An M14 × 2 hex-head bolt with a nut is used to clamp together two 20-mm steel plates. Compare the results of finding the overall member stiffness by use of Eqs. (8-20), (8-22), and (8-23).
6-27 Using the modified Goodman criterion for infinite life, repeat Prob. 6-25 for each of the following loading conditions:
- (a) 0 kN to 28 kN
- (b) 12 kN to 28 kN
- (c) −28 kN to 12 kN
(a)
The yield factor of safety.
The fatigue factor of safety using Goodman criterion.
The number of cycle to failure.
Answer to Problem 27P
The yield factor of safety is
The fatigue factor of safety using Goodman criterion
The number of cycle to failure is
Explanation of Solution
Write the expression of endurance limit.
Here, endurance limit is
Write the expression for surface modification factor.
Here, surface modification factor is
Write the expression for endurance limit at critical location of a machine part in the geometry.
Here, the endurance limit at critical location is
Write the expression for fatigue stress concentration factor.
Here, the fatigue stress concentration is factor is
Write the expression for area of the steel bar at the hole or the minimum cross section area on which load is acting.
Here, width of the bar is
Write the expression for the maximum stress.
Here, the maximum force acting on the bar is
Write the expression for the minimum stress.
Here, the minimum force acting on the bar is
Write the expression for the nominal amplitude stress.
Here, the nominal amplitude stress is
Write the expression for the nominal midrange stress.
Here, the nominal amplitude stress for is
Write the expression for the amplitude component.
Here, the amplitude component is
Write the expression for the midrange component.
Here, the midrange component is
The Equation (XI) is valid when notch is present in the component.
Write the Expression for the yield factor of safety.
Here, the yield factor of safety is
Write the expression for the fatigue factor of safety using the modified Goodman criterion.
Write the expression for the completely reversed stress.
Here, the fatigue factor of safety using Goodman criterion is
Write the expression of number of cycle in case of completely reversed stress.
Here, the number of cycle are
Write the expression for the constant
Here, the strength fraction is
Write the expression for the constant
Conclusion:
Substitute
Refer to Table 6-2 “Parameter of Marin surface modification factor” to obtain the constant
Substitute
Refer to equation
Substitute
Refer to fig
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the yield factor of safety is
Substitute
Thus, the fatigue factor of safety using Goodman criterion is
Substitute
From fig-
Substitute
Substitute
Substitute
Thus, the number of cycle to failure is
(b)
The Yield factor of safety.
The fatigue factor of safety using Goodman criterion.
Answer to Problem 27P
The yield factor of safety is
The fatigue factor of safety is
Explanation of Solution
Write the expression of maximum stress.
Here, the maximum force acting on the bar is
Write the expression of minimum stress.
Here, the minimum force acting on the bar is
Write the expression of nominal amplitude stress.
Here, the nominal amplitude stress is
Write the expression of nominal midrange stress.
Here, the nominal amplitude stress for is
Write the expression of amplitude component.
Here, the amplitude component is
Write the expression of midrange component.
Here, the midrange component is
Write the Expression of yield factor of safety.
Here, the yield factor of safety is
Write the expression of fatigue factor of safety using the modified Goodman criterion.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the yield factor of safety is
Substitute
Thus, the fatigue factor of safety using Goodman criterion is
(c)
Yield factor of safety.
The fatigue factor of safety using Goodman criterion.
Number of cycle to failure.
Answer to Problem 27P
The yield factor of safety is
The fatigue factor of safety is
The number of cycle to failure is
Explanation of Solution
Write the expression of maximum stress.
Here, the maximum force acting on the bar is
Write the expression of minimum stress acting on the bar.
Here, the minimum force acting on the bar is
Write the expression of nominal amplitude stress.
Here the nominal amplitude stress is
Write the expression of nominal midrange stress.
Here, the nominal amplitude stress for is
Write the expression of amplitude component.
Here, the amplitude component is
Write the expression of midrange component.
Here, the midrange component is
Write the Expression of yield factor of safety.
Here the yield factor of safety is
Write the expression of fatigue factor of safety using the modified Goodman criterion.
Here the fatigue factor of safety is
Write the expression of number of cycle in case of completely reversed stress.
Here, the number of cycle are
Simplify the Equation (IX) for completely reversed stress and substitute
Write the expression of constant
Here, the strength fraction is
Write the expression of the constant
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the yield factor of safety is
Substitute
Thus, the fatigue factor of safety is
From fig-
Substitute
Substitute
Substitute
Thus, the number of cycle to failure is
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Chapter 6 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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