All parts please thank you so muchPart b) Bending moment by real forces_1Let the origin of the horizontal coordinate x be at the support A and the positive x-axis points to the right.The bending moment caused by the real forces as a function of x can be discribed as For 0≤x≤ 0≤x≤8 m, ( please use units kN.m for bending moment)Part c) Bending moment by real forces_2The bending moment caused by the real forces as a function of x can be discribed as For 8 <x≤<x≤ ( 8+3.2 ) m, ( please use units kN.m for bending moment)Part d) Vertical defection at Point cUse the principle of virtual work to determine the vertical deflection at Point C. ( the positive direction of a vertical deflection points upwards )Part e) Rotation_at_BUse 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.) Radians For the beam shown in Fig.Q4, use the principle of virtual work to determine (1) the vertical deflection atPoint C, and (2) the rotation at the right-hand bearing (Point B). The Young's modulus of the material isE = 200 GPa. The cantilever beam has a circular cross section with the second moment of area / = 30 x10-6 m4. The beam is under a uniformly distributed load q=15 kN/m at the AB span and a point forceP=27 kN at Point C. The length of AB span is L=8 m and the length of BC span is L₁ =3.2 m.(In this question, we assume (1) the positive direction of a vertical force points upwards; (2) thepositive direction of a horizontal force points to the right; and (3) the postive direction of an appliedmoment is clockwise.)k9ΑΔLBooL₁рс Part a) ReactionsThe vertical reaction force at support A can be calculated asThe vertical reaction force at support B can be calculated asThe horizontal reaction force at support A can be calculated asKNKNKN

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Answered: All parts please thank you so much Part…

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Chapter3: Torsion

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All parts please thank you so much

Part b) Bending moment by real forces_1

Let the origin of the horizontal coordinate x be at the support A and the positive x-axis points to the right.

The bending moment caused by the real forces as a function of x can be discribed as

For 0≤x≤ 0≤x≤8 m, ( please use units kN.m for bending moment)

Part c) Bending moment by real forces_2

The bending moment caused by the real forces as a function of x can be discribed as

For 8 <x≤<x≤ ( 8+3.2 ) m, ( please use units kN.m for bending moment)

Part d) Vertical defection at Point c

Use the principle of virtual work to determine the vertical deflection at Point C. ( the positive direction of a vertical deflection points upwards )

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.) Radians

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
10-6 m4. 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=8 m and the length of BC span is L₁ =3.2 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.)
k
9
ΑΔ
L
Boo
L₁
р
с

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

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