A hollow cylindrical steel tube of 38 mm external diameter and 2.5 mm thick is used as a column of 2.3 m long with both ends fixed. The slenderness ratio is
Answers
Answer:
1. The external and internal diameters of the hollow cast iron column are 5cm and 4cm respectively. If the length of this column is 3m and both of its ends are fixed, determine the crippling load using Rankine’s formula. Take σc= 550N/mm2 and a=1/1600.
Step 1: Data:
D = external diameter = 50mm
d= internal diameter = 40mm
Rankine's constant=a=1/1600.
length of column= 3m = 3000mm
condition=both of its ends are fixed
crippling load =??
critical stress = σc= 550N/mm2
Step 2: Calculation of the area of the column
A= π/4(D2-d2)
A= π/4(502-402)
A = 706.85 mm2
Step 3 :Calculation of the moment of inertia of the column
I = π/64(D4-d4)
I = π/64(504-404)
I = 181.04X103 mm4
Step 4:Calculation of Effective length
condition=both of its ends are fixed
therefore,
Le=l / 2
Le = 3000/ 2
Le = 1500mm
Step 5:Calculation of radius of gyration
K= √(I/A)
K = √(181.04X103 /706.85)
K = 16.00 mm
Step 6:Calculation of crippling load
P= (σc A)/(1+a(Le/k)2)
P = ((550) (706.85))/(1+(1/1600)(1500/16)2)