Transcript Structrual Analysis-1_130604

Columns and Struts
Q. Compare Column and Struts
A.
• Effective length (le)
Where l is actual length
Radius of Gyration , k = √(I/A)
I = Moment of Inertia (mm4)
A = Area of Section (mm2)
Slenderness ratio, λ = le/kmin
Long Column v/s Short Column
Le/kmin > 50 for long
Le/kmin < 50 for short
Or,
Le/d > 15 for Long
Le/d < 15 for short
Euler’s Formula
Euler’s Crippling Load,
PE = ∏²EI /le²
Where, E is Modulus of Elasticity (Mpa)
I is MOI or 2nd Moment of area (mm4)
Le is Effective length (mm)
Also known as Critical Buckling Load
Rankine’s Formula
1/P = 1/PC + 1/PE
Where, P is Rankine’s crippling Load
PC is Crushing Load
PE is Euler’s crippling Load
If A is the Cross section area of column
PC = fC . A
PE = ∏²EI /le²
I = Ak2
Where Rankine’s Constant, α = fc/(∏²E)
Thus, P = PR = (fC . A) / (1 + α λ)
Eccentric Loading
• Short Column
σmax = P/A + P.e/Z = P/A (1 + eyc/k2)
Z = Ak2/ yc
• Long Column
– Rankine’s Formula σc= P/A (1 + eyc/k2) (1 + αle/k)
– Euler’s Formula
– σmax = P/A + Pe v /Z
– σmin = P/A – Pe v /Z
v = sec {(le/2) /√[P/(EI)]}
For Discussion / Self Study
• Prof. Perry’s formula:
(Refer to Section 9.15 Rethaliya, page 627)
• Column with Initial Curvature- Axial Load
(Refer to Section 9.16 Rethaliya, page 629)
• Column with Lateral loading
– Pinned, Subject to Point Load
– Pinned, Subject to UDL
(Refer to Section 9.17a and 9.17b, Rethaliya, page
632)
Tutorial
Columns and Struts (Chapter 9 Rethaliya)
1. Page 694: Exercises 1 to 7
2. Examples: No. 1, 3, 5, 6, 8, 10, 11