A rigid beam ABC is pin connected to the ground at A. A cable BD is pin-connected to the beam at B and pin-connected to the ground at D (see figure (a) below). The cross-section area of BD is 200 mm². Two forces with a magnitude of P are applied on the beam at C and E. The cable BD is made of steel and has the bilinear stress-strain behavior shown in figure (b). The slope between 0- 400 MPa is 200 GPa. The slope for stresses larger than 400 MPa is 20 GPa. Note that Hooke's law is only valid for stresses below 400 MPa. a) What is the elongation of the cable BD when P = 5 kN? b) If a vertical displacement at B is 25 mm due to forces P, what is the magnitude of P? c) In part b), if all loads are released, what is the residual vertical displacement of point C? Note: you can assume that strains are small enough that changes of geometry due to the deformation can be neglected when performing statics calculations and that the small angle approximation can be used to analyze deformations due to the rotation of the rigid beam. MPa 3 m D A 2m JP E 4 m B 2 m C 400 E = 200 GPa (a) Rigid beam with cable and (b) stress-strain curve. E' = 20 GPa E (b)

A rigid beam ABC is pin connected to the ground at A. A cable BD is pin-connected to the beam at B and pin-connected to the ground at D (see figure (a) below). The cross-section area of BD is 200 mm². Two forces with a magnitude of P are applied on the beam at C and E. The cable BD is made of steel and has the bilinear stress-strain behavior shown in figure (b). The slope between 0- 400 MPa is 200 GPa. The slope for stresses larger than 400 MPa is 20 GPa. Note that Hooke's law is only valid for stresses below 400 MPa. a) What is the elongation of the cable BD when P = 5 kN? b) If a vertical displacement at B is 25 mm due to forces P, what is the magnitude of P? c) In part b), if all loads are released, what is the residual vertical displacement of point C? Note: you can assume that strains are small enough that changes of geometry due to the deformation can be neglected when performing statics calculations and that the small angle approximation can be used to analyze deformations due to the rotation of the rigid beam. MPa 3 m D A 2m JP E 4 m B 2 m C 400 E = 200 GPa (a) Rigid beam with cable and (b) stress-strain curve. E' = 20 GPa E (b)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Question

A rigid beam ABC is pin connected to the ground at A. A cable BD is pin-connected to the beam
at B and pin-connected to the ground at D (see figure (a) below). The cross-section area of BD is
200 mm². Two forces with a magnitude of P are applied on the beam at C and E. The cable BD is
made of steel and has the bilinear stress-strain behavior shown in figure (b). The slope between 0-
400 MPa is 200 GPa. The slope for stresses larger than 400 MPa is 20 GPa. Note that Hooke's law
is only valid for stresses below 400 MPa.
a) What is the elongation of the cable BD when P = 5 kN?
b) If a vertical displacement at B is 25 mm due to forces P, what is the magnitude of P?
c) In part b), if all loads are released, what is the residual vertical displacement of point C?
Note: you can assume that strains are small enough that changes of geometry due to the
deformation can be neglected when performing statics calculations and that the small angle
approximation can be used to analyze deformations due to the rotation of the rigid beam.
o MPa
3 m
D
A
2 m
↓
E
4 m
B
2 m
400
E = 200 GPa
(a) Rigid beam with cable and (b) stress-strain curve.
E' = 20 GPa
(b)

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