Columns and Struts

Q. Compare Column and StrutsA.

• 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 Formula1/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 columnPC = 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 Columnσmax = 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)]}

• 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)

For Discussion / Self Study

Tutorial Columns and Struts (Chapter 9 Rethaliya)

1. Page 694: Exercises 1 to 72. Examples: No. 1, 3, 5, 6, 8, 10, 11