steel column design examples

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

Indian Institute of Technology Madras

8.5 Design Examples

8.5.1 Design example (slab base)

A built-up steel column comprising two ISWB 400 RSJ sections with their

webs spaced at 325mm and connected by 10 mm thick battens transmits an

axial load of 2000 kN. SBC of boil at site=300kN/m2. The safe permissible stress

on the concrete bed= 4N/mm2. Design a suitable foundation for the column

adopting a slab base, and sketch the details of the foundation.

1. Data

Axial load on column = 2000kN

Permissible compressive stress on concrete = 4N/mm2

Column built up of two ISWB 400 RSJ sections connected by 10 mm thick

battens.

2. Column base

Area of base plate = (2000 / 4000) = 0.5 m2

using a square base plate,

Side length of base plate = = 0.706 m

Adopt a base plate of size 750mm x 750mm.

Referring to figure 8.10, the projection of the base plate from the edge of the

column is obtained as

a = greater projection

= 0.5(750 - 420) = 165 mm

b = smaller projection

= 0.5(750 - 525) = 112.5 mm



Intensity of pressure on base plate

= 3.56 N/mm2

Permissible bearing stress in base plate sbs = 185N/mm2

The thickness of the base plate is obtained from the relation

22

bs

3w bt a4

=

Aiming the thickness of base plate

( )2 2 m0s fy

t 2.5w a 0.3b tf= >

Figure 8.10 Column base plate

223 x 3.56 112.5165 37mm

185 4 =



Adopt a base plate of size 750mm x 750mm x 40mm.

3. Cleat angle

For connecting the column section to the base plate, adopt ISA 100 x 100

x 10 mm angles with four 22mm diameter rivets on flange side and ISA 75 x 75 x

8 mm with three 22mm diameter rivets in the webs.

8.5.2 Design example (gusseted base)

For the built-up column of design example 8.5.1, design a suitable

foundation adopting a gusseted base.

1. Size of base plate

Area of base plate = (2000 / 4000) = 0.5 m2

Adopt ISA 150 x 100 x 12 mm gusset angles on the flange side with

100mm leg horizontal, gusset plate 12mm thick, 10 mm batten, and cover plates.

Minimum length required allowing 30mm projection on either side in the direction

parallel to the webs

= (400 + 20 + 24 + 200 + 60) = 704mm

Length of base plate parallel to the flanges = 750mm.

Adopt a base plate of size 750mm x 750mm as shown in Fig 5.2a

2. Thickness of base plate

Intensity of pressure below the plate



w = (2000 x 103 / 750 x 750) = 3.55 Nmm2

Referring to Fig 5.2b, cantilever projection of plate from the face of the

gusset angle = 141 mm.

Bending moment 22 3.55 x 141wLM 35288 N / mm

2 2 = = =

If t = thickness of plate required,

2bs

bs

btM

6

6 x 352886Mt 33.8mmb 185 x 1

= = = =

In LSD, No allowable being stress,

In WSD b allow =0.75 fy

Thickness of base plate = (t - thickness of angle leg) = (33.8 - 12) = 21.8mm

Adopt 750 x 750 x 22 mm base plate.

3. Connections

Outstand on each side = (750 - 400)/2 = 175 mm

Load on each connection = (175 x 750 x 3.55)/1000 = 466 kN

Using 22mm diameter rivets,

Rivet value in single shear =2x 23.5 x 100 43.4kN

4 x 1000 =

Rivet value in bearing = 23.5x12 x 300 84.6kN1000

=



Therefore least value of rivet = 43.4kN

Number of rivets = (466/43.4) = 11

Adopt 16 rivets connecting gusset angles with plate and the same number of

rivets to connect the gusset plate with the column. The arrangement of rivets and

the details of the gusseted base are shown in Fig 8.12

8.12 (a) Details of base plate



(b) Cantillever projection

Fig 8.12 Gusset and base plate details

8.5.3 Design example (grillage foundation)

Design a suitable grillage foundation for the gusseted column of design

example 8.5.2 which supports an axial load of 2000kN. Assuming SBC of soil at

site = 300 kN/m2, draw the elevation and plan of the grillage foundation.

1. Area of grillage

Using gusseted base for the column,

Total load on foundation

= (2000kN + 10% for self weight of foundation)

= 2200 kN



Two tiers of girders will be used.

Bottom-tier area = (2200/300) = 7.33 m2

Using a square grillage, side length = 7.33 = 2.72 m

Adopt a grillage of size 2.75m x 2.75m.

Allowing 125mm concrete cover on all the sides, the overall size of the grillage

block = (3.0m x 3.0m)



Fig 8.13 Arrangement of rivets and details of gusseted base

2. Design of top-tier girders

The bending moment is obtained as M = W/8 (L - L1)

Where W = axial load on column = 2000kN

L = length of grillage = 2.75m

L1 = length of base plate = 0.75m

M = 2000/8 (2.75 - 0.75) = 500kNm

Allowable stress can be increased by 33.33% since the beams are encased in concrete.

Therefore bt = (165 x 1.33) = 220 N/mm2 6

4 3

bt

500 x10MZ 227 x10 mm220

= = =

Section modulus



Using three beams in top tier,

Z for each beam = (227 x 104 / 3) = 756600mm3

Use ISBM 350 having the section properties

Zxx = 778900 mm3

tf = 14.2 mm

tw = 8.1 mm

The maximum shear force is given by ( )1WV L L2L =

V = (2000 / 2 x 2.75) (2.75 - 0.75) = 730 kN

Shear force per beam = (730 / 3) = 243.33 kN

Average shear stress v = (243.33 x 103 / 8.1 x 350) = 78 N/mm2 < 100 N/mm2

minimum gap between two beams = 75mm

3. Design of bottom-tier girders



BM is obtained as

( )( )

2

64 3

bt

WM L L82000 2.75 0.75

8

500 x10MZ 227 x10 mm165x1.33

= =

= = =

Using eight beams in the bottom tier,

Z for each beam = (239 x 104 / 8) = 298 x 103

Use ISLB 250, Zxx = 297 x 103mm3

Spacing of beams = 1 / 7(2.75 - 0.125) = 0.375 m

Use eight beams of ISLB 250 spaced at 375 mm c/c.

Maximum shear force is given by

( ) ( )2W 2000V L L 2.75 0.75 730kN2L 2 x 2.75 = = =

Shear force per beam = (730 / 8) = 91.25 kN

Shear stress = v = (91.25 x 103 / 6.1 x 250 ) = 60 N/mm2 < 100N/mm2 Adopt separators made up of angles ISA 50 x 50 x 6mm and 2.75 m long,

welded or bolted with 12mm diameter bolts to the flanges of the lower-tier girders

at two ends to prevent displacement of girders.

The plan and elevation of the grillage foundation is shown in figure 8.14.



Fig 8.14 Plan and elevation of grillage foundation

steel column design examples

Documents