02-07ChapGere.0011

02-07ChapGere.0011 - 170 A-PDF Axially Loaded : Purchase...

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Problem 2.11-6 A rigid bar AB , pinned at end A , is supported by a wire CD and loaded by a force P at end B (see figure). The wire is made of high-strength steel having modulus of elasticity E 5 210 GPa and yield stress s Y 5 820 MPa. The length of the wire is L 5 1.0 m and its diameter is d 5 3 mm. The stress-strain diagram for the steel is defined by the modified power law , as follows: s 5 E e 0 # s # s Y s 5 s Y 1 } E s e Y } 2 n s $ s Y (a) Assuming n 5 0.2, calculate the displacement d B at the end of the bar due to the load P . Take values of P from 2.4 kN to 5.6 kN in increments of 0.8 kN. (b) Plot a load-displacement diagram showing P versus d B . Solution 2.11-6 Rigid bar supported by a wire 170 CHAPTER 2 Axially Loaded Members P AD C B L b 2 b Wire: E 5 210GPa s Y 5 820MPa L 5 1.0m d 5 3mm S TRESS - STRAIN DIAGRAM (1) (2) (a) D ISPLACEMENT d B AT END OF BAR (3) Obtain e from stress-strain equations: (4) From Eq. (1): Ê e 5 s E Ê (0 # s # s Y ) d 5 elongation of wire Ê d B 5 3 2 d 5 3 2 e
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