from initial length and width, Ao
 = Lo×Wo = 4.00 m2
Min. area required from bearing pressure, Amin
 = Pqmax = 1.20 m2
Note: Amin is an initial estimation.
P = Vertical load from column + selfweight of footing + weight of soil.
qmax = Respective Factored Bearing Capacity.


Final Footing Size
Length (L2) = 2.40 m Governing Load Case : # 8
Width (W2) = 2.40 m Governing Load Case : # 8
Depth (D2) = 0.70 m
Area (A2) = 5.76 m2
Depth is governed by Ultimate Load Case
(Service check is performed with footing thickness requirements from concrete check)
Final Pedestal Height = 0.30 m
Final Soil Height = 0.50 m
Weight of the footing + pedestal (if any) = 98.90 kN
Weight of the soil above the footing (dry) = 48.12 kN
Uplift force due to buoyancy = 0.00 kN
Effect due to adhesion = 0.00 kN
------------------------------------------------------

Gross Pressures at 4 Corners

Load Case Pressure at top left corner
(kN/m2) 		Pressure at top right corner
(kN/m2) 		Pressure at bottom right corner
(kN/m2) 		Pressure at bottom left corner
(kN/m2) 		Area of footing in uplift (Au)
(m2) 		Gross Bearing Capacity
(kN/m2)
8 33.5595 33.6293 32.0186 31.9488 0.00 120.0000
8 33.5595 33.6293 32.0186 31.9488 0.00 120.0000
8 33.5595 33.6293 32.0186 31.9488 0.00 120.0000
8 33.5595 33.6293 32.0186 31.9488 0.00 120.0000

If Au is zero, there is no uplift and no pressure adjustment is necessary. Otherwise, to account for uplift, areas of negative pressure will be set to zero and the pressure will be redistributed to remaining corners.

Summary of adjusted Gross Pressures at Four Corners
Load Case Pressure at
top left corner
(kN/m2) 		Pressure at
top right corner
(kN/m2) 		Pressure at
bottom right corner
(kN/m2) 		Pressure at
bottom left corner
(kN/m2) 		Gross Bearing Capacity
(kN/m2)
8 33.5595 33.6293 32.0186 31.9488 120.0000
8 33.5595 33.6293 32.0186 31.9488 120.0000
8 33.5595 33.6293 32.0186 31.9488 120.0000
8 33.5595 33.6293 32.0186 31.9488 120.0000
Details of Out-of-Contact Area
(If Any)
Governing load case = N/A
Plan area of footing = 5.76 sq.m
Area not in contact with soil = = 0.00 sq.m
% of total area not in contact = 0.00%
------------------------------------------------------

Stability Check










0.3 m1 m0.7 m0.5 m.Frictional ForceSliding ForceOTM


- Factor of safety against sliding Factor of safety against overturning
Load Case No. Along X-Direction Along Z-Direction Resultant Required FOS About X-Direction About Z-Direction Required FOS
1 40.53 N/A 40.52 1.50 N/A 96.82 1.50
2 N/A 5.28 5.28 1.50 12.60 N/A 1.50
5 8.68 41.10 8.49 1.50 98.17 20.72 1.50
6 3.67 68.48 3.66 1.50 163.57 8.76 1.50
7 2.18 2.36 1.60 1.50 5.63 5.20 1.50
8 1179.95 51.14 51.09 1.50 122.14 N/A 1.50
4 283.97 N/A 283.96 1.50 N/A 678.27 1.50
3 570.73 N/A 570.71 1.50 N/A 1363.21 1.50
Critical Load Case And The Governing Factor Of Safety For Overturning and Sliding X Direction
Critical Load Case for Sliding along X-Direction : 7
Governing Disturbing Force : 19.52 kN
Governing Restoring Force : 42.48 kN
Minimum Sliding Ratio for the Critical Load Case : 2.18
Critical Load Case for Overturning About X-Direction : 7
Governing Overturning Moment : 18.12 kNm
Governing Resisting Moment : 101.94 kNm
Minimum Overturning Ratio for the Critical Load Case : 5.63
Critical Load Case And The Governing Factor Of Safety For Overturning and Sliding Z Direction
Critical Load Case for Sliding along Z-Direction : 7
Governing Disturbing Force : 18.03 kN
Governing Restoring Force : 42.48 kN
Minimum Sliding Ratio for the Critical Load Case : 2.36
Critical Load Case for Overturning About Z-Direction : 7
Governing Overturning Moment : -19.62 kNm
Governing Resisting Moment : : 101.94 kNm
Minimum Overturning Ratio for the Critical Load Case : 5.20
Critical Load Case And The Governing Factor Of Safety For Sliding Along Resultant Direction
Critical Load Case for Sliding along Resultant Direction : : 7
Governing Disturbing Force : 26.58 kN
Governing Restoring Force : 42.48 kN
Minimum Sliding Ratio for the Critical Load Case : 1.60
------------------------------------------------------
Top Reinforcement Design Requirement
Top Reinforcement needs to be provided because of resultant negative pressure coming from net pressure calculations for bending.
Ultimate Gross Pressures

