A column of timber section 15cmx 20cm is 6m long both ends being fixed .E for timber is 17.5KN/mm2, Determine a) Crippling load b) Safe load for the column if factor of safety=3

A column of timber section 15cmx 20cm is 6m long both ends being fixed .E for timber is 17.5KN/mm², Determine

a) Crippling load

b) Safe load for the column if factor of safety=3

Step 1: Data

Length of the column = 6000mm

Width of the column = 150mm

Depth of the column = 200mm

Condition = Both ends being fixed

Crippling load =??

FOS=3

E=17.5 KN/mm²

Step 2: Calculation of moment of inertia

I _xx = bd ³ / 12

I _xx = 150 (200)³ / 12

I _xx = 100X10⁶mm⁴

I _yy = db ³ / 12

I _yy = 200 (150)³ / 12

I _yy= 56.25X10⁶mm⁴

Choose whichever is least

Therefore, I = 56.25X10⁶mm⁴

Step 3: Calculation of crippling load

Condition = Both ends being fixed

P = 4Π ²E I/ L²

P = 4Π ²⁽17.5 x1000) (56.25 X 10⁶ ) /  (6000)²

P = 1079.48 KN

Step 4: Calculation of safe load

Safe load = crippling load /FOS

Safe load = 1079.48/3

Safe load = 359.82KN