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Two tempered-steel bars, each 3/16 in. thick, are bonded
Chapter 2, Problem 2.111(choose chapter or problem)
Two tempered-steel bars, each \(\frac{3}{16} \text { in. }\) thick, are bonded to a 12 -in. mild-steel bar. This composite bar is subjected as shown to a centric axial load of magnitude P. Both steels are elastoplastic with \(E=29 \times 10^{6} \mathrm{psi}\) and with yield strengths equal to 100 ksi and 50 ksi, respectively, for the tempered and mild steel. The load P is gradually increased from zero until the deformation of the bar reaches a maximum value \(\delta_{m}=0.04 \mathrm{in}\) and then decreased back to zero. Determine (a) the maximum value of P, (b) the maximum stress in the tempered-steel bars, (c) the permanent set
Questions & Answers
QUESTION:
Two tempered-steel bars, each \(\frac{3}{16} \text { in. }\) thick, are bonded to a 12 -in. mild-steel bar. This composite bar is subjected as shown to a centric axial load of magnitude P. Both steels are elastoplastic with \(E=29 \times 10^{6} \mathrm{psi}\) and with yield strengths equal to 100 ksi and 50 ksi, respectively, for the tempered and mild steel. The load P is gradually increased from zero until the deformation of the bar reaches a maximum value \(\delta_{m}=0.04 \mathrm{in}\) and then decreased back to zero. Determine (a) the maximum value of P, (b) the maximum stress in the tempered-steel bars, (c) the permanent set
ANSWER:
Step 1 of 4
We will first calculate the yield point elongation of each metal. Upon comparing yield point deformation with given deformation, we will find the load and corresponding stress in it.
Given Data
Area of mild steel
Area of tempered steel
Total Area
Ultimate stress of tempered steel
Ultimate stress of mild steel
Modulus of Elasticity
Yield point Deformation
For Mild Steel
For tempered Steel
Since, the deformation of $0.04$ in is more than yield point deformation of mild steel but less than yield point deformation of tempered steel. The mild steel yields but tempered steel is elastic.