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14 September, 10:28

A solid square rod is cantilevered at one end. The rod is 0.6 m long and supports a completely reversing transverse load at the other end of + / - 2 kN. The material is AISI 1080 hot-rolled steel. If the rod must support this load for 104 cycles with a factor of safety of 1.5, what dimension should the square cross section have? Neglect any stress concentrations at the support end. Hint: Initially, assume the size endurance limit modification factor is kb=0.85; then check this assumption after the actual size is determined.

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  1. 14 September, 11:42
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    Answer / Explanation:

    Given the data:

    Length of the rod (L) = 0.6m

    Load; F = ± 2 KN

    Ultimate strength; S u t = 770 M P a = 770 / 6.89 kpsi = 112 kpsi

    Yield strength; S y = 420 M P a

    Design factor = 1.5

    Surface factor; k a = 0.488

    Size factor; k b = 0.85

    Now by using mechanical engineering design data book,

    We calculate for fatigue strength

    So, Se¹ = 0.5 * 770

    Se¹ = 385 M P a

    K a = 57.7 * 770⁻⁰⁷¹⁸

    Kₐ = 0.488

    Assume Kb = 0.85 (check later)

    Se = Kₐ Kb Se¹

    Se = 0.488 * 0.85 * 385

    S e = 160 M P a

    By using design data book,

    a = (f Sut) ² / Se

    b = - 1 / 3 log f Sut / Se

    S f = ₐ N ᵇ

    Sf = 2553 (10⁴) ⁻ ⁰.²⁰⁰⁵

    S f = 403 M P a

    The expression for stress,

    M max = 2000 * 0.6

    M max = 1200 Newton per meter

    = M (b/2) / I = M (b/2) / bb³/12

    = 6M / b³ = 6 x 1200 / b³

    = 7200 / b³ Pa

    Now by comparing strength and stress,

    S f = n * σ a

    = 403 * 10 ⁶

    = 1.5 * 7200 / b³

    where b = 0.0299 m

    b = 30 m m

    So, we assume the size factor, so the expression for checking the size factor is,

    By using design data book,

    de = 0.808 (hb) ∧ 1/2

    de = 0.808 b

    de = 0.808 * 30

    de = 24.2

    Kb = (24.2 / 7.62) ∧-0.107

    Kb = 0.88

    We have assume 0.85 which is nearer to the 0.88 and it is acceptable.

    So the dimension of the square is 30 mm
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