solid round bar 3m long and 5cm in diameter is used as a strut, determine the crippling load. Take E=2x105N/mm2. a) One end hinged and other end fixed b) One end is fixed and other end is free. c) Both the ends are fixed.

 A solid round bar 3m long and 5cm in diameter is used as a strut, determine the crippling load. Take E=2x10⁵N/mm².

a) One end hinged and other end fixed

b) One end is fixed and other end is free.

c) Both the ends are fixed.

Solution

Step 1: Data

Length of the column = 3000mm

Diameter of the column = 50mm

Crippling load =??

E=2x10⁵N/mm².

 Step 2: Calculation of moment of inertia

I = π d ⁴ / 64

I= π (50)⁴ / 64

I = 0.306X10⁶mm⁴

Step 3: Calculation of crippling load

Condition = One end hinged and other end fixed

P = 2Π ²E I/ L²

P = 2Π ²⁽2x10⁵) (0.306X10⁶ ) /  (3000)²

P = 134.22 KN

Step 4: Calculation of crippling load

Condition = One end is fixed and other end is free.

P = Π ²E I/4 L²

P = Π ²⁽2x10⁵) (0.306X10⁶) / 4(3000)²

P = 16.778 KN

Step 5: Calculation of crippling load

Condition = Both the ends are fixed

P = 4Π ²E I/ L²

P = 4Π ²⁽2x10⁵) (0.306X10⁶ ) /  (3000)²

P = 268.45 KNa