Shear Design of Concrete Beam

Civil Guide

Shear Design of Concrete Beam - Shear reinforcement Design

This example goes through the shear design of a simply supported concrete beam in accordance to Eurocode 2, and is a very common and easy hand calculation that can be undertaken.

Beam shown below is a simply supported beam, where span is taken as 7000mm. The characteristic strengths of the concrete and steel are fck = 32 N/mm2. Effective depth, d=550mm and breadth = 400mm.

Permanent load, g = 50 kN/m (including self weight)

Variable load, qk = 35 kN/m

Shear Design of Concrete Beam Design
How to design a concrete beam

Ultimate loading and maximum shear

Ultimate load, wu = (1.35gk + 1.5qk) kN/m

= (1.35 x 50 + 1.5 x 35) = 120 kN/m

therefore,

maximum design shear V = wu x effective span/2 = 120 x 7.0/2 = 420 kN

Design shear at face of support VED = 420 – 120×0.15 = 402 kN

Maximum shear at face of support,

Crushing strength VRd,max of diagonal strut, assuming angle ϑ = 22°, cot ϑ = 2.5

VRd,max = 0.124 bw d (1-fck /250) fck

= 0.124 x 400 x 550 (1-32/250) x 32 x 10-3

= 761 kN (> 402 kN)

Therefore, angle ϑ = 22°, cot ϑ = 2.5 will be taken.

Shear Links

The required shear links in a beam is defined the the equation below:

Asw/s = Ved/0.78dfykcotθ  = 402 x 103 / (0.78 x 550 x 500 x 2.5) = 0.75

Referring to the shear reinforcement table (click on link). We can calculate the link spacing and size.

Provide 2 Legs 10mm shear links at 200mm spacing = 0.785 … OKAY

Minimum Shear Links

Asw,min/s = 0.08fck0.5bw/fyk  = 0.08 x 320.5 x 400 / (500) = 0.36

We have already provided 10mm links at 200mm spacing (0.785) which is adequate.

The shear resistance of the links can be calculated below:

Vmin = Asw/s x 0.78dfykcotθ = 0.785 x 0.78 x 550 x 500 x 2.5 x 10-3 = 420 kN

Guidance Notes - General sizing

Asw = the cross-sectional area of two legs of the stirrup

S = the spacing of the legs

Z = the lever arm between the upper and lower chord members

Fywd = the design yield strength of the stirrup/link

Fyk = the characteristic strength of the stirrup reinforcement

VEd = the shear force due to the actions at the ultimate limit state

Vwd = the shear force in the stirrup

VRd,s = the shear resistance of the stirrups

VRd,max = the maximum design value of the shear which can be resisted by the concrete strut

 

Maximum longitudinal spacing between shear links = 0.75 d

Maximum transverse spacing between legs in a series of shear links = 0.75 d (≤600mm)

Main steel reinforcement bars should be within a 150mm distance to a shear leg (i.e, check the min distance between bottom/top bar to shear leg)

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