The two rods (A-B and B-C) shown in the left panel are connected by pins at A, B, and C. The cross sections of A-B and B-C are 10mm×13mm and 10mm×10mm, respectively. The bilinear stress-strain relation shown in the right panel is for the material used to make the two rods, where Ei is the slope of the stress-strain curve for stresses between 0 and 80 MPa and E2 is the slope for stresses larger than 80 MPa. Note that Hooke's law is only valid for stresses up to 80 MPa.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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The two rods (A-B and B-C) shown in the left panel are connected by pins at A, B, and C. The
cross sections of A-B and B-C are 10mm×13mm and 10mm×10mm, respectively. The bilinear
stress-strain relation shown in the right panel is for the material used to make the two rods, where
Ei is the slope of the stress-strain curve for stresses between 0 and 80 MPa and E2 is the slope for
stresses larger than 80 MPa. Note that Hooke's law is only valid for stresses up to 80 MPa.
A
1
1
B
0.900 m
3
P = 30 kN
2.44 m
C
σ MPa
80
E₂ = 40 GPa
E₁ = 80 GPa
E
a) Given the conditions above, find the axial elongation for each rod when subjected to
P=30KN.
b) Find the final position of Point B due to the applied load P at that location. Hint: Assume
point B moves by unknown amounts Ax and Ay from its initial position, and then use right
triangles to write the known final lengths of the cables in terms of Ax and Ay. The equations
can be simplified by assuming terms Ax² and Ay² are so small they can be neglected.
Transcribed Image Text:The two rods (A-B and B-C) shown in the left panel are connected by pins at A, B, and C. The cross sections of A-B and B-C are 10mm×13mm and 10mm×10mm, respectively. The bilinear stress-strain relation shown in the right panel is for the material used to make the two rods, where Ei is the slope of the stress-strain curve for stresses between 0 and 80 MPa and E2 is the slope for stresses larger than 80 MPa. Note that Hooke's law is only valid for stresses up to 80 MPa. A 1 1 B 0.900 m 3 P = 30 kN 2.44 m C σ MPa 80 E₂ = 40 GPa E₁ = 80 GPa E a) Given the conditions above, find the axial elongation for each rod when subjected to P=30KN. b) Find the final position of Point B due to the applied load P at that location. Hint: Assume point B moves by unknown amounts Ax and Ay from its initial position, and then use right triangles to write the known final lengths of the cables in terms of Ax and Ay. The equations can be simplified by assuming terms Ax² and Ay² are so small they can be neglected.
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