Question 3.16: The stepped bar shown in Figure 3–9 is subjected to an axial...
The stepped bar shown in Figure 3–9 is subjected to an axial tensile force of 55 600 N. Compute the maximum tensile stress in the bar for the following dimensions:
D= 20.0 mm; d= 10.0 mm; r= 0.8 mm.
Objective Compute the maximum tensile stress.
Given F = 55 600 N; D = 20.0 mm; d = 10.0 mm; r = 0.8 mm.
Analysis Because of the change in diameter, use Equation (3–18).
\sigma_{max} = K_{t} \sigma_{nom} (3-18)
Use the chart in Appendix A-18-2 to find the value of K_{t} using r/d and D/d as parameters.
Results \sigma_{max} = K_{t} \sigma_{nom}
\sigma_{nom} = \sigma_{2} = F/A_{2} =F/(\pi d^{2}/4) = (55600 N)/[π(10.0 mm)²/4]
\sigma_{nom} = 707.9 N/mm² = 707.9 MPa
r/d = 0.8/10 = 0.080 and D/d = 20.0/10.0 = 2.00
Read K_{t} 2.12 from Appendix A-18-2.
Then, \sigma_{max} = K_{t} \sigma_{nom} = 2.12(707.9 MPa) = 1501 MPa.
Comment The actual maximum stress of 1501 MPa is more than double the value that would be pre-dicted by the standard formula.