The base pressures reported in this table and the area of footing in contact include the effect of buoyancy (if any).

Load Case / Load Combination ID
 Pressure at top left corner
(kN/m2) 		Pressure at top right corner
(kN/m2) 		Pressure at bottom right corner
(kN/m2) 		Pressure at bottom left corner
(kN/m2) 		Gross Factored Bearing Capacity For Ultimate Load Case
(kN/m2) 		Area of footing in Contact with soil (Au)
(m2)
1 24.0337 25.5719 25.6063 24.0681 204.0000 5.76
2 17.4668 17.4760 28.3955 28.3863 204.0000 5.76
5 20.1388 26.7222 25.3327 18.7493 204.0000 5.76
6 13.8132 28.6091 29.4017 14.6058 204.0000 5.76
7 0.0000 15.3955 31.1412 14.0972 204.0000 5.73
8 33.5595 33.6293 32.0186 31.9488 204.0000 5.76
4 26.8658 26.6292 26.6276 26.8642 204.0000 5.76
3 27.9556 27.8329 27.8318 27.9546 204.0000 5.76
Minimum Required Contact Area for Ultimate Loads : 0.00 m2

Actual Area in Contact for all ultimate load cases exceeds the minimum required. Hence Safe

Maximum Corner Pressure from all ultimate load cases is less than the allowable. Hence Safe

Moment Calculation
Check Trial Depth against moment (About Z Axis)
Critical Load Case = #8
Effective Depth = D-(cc+1.5 × db) = 0.63 m
Governing moment (Mu) = = 7.36 kNm
As Per IS 456 2000 ANNEX G G-1.1C
Limiting Factor1 (Kumax) = 700[1100+(0.87 × fy )] = 0.46
Limiting Factor2 (Rumax) = 0.36×fck×kumax×(1-0.42×kumax) = 5309.03 kN/m2
Limiting Moment Of Resistance (Mumax) = Rumax×B×d2 = 4993.07 kNm
Mu <= Mumax hence, safe
Check Trial Depth against moment (About X Axis)
Critical Load Case = #8
Effective Depth = D-(cc+1.5 × db) = 0.63 m
Governing moment (Mu) = = 7.92 kNm
As Per IS 456 2000 ANNEX G G-1.1C
Limiting Factor1 (Kumax) = 700[1100+(0.87×fy )] = 0.46
Limiting Factor2 (Rumax) = 0.36×fck×kumax×(1-0.42×kumax) = 5309.03 kN/m2
Limiting Moment Of Resistance (Mumax) = Rumax × B × d2 = 4993.07 kNm
Mu <= Mumax hence, safe
------------------------------------------------------

One-Way Shear in XY plane

(Shear Plane Parallel to Global X Axis)



1.2 m1.2 m0.265 m0.265 mPlanXZ
Critical Load Case = # 8
Distance of critical section from top left corner along Z, DZ = 0.27 m
Shear Force(S) = 5.46 kN
Shear Stress(Tv) = 3.63 kN/m2
Percentage Of Steel(Pt) = 0.1338
As Per IS 456 2000 Clause 40 Table 19
Shear Strength Of Concrete(Tc) = 300.00 kN/m2
Shear Enhancement Factor (if considered) is applied to (Tc), as per IS456 -2000 Clause No 40.5.1 and Fig 24
Tv< Tc hence, safe

One-Way Shear in YZ plane

(Shear Plane Parallel to Global Z Axis)

