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Columns and Struts

Columns and Struts. Q. Compare Column and Struts A. Effective length (l e ) Where l is actual length. Radius of Gyration , k = √(I/A) I = Moment of Inertia (mm 4 ) A = Area of Section (mm 2 ) Slenderness ratio, λ = le/k min Long Column v/s Short Column Le/k min > 50 for long

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Columns and Struts

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  1. Columns and Struts

  2. Q. Compare Column and Struts A.

  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 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 + αλ)

  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

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