Q1 - A 220 mm thick rectangular concrete plate structure is simply supported alo
ID: 1765317 • Letter: Q
Question
Q1 - A 220 mm thick rectangular concrete plate structure is simply supported along its two opposite ends as shown in figure below. It supports a dead load of 1.5 kPa and live load of 3 kPa (excluding self-weight). Density of concrete 2400 kg/m3. E = 32 GPa 4 m v = 0.2 6 m Plan view Elevation Ullllll Model this structure using Stand 7 plate elements and determine the maximum deflections. Note: You are NOT required to do a convergence study, however reasonable number of elements need to be used to derive the respective solutions.Explanation / Answer
Since the slab is suppprted only along two parallel edges, the slab is nothing but a simply supported beam of length 6m,width 4m and 220 mm thick.
The uniform dead load on slab=1.5 kPa
Uniform.live load on slab=3 kPa
Self weight of slab=0.22*2.4*9.8=5.17 kPa
Therefore, total dead load=1.5+5.17=6.67 kPa
Total live load=3 kPa
Total uniform load=6.67+3=9.97 kPa
Therefore, line load on 4 m wide beam=4*9.97=w=39.88 kN/m
The deflection at midspan=(5/384)*2*l?/EI
Here w=39.88 kN/m, l=6m,E=modulus of elasticity of concrete=32GPa, I =moment of inertia of section=4*0.22³/12
Substitute these values in deflection equation and you will get the theoritical deflection at midspan of slab
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