1.2 m1.2 m0.265 m0.265 mPlanXZ
Critical Load Case = # 8
Distance of critical section from top left corner along X, DX = 0.27 m
Shear Force(S) = 5.02 kN
Shear Stress(Tv) = 3.34 kN/m2
Percentage Of Steel(Pt) = 0.13
As Per IS 456 2000 Clause 40 Table 19
Shear Strength Of Concrete(Tc) = 300.00 kN/m2
Shear Enhancement Factor (if considered) is applied to (Tc), as per IS456 -2000 Clause No 40.5.1 and Fig 24
Tv< Tc hence, safe

Punching Shear Check

1.2 m1.2 m0.315 mPlanXZ
Critical Load Case = #8
Shear Force(S) = 36.36 kN
Shear Stress(Tv) = 16.53 kN/m2
As Per IS 456 2000 Clause 31.6.3.1
Ks = min⁡[0.5+β,1] = 1.00
Shear Strength(Tc) = 0.25×fck = 1581.14 kN/m2
Ks x Tc = 1581.14 kN/m2
Tv<= Ks x Tc hence, safe
------------------------------------------------------
Reinforcement Calculation
Calculation of Maximum Bar Size
Along X Axis
Bar diameter corresponding to max bar size (db) = 20 mm
As Per IS 456 2000 Clause 26.2.1
Development Length(ld) = db×0.87×fy4×τbd = 0.72 m
Available Development Length(ldb) = (B-b)2-cc = 0.85 m
ldb >=ld hence, safe
Along Z Axis
Bar diameter corresponding to max bar size(db) = 20 mm
As Per IS 456 2000 Clause 26.2.1
Development Length(ld) = db×0.87×fy4×τbd = 0.72 m
Available Development Length(ldb) = (H-h)2-cc = 0.85 m
ldb >=ld hence, safe

Flexure About X-Axis

Design For Bottom Reinforcement Parallel to Z Axis

10 - 16 mmXZ
For moment About X Axis (Mx)
As Per IS 456 2000 Clause 26.5.2.1
Critical Load Case = #8
Minimum Area of Steel (Astmin) = 2016 mm2
Calculated Area of Steel (Ast) = 2016 mm2
Note - "Area of Steel required" reported here is the larger value between the calculated area of steel and minimum steel required as per code stipulations
Provided Area of Steel (Ast,Provided) = 2011 mm2
Ast,Provided >= Astmin Hence OK.

Selected bar Size (db) = Ø16
Minimum spacing allowed (Smin) = 100.00 mm
Selected spacing (S) = 253.78 mm
Smin<= S <= Smax and selected bar size < selected maximum bar size. Hence OK.

Based on spacing reinforcement increment; provided reinforcement is

Ø16 @ 250mm o.c.

Flexure About Z-Axis

Design For Bottom Reinforcement Parallel to X Axis

10 - 16 mmXZ
For moment About Z Axis (Mz)
As Per IS 456 2000 Clause 26.5.2.1
Critical Load Case = #8
Minimum Area of Steel (Astmin) = 2016 mm2
Calculated Area of Steel (Ast) = 2016 mm2
Note - "Area of Steel required" reported here is the larger value between the calculated area of steel and minimum steel required as per code stipulations
Provided Area of Steel (Ast,Provided) = 2011 mm2
Ast,Provided >= Astmin Hence OK.

Selected bar Size (db) = Ø16
Minimum spacing allowed (Smin) = 100.00 mm
Selected spacing (S) = 253.78 mm
Smin<= S <= Smax and selected bar size < selected maximum bar size. Hence OK.

Based on spacing reinforcement increment; provided reinforcement is

Ø16 @ 250mm o.c.

Pedestal Design

Pedestal at Support No. Axial Capacity Ratio, Critical Load Case, Location Flexural Capacity Ratio % of Main Steel Main Reinforcement Links
1 0.01, 8, Bottom 0.17 0.54 14-T12 8 @ 175mm

