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.

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

answer: chicken nuggets.

explanation:

answer:

a

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