1. Columns and Struts

2. Q. Compare Column and Struts

3. Effective length (le)
Where l is actual length

4. 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

5. Euler’s Crippling Load, PE = ∏²EI /le²
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

6. 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)

7. 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)]}

8. 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)

9. Tutorial
Columns and Struts (Chapter 9 Rethaliya)
1. Page 694: Exercises 1 to 7
2. Examples: No. 1, 3, 5, 6, 8, 10, 11