Pedestal Size

Pedestal Shape = Circular
Pedestal Diameter = 609.60 mm

Longitudinal Reinforcement Details

Area of Longitudinal Bars = 1583.40 sq.mm
Number of Bars and Bar Dia = 14-T12
Longitudinal Steel Percentage = 0.54
Flexure - Governing Load Case Details
Governing Load Case Number = 7
Critical Location = Bottom
Axial load = -55.03 kN
Moment about X axis = 18.12 kNm
Moment about Z axis = -19.62 kNm
Resultant moment = 26.70 kNm
Moment Capacity = 154.69 kNm
Angle of inclination of Neutral Axis with respect to local Z = 42.73 degrees
Serial No. P
(kN) 		M
(kNm)
1 -688.78 0.00
2 -681.48 2.10
3 -614.23 21.44
4 -387.31 79.27
5 -112.24 142.68
6 159.98 199.81
7 445.32 250.86
8 733.86 295.88
9 1032.88 334.05
10 1186.51 350.31
11 1340.23 364.52
12 1493.98 376.85
13 1650.04 387.07
14 1812.08 394.89
15 1974.41 400.74
16 2136.04 404.58
17 2298.19 406.40
18 2463.96 405.59
19 2628.76 403.01
20 2795.57 397.92
21 2958.96 391.48
22 3118.49 383.62
23 3274.74 374.51
24 3428.11 364.10
25 3578.44 352.36
26 3725.47 339.43
27 3869.27 325.36
28 4145.80 294.22
29 4406.06 259.79
30 4646.25 223.49
31 4861.85 187.41
32 4995.50 161.06
33 5101.14 140.13
34 5186.20 123.22
35 5255.82 109.36
36 5361.93 88.15
37 5437.91 72.81
38 5494.47 61.34
39 5537.81 52.53
40 5571.82 45.59
41 5599.05 40.01
42 5621.24 35.45
43 5639.58 31.67
44 5667.94 25.80
45 5688.47 21.50
46 5703.49 18.24
47 5715.13 15.70
48 5724.35 13.67
49 5825.71 0.00
Moment [kNm]Axial Load [kN]070140210280350406.403637-100001000ϕM (42.73 deg) (kNm)
Shear - Governing Load Case Details
Critical Load Case for Shear Along Resultant Direction = 7
Shear Force Along Resultant Direction = 26.58 kN

Transverse Stirrups Details

Rebar Links = 8 @ 175 mm
Crack Width Calculation (for Mz)
Modulus of Elasticity of Concrete(Ec) = 31622776.60 kN/m2 Clause No. 6.2.3.1
Modulus of Elasticity of Steel(Es) = 200000000.00 kN/m2 Annexure F
Depth of Neutral Axis(Xu) = 0.30 m Annexure G, Clause No. G-1.1.a
Effective MOI(Ieff) = 23054910909.11 mm4
Average Steel Strain at Considered Level(Ɛm) = 0.00 X 10-5
Distance from Nearest Tension Rod (acr) = 0.14 m
Crack Width (Wcr) = 0.00 mm Annexure F
From IS 456-2000 Clause No. 35.3.2
Section is uncracked.
Crack Width Calculation (for Mx)
Modulus of Elasticity of Concrete(Ec) = 31622776.60 kN/m2 Clause No. 6.2.3.1
Modulus of Elasticity of Steel(Es) = 200000000.00 kN/m2 Annexure F
Depth of Neutral Axis(Xu) = 0.30 m Annexure G, Clause No. G-1.1.a
Effective MOI(Ieff) = 23054910909.11 mm4
Average Steel Strain at Considered Level(Ɛm) = 0.00 X 10-5
Distance from Nearest Tension Rod (acr) = 0.14 m
Crack Width (Wcr) = 0.00 mm Annexure F
From IS 456-2000 Clause No. 35.3.2
Section is uncracked.
------------------------------------------------------
1.2 m1.2 mPlan2.4 m2.4 m0.61 mXZ0.3 m1 m0.7 m0.5 mElevationFoundationPedestalDimensions (m)ReinforcementLBD2.4 m2.4 m0.7 mlbh0.61 m0.61 m0.3 mAstX(T)AstZ(T)AstX(B)AstZ(B)N/AN/A10 - 16 mm10 - 16 mmMain ReinforcementTrans Reinforcement12 mm - 148 mm @ 175 mm1.2 m1.2 mTOP N/ATOP N/ABOTTOM 10 - 16 mmBOTTOM 10 - 16 mmPlan

