P
A B C
σ
σy = ∞
ε
(a) Elastic
σ
σy
ε
(b) Elastic Perfectly Plastic
Points Prob 10
The rod shown has a radius of 4 mm and the lengths AB and BC are 100 mm and 400 mm.
a) Elastic: E=70 GPa, YS=infinity: DETERMINE:
Reactions Ax and Cx when the force of 39 kN is applied (kN)
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b) Elastic-Perfectly Plastic: E=70 GPa, YS=440 MPa: DETERMINE:
1- Reactions Ax and Cx when the force of 39 kN is applied (kN)
2- Elastic recovery of BC when the load is removed (mm)
3- Elastic recovery of AB when the load is removed (mm)
4- Permanent reduction in length ABC when the load is removed (mm)
5- Residual strain when the load is removed (mm/mm)
6- Residual stress when the load is removed (MPa)
7- Reactions when load is removed (kN)
r YS E P LAB LBC
4 440 70 39 100 400
A ΔLA (a) Ax Cx (b) 1 Ax Cx (b) 2 ΔLBC (b) 3 ΔLAB (b) 4 ΔLBC (b) 5 εresidual (b) 6 σresidual (b) 7 Ax, C residual
50.265 0.886 31.200 7.800 22.11 16.880 1.91 0.6285 1.290000 0.002500 -301.170
YES NO YES YES YES YES YES YES YES NO NO
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