## Worked examples

The worked examples in this chapter look at a shear wall under combined loading (Example 2.1); combination of actions on a pile group supporting an elevated bridge deck (Example 2.2); and the statistical determination of characteristic strength from the results of concrete cylinder tests (Example 2.3).

Specific parts of the calculations are marked O, ©, ©, etc., where the numbers refer to the notes that accompany each example.

### 2.15.1 Shear wall under combined loading

Example 2.1 looks at Vck (permanent combinations of actions for VQk (variable the foundation shown in Figure 2.23.12 The footing carries imposed loads from the superstructure and a horizontal force and moment from wind.

Notes on Example 2.1

O The combination factors for variable actions that are given in EN 1991 depend on the source of loading and the type of structure.

© In Combination 1, the g imposed action is leading Figure 2.23. Shear wall subject to vertical and

= 1) and the wind is horizontal forces and moment ignored = 0).

© As wind is not included, there is no moment applied and the bearing pressure beneath the base is constant (Aq = 0).

© In Combination 2, the imposed action is leading (^ = 1) and wind is accompanying (^0 = 0.5).

© As wind is now included, the moment from it causes a variable bearing pressure beneath the base (qav ± Aq/2).

Example 2.1 Shear wall under combined loading Combination of actions

### Design situation

Consider a b = 500mm thick shear wall that is resting on a rectangular footing founded at a depth d = 2m. The footing is B = 2m wide, L = 8m long, and t = 500mm thick. The characteristic weight density of the backfill on kN

top of the footing is Yk = 16.9-and of unreinforced concrete is m kN

Yck = 24-(as per EN 1991-1-1). The shear wall is subject to characteristic m imposed vertical actions V^ = 2000kN (permanent) and Vqk = 1600kN

(variable) from the superstructure. In addition, wind applies a characteristic variable moment MQk = 1200kNm and a characteristic horizontal force

Self-weight of foundation (characteristic actions)

Weight of concrete base (permanent) Wgk = Yck x B x L x t = 192 kN

Weight of concrete wall (permanent) Wgk = Yck x b x L x (d -1) = 144 kN

Weight of backfill (permanent) W^ = Ykx (B - b) x L x (d -1) = 304.2 kN

Total self-weight of foundation Wgk =

Average pressure on foundation due to self-weight alone-= 40 kPa

Combination factors on variable actions/action effects O Imposed loads in buildings, Category B: office areas: ^0 i = 0.7

Wind loads on buildings, all cases (from BS EN 1990): ^0w = 0.5

Partial factors on actions/action effects

Unfavourable permanent actions yg = 1.35 Unfavourable variable actions yq = 1.5

Combination 1 (leading variable = imposed, accompanying = none) © Total permanent vertical action = Wgk + Vgk = 2640 kN

Design vertical action Vd = yg x ( Wgk + Vgk) + yq x 1.0 x Vqk = 5964 kN

Design horizontal action Hd = yQx x 0kN = 0kN

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