Title Design of Base Plate
Step 1 Strength of concrete fcu = 50 N/mm2
Yield strength of steel fy = 500 N/mm2
Material factor γm = 1.1 kN
Factored load = 2000 kN
Step 2 Steel column section
Thickness of flange T = 14.2 mm
Step 3 Area required
Bearing strength of concrete = 0.4 fcu
= 20 N/mm2
Area required = 100000 mm2
Let size of plate Bplate = 350 mm
Dplate = 350 mm
Area of plate = 122500 mm2
Let projection on each side a = b = 25 mm
w = 16.33 N/mm2
Cl 7.4.3.1 Thickness of slab base ts = 6.3 mm
< 14.20 mm
So use base plate of size 350mm x 350mm x 12mm
Title Design of Column
Height of column h = 9 m
Yield strength fy = 500 N/mm2
Elastic modulus E = 300000 N/mm2
Material factor γm = 1.1
Step 1 Section classification
Properties of selected section
ISHB 400
A 10466 mm2
h 400 mm d 374.6
B 250 mm
t 10.6 mm
T 12.7 mm
rx 166.1 mm
ry 51.6 mm
Zp cm3
Flange criterion b/T = 9.84
Web criterion d/t = 35.34
Ɛ = 0.71
b/T > 7.42462
d/t > 29.6985
The section is classified as COMPACT
Step 2 Effective Length
T7.5 As both ends pin-jointed
KLx = 9.00 m
KLy = 9.00 m
KLz = 9.00 m
Slenderness ratio
KLx/rx = 54.18
KLy/ry = 174.42
Non-dimensional effective slenderness ratio
Cl 7.1.2.1 λ =
= 2.268
Step 3 To calculate φ
φ = 0.5[1+α(λ-0.2)+λ2]
h/bf = 1.60
> 1.2
T = 12.7 mm
T 7.1 so, buckling class = b
α = 0.34
φ = 3.42
Step 4 Calculation of χ
χ =
χ = 0.167 N/mm2
Step 5 Calculation of fcd
fcd = χfy/γm
= 75.93
Step 6 Factored Axial Load
Pd = Afcd
= 794.665 kN
Title Design of Rafter
Span of I beam = 5 m
Dead Load = 12 kN/m
Imposed Load = 28 kN/m
Length of bearing = 150 mm
Yield strength = 500 N/mm2
40
5
Step 1 Design load calculation
Factored Load = 60.00 kN/m
Factored bending moment = 187.50 kNm
Step 2 Section modulus - Required
Z reqd = 412500.0 mm3
= 412.50 cm3
Step 3 Section classification
Properties of selected section
ISMB 250
A 475.5 mm2
D 250 mm
B 125 mm
t 6.9 mm
T 12.5 mm
Izz 5131.6 cm4
Iyy 344.5 cm4
Zp 459.76 cm3
Flange criterion B/2T = 5
Web criterion (D-2T)/t = 32.61
Ɛ = 0.70711
B/2T < 9.4
(D-2T)/t < 59.3263
The section is classified as PLASTIC
Step 3 Moment of resistance of the cross section
Moment Md = (Zpxfy)/γm
Md = 208.982 kNm
> 187.50
Hence section ISMB 250 is adequate for flexure
Step 4 Shear resistance of the cross section
Shear capacity Vc = 0.6fyAv/γm
Av = 1725 mm2
Vc = 470.45 kN
Factored shear V = 150.00 kN
V/Vc = 0.32
< 0.6
Step 5 Check for Web Buckling
Slenderness ratio of web = 2.5d/t
d = 225
= 70.33
Design compressive stress fc = 203 N/mm2
Pw = 385193
= 385.19 kN
> 150.00
Hence web is safe against shear buckling
Step 6 Check for web crippling at support
Root radius of ISMB 250 R = 13 mm
tf + R = 25.5 mm
Dispersion length n2 = 63.75 mm
Pcrip = 641250 N
= 641.25 kN
> 150.00
Hence section adequate for web crippling
Step 7 Check for serviceability - Deflection
Design load = 40 kN/m
Deflection δ = 31.72 mm
Allowable deflection = 25 mm
Hence serviceability is satisfied

Week 9
Session 2
Title Gantry girder calculation

Step 1 Span of gantry girder = 7 m
Span of crane girder = 9 m
Crane capacity = 250 kN
Self weight (trolley,hook,motor) = 40 kN
Self weight of crane girder = 100 kN
Minimum hook approach = 1 m
Distance between wheels = 3 m
Self weight of rails = 0.2 kN/m


Step 2 Maximum moment due to vertical load
Weight of trolley + Weight of load lifted = 290 kN
Self weight of crane girder = 100 kN

For maximum reaction on girder, the moving load should be as close to the gantry as possible
240 kN

200 kN
A 1 14 B

For maximum reaction on girder, the moving load should be as close to the gantry as possible
240 kN
200 kN
A 1 14 B
15 m


