BAse Plate Design Examples

Design of Steel Structures

Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

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

Indian Institute of Technology Madras



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

3w σbs

t=

⎛ 2 b2 ⎞ ⎜⎜ a − ⎟ 4 ⎟⎠ ⎝

Aiming the thickness of base plate

(

t s = 2.5w a 2 − 0.3b 2

) γ m0 f y > t f

Figure 8.10 Column base plate

2 3 x 3.56 ⎛ 2 112.5 ⎜⎜165 − 185 ⎝ 4


⎞ ⎟⎟ = 37mm ⎠



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.

⎛ wL2 Bending moment M = ⎜ ⎜ 2 ⎝

⎞ ⎛ 3.55 x 1412 ⎟⎟ = ⎜⎜ 2 ⎠ ⎝

⎞ ⎟⎟ = 35288 N / mm ⎠

If t = thickness of plate required, ⎛ σbs bt 2 M=⎜ ⎜ 6 ⎝ t=

6M = σ bs b

⎞ ⎟ ⎟ ⎠ 6 x 35288 = 33.8 mm 185 x 1

In LSD, No allowable being stress, In WSD σb 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,

⎛ π x 23.52 x 100 ⎞ Rivet value in single shear = ⎜ ⎟⎟ = 43.4 kN ⎜ 4 x 1000 ⎝ ⎠

⎛ 23.5 x12 x 300 ⎞ Rivet value in bearing = ⎜ ⎟ = 84.6 kN 1000 ⎝ ⎠




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 σbt = (165 x 1.33) = 220 N/mm2

⎛ M Z=⎜ ⎝ σbt

⎞ ⎛ 500 x106 ⎟ = ⎜⎜ ⎠ ⎝ 220

Section modulus


⎞ 4 3 ⎟⎟ = 227 x10 mm ⎠



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

⎛W⎞ The maximum shear force is given by V = ⎜ ⎟ ( L − L1 ) ⎝ 2L ⎠ V = (2000 / 2 x 2.75) (2.75 - 0.75) = 730 kN Shear force per beam = (730 / 3) = 243.33 kN Average shear stress τv = (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

W ( L − L2 ) 8 ⎛ 2000 ⎞ =⎜ ⎟ ( 2.75 − 0.75 ) ⎝ 8 ⎠ ⎛ M ⎞ ⎛ 500 x106 ⎞ 4 3 Z=⎜ ⎟⎟ = 227 x10 mm ⎟ = ⎜⎜ σ 165 x1.33 ⎝ bt ⎠ ⎝ ⎠

M=

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 V=

⎛ 2000 ⎞ W ( L − L2 ) = ⎜ ⎟ ( 2.75 − 0.75 ) = 730kN 2L ⎝ 2 x 2.75 ⎠

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


BAse Plate Design Examples

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