This set of Structural Analysis Questions and Answers focuses on “Analysis of Beams-4”.
1. What is the extra condition you get when conserving moment near joint B in a beam with fixed support at A, roller supports at B and C, a uniformly distributed load of 2 kN/m on span AB, and additional point loads at specific locations?
a) mBA + mCA = 0
b) mBA + mCB = 0
c) mBA + mBC = 0
d) mAB + mBC = 0
View Answer
Explanation: By cutting a small part near joint B and conserving the moment, we get the condition mBA + mBC = 0, where the moment in the beam at joint B and the external moment in beam BC are related.
2. How many equations are generated in the system with fixed support at A, roller supports at B and C, a uniformly distributed load of 2 kN/m on AB (length AB = 24 m), a 12 kN load between B and C (length BC = 8 m), and a 24 kN load at the center of BC?
a) 1
b) 2
c) 3
d) 4
View Answer
Explanation: Beam AB generates two equations from the uniformly distributed load and the reaction forces, and beam BC generates one equation from the point loads at B and C.
3. What is the value of the rotation at point B after solving the equations for the system with the given loads and supports?
a) 317/EI
b) -117/EI
c) -144/EI
d) 344/EI
View Answer
Explanation: After solving the equations, the rotation at point B due to the given loads is found to be -144/EI.
4. What is the value of mAB after solving the equations for the system with fixed support at A and roller supports at B and C, subjected to a uniformly distributed load of 2 kN/m on span AB and other point loads?
a) 108
b) 72
c) -72
d) -108
View Answer
Explanation: Substituting the value of the rotation at point B into the first equation, mAB is calculated to be -108 kN·m.
5. What is the value of mBC after solving the equations for the system with fixed support at A and roller supports at B and C, subjected to a uniformly distributed load of 2 kN/m on span AB and additional point loads of 12 kN and 24 kN?
a) 108
b) 72
c) -72
d) -108
View Answer
Explanation: Substituting the value of the rotation at point B into the third equation gives mBC as -72 kN·m.
6. What will be the value of mCB after solving the equations for the system described below?
a) 3.09
b) 1.54
c) 12.86
d) 0
View Answer
Explanation: Since support C is assumed to be a pin, mCB is zero.
7. What is the value of mBA after solving the equations for the system with fixed support at A and roller supports at B and C, and the given loads on the beam?
a) 108
b) 72
c) -72
d) -108
View Answer
Explanation: mBA is found to be the inverse of mBC, giving a value of 72 kN·m.
8. What is the shear at point A in the system with a uniformly distributed load of 2 kN/m on AB and point loads between B and C?
a) 25.5
b) 22.5
c) 15
d) -3
View Answer
Explanation: The shear at point A is calculated by conserving moment in beam AB about point B, taking into account the distributed load on span AB and the reaction forces at the supports.
9. What is the shear at point C in the system with fixed support at A, roller supports at B and C, and the given point loads and distributed load?
a) 25.5
b) 22.5
c) 15
d) -3
View Answer
Explanation: The shear at point C is found by conserving moment in beam BC about point B, considering the point loads and the distributed load on the beam.
10. What will be the support reaction at point B in the system with the given loads and supports?
a) 25.5
b) 22.5
c) 15
d) 37.5
View Answer
Explanation: To find the support reaction at point B, the shear at point B is determined for both beam AB and beam BC, and vertical force equilibrium is applied to conserve the force at support B.
11. Is there a point of discontinuity in the shear diagram of the beam in the system described, with the loads and supports as stated?
a) true
b) false
View Answer
Explanation: The external loads (12 kN and 24 kN) applied in the middle of span BC create a point of discontinuity in the shear diagram between the supports.
12. Is there a point of discontinuity in the bending moment diagram of the beam in the given system with the specified loads and supports?
a) true
b) false
View Answer
Explanation: There is no discontinuity in the bending moment diagram as no external moments are applied between the supports.
13. What is the final moment at point C in the system with the given loads and supports?
a) -108
b) 54.6
c) 0
d) 108
View Answer
Explanation: Since point C is a free end, the final moment at point C is zero.
14. What is the final moment at point A in the system with fixed support at A, roller supports at B and C, and the given loads?
a) -108
b) 54.6
c) 0
d) 108
View Answer
Explanation: The final moment at point A is the same as mAB, which is -108 kN·m, as no external moment is applied elsewhere.
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