15 m
Reaction at A RA = 501 kN
Load on gantry girder from each wheel = 251 kN
Factored wheel load = 375.8333333 kN

RD = 281.875 kN
Maximum moment ME = 634.22 kNm
let self weight of girder = 2 kN/m
Dead load (self weight + rails) = 2.2 kN/m
Factored DL = 3.30 kN/m
M due to DL = 20.21 kNm
M due to impact load = 158.55 kNm
Factored moment due to all vertical loads
M = 812.99 kNm

Step 3 Maximum moment due to lateral load
Hzl. Force transferred to rails = 29 kN
Horizontal force on each wheel = 7.25 kN
Factored horizontal force = 10.875 kN



Maximum moment = 18.35 kNm
Vertical shear due to
wheel loads = 563.75 kN
impact = 140.94 kN
self weight = 9.90 kN
Total shear = 714.59 kN
Lateral shear due to surge = 20.68 kN


Step 4 Preliminary section determination
Minimum economic depth D = L/12
= 583.3333333 mm
Width of compression flange b = L/40 to L/30
= 175 233
Required plastic modulus Zp = 1.4 x M / fy
= 4552721.25
= 4552.72 x103 mm3

Let us try ISMB 600 with ISMC 400 on compression flange

Step 5 Properties of selected section

ISMB 650 @ 1.21 kN/m ISMC 400 @ 0.49 kN/m
A 15600 mm2 A 6380 mm2
h 600 mm h 400 mm
b 210 mm b 100 mm
tf 20.3 mm tf 15.3 mm
tw 12 mm tw 8.8 mm
Izz 91800 x104mm4 Izz 15200 x104mm4
Iyy 2650 x104mm4 Iyy 508 x104mm4
R 20 mm Cyy 2.42 mm

Step 6 Determination of section modulus
Let the distance of N.A from the tension range by y'

y' =
y' = 388.93 mm
Izz = 1348.128426 x106mm4
Zez = 3466240.196 mm3

For compression flange about y-y axis
I = 16766.6525 x104mm4
Zey = 838332.625 mm3
Total area of section = 21980 mm2

Let plastic NA be at a distance Yp from tension flange.
Yp = 580.88 mm
Zpz = 4410317.327 mm3
For top flange Zpy = 1078488.402 mm3


Step 7 Section classification
For ISMB b/t = 4.90
< 9.4
d/t = 43.28
< 84

For ISMC b/t = 5.96
< 9.4
Hence section is plastic

Step 8 Check for local moment capacity
Local moment capacity for bending in vertical plane
Mdz = fyZp / 1.1
= 1002.34 kNm
= 1.2 Zefy / 1.1
= 945.34 kNm
Mdz = 945.34 kNm
For top flange
Mdy = 245.11 kNm
= 228.6361705 kNm
Mdy = 228.64 kNm

Step 9 Check for combined local capacity
0.94 < 1


Step 10 Check for buckling resistance
Md = βb Zp fbd
For plastic section βb = 1


LLT = 7000 mm
E = 200000 N/mm2
hf = 597.5 mm
Iy = 17850 x104mm4
A = 21980 mm2
ry = 90.12 mm
fcr,b = 417.43 N/mm2

λ = 0.774
ϕ = 0.95
X = 0.97 N/mm2
fbd = 166.5909091

Mdz = 734.72 kNm
Mdy = 202.84 kNm

Hence 1.20 > 1
Hence section is unsafe against torsional buckling

Step 11 Check for shear
Vz = 714.59 kN
Shear capacity = Av*fyw / √3 *1.1
= 944754.9859 N
= 944.7549859 kN
> 714.59
Now = 566.8529916 kN
low shear

Step 12 Check for web buckling
b = 175 mm
n1 = 232.6 mm
d = 519.4 mm
t = 12 mm
λ = 104.7456667
For buckling Class a Table 9a
Fcd = 128.6 N/mm2
Buckling resistance = 629008 kN
> 714.59 kN

Step 13 Check for deflection at working load
Vertical deflection
Serviceability vertical wheel load = 251 kN

Deflection at mid span


a = 2000 mm
Izz = 1348.13 x106mm4
δ = 25.32 mm

Horizontal deflection
I = 16766.65 x104mm4
δ = 4.88 mm
L/750 = 9.33 mm
Unsafe in vertical direction
Safe in lateral direction

hence , greater section is adopted for this design as it failing

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