A simply supported beam of length 4m is subjected to a uniformly distributed load of 30KN/m over the whole span and deflects 15mm at the centre. Determine the crippling load when the beam is used as a column for the following conditions. a) One end is fixed and other end is hinged b) Both the ends are pin jointed.

 A simply supported beam of length 4m is subjected to a uniformly distributed load of 30KN/m over the whole span and deflects 15mm at the centre. Determine the crippling load when the beam is used as a column for the following conditions.

a) One end is fixed and other end is hinged

b) Both the ends are pin jointed.

 Solution
Step 1: Data

Length of the column = 4000mm

Udl = 30KN/m

Deflection = 15mm

Crippling load =??

Step 2: Calculation of flexural rigidity

Δ =   5wL^{4   /} 384EI

15 = 5(30) (4000)⁴/384 EI

EI ⁼ 6.667X10¹² N-mm²

Step 3: Calculation of crippling load

Condition = One end hinged and other end fixed

P = 2Π ²E I/ L²

P = 2Π ²(6.667X10¹²) / (4000)²

P = 822.5 KN        

Step 4: Calculation of crippling load

Condition = Both ends pinned

P = Π ²E I/ L²

P =Π ²(6.667X10¹²) / (4000)²

P = 411.20 KN