Columns and Struts

Q. Compare Column and Struts

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 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

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