For the beam shown in Fig. Q4, use the principle of virtual work to determine (1) the vertical deflection at Point C, and (2) the rotation at the right-hand bearing (Point B). The Young's modulus of the material is E = 200 GPa. The cantilever beam has a circular cross section with the second moment of area / = 30 x 106 m²4. The beam is under a uniformly distributed load q=15 kN/m at the AB span and a point force P=27 kN at Point C. The length of AB span is L=9 m and the length of BC span is L₁ =3.6 m. (In this question, we assume (1) the positive direction of a vertical force points upwards; (2) the positive direction of a horizontal force points to the right; and (3) the postive direction of an applied moment is clockwise.)

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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For the beam shown in Fig.Q4, use the principle of virtual work to determine (1) the vertical deflection
at Point C, and (2) the rotation at the right-hand bearing (Point B). The Young's modulus of the
material is E = 200 GPa. The cantilever beam has a circular cross section with the second moment of
area / = 30 x 106 m². The beam is under a uniformly distributed load q=15 kN/m at the AB span and
a point force P=27 kN at Point C. The length of AB span is L=9 m and the length of BC span is L₁ =3.6
m.
(In this question, we assume (1) the positive direction of a vertical force points upwards; (2) the
positive direction of a horizontal force points to the right; and (3) the postive direction of an applied
moment is clockwise.)
L
BA
L₁
Part a) Reactions
The vertical reaction force at support A can be calculated as
The vertical reaction force at support B can be calculated as
The horizontal reaction force at support A can be calculated as
KN
KN
KN
р
Transcribed Image Text:For the beam shown in Fig.Q4, use the principle of virtual work to determine (1) the vertical deflection at Point C, and (2) the rotation at the right-hand bearing (Point B). The Young's modulus of the material is E = 200 GPa. The cantilever beam has a circular cross section with the second moment of area / = 30 x 106 m². The beam is under a uniformly distributed load q=15 kN/m at the AB span and a point force P=27 kN at Point C. The length of AB span is L=9 m and the length of BC span is L₁ =3.6 m. (In this question, we assume (1) the positive direction of a vertical force points upwards; (2) the positive direction of a horizontal force points to the right; and (3) the postive direction of an applied moment is clockwise.) L BA L₁ Part a) Reactions The vertical reaction force at support A can be calculated as The vertical reaction force at support B can be calculated as The horizontal reaction force at support A can be calculated as KN KN KN р
Part e) Rotation_at_B
Use the principle of virtual work to determine the rotation at Support B. (The positive direction of a
rotation is clockwise. Please present your result to 4 decimal places.)
Transcribed Image Text:Part e) Rotation_at_B Use the principle of virtual work to determine the rotation at Support B. (The positive direction of a rotation is clockwise. Please present your result to 4 decimal places.)
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