Q. For a cantilever beam with a uniformly distributed load, what is the formula for the maximum deflection at the free end?
A.
5wL^4/384EI
B.
wL^4/8EI
C.
wL^3/3EI
D.
wL^4/12EI
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Solution
The maximum deflection δ for a cantilever beam with a uniformly distributed load w is given by δ = 5wL^4/384EI.
Correct Answer:
A
— 5wL^4/384EI
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Q. For a fixed beam subjected to a point load at the center, what is the ratio of the maximum moment to that of a simply supported beam?
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Solution
The maximum moment in a fixed beam subjected to a point load at the center is twice that of a simply supported beam, hence the ratio is 2.
Correct Answer:
B
— 2
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Q. For a statically indeterminate beam, which method is typically used to analyze the structure?
A.
Superposition
B.
Method of Sections
C.
Compatibility Conditions
D.
Method of Joints
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Solution
For a statically indeterminate beam, the Compatibility Conditions method is typically used to analyze the structure.
Correct Answer:
C
— Compatibility Conditions
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Q. In a simply supported beam with a uniform load, where does the maximum shear force occur?
A.
At the supports
B.
At the midpoint
C.
At one-third the span
D.
At the free end
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Solution
In a simply supported beam with a uniform load, the maximum shear force occurs at the supports.
Correct Answer:
A
— At the supports
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Q. What is the effect of increasing the moment of inertia of a beam on its deflection?
A.
Increases deflection
B.
Decreases deflection
C.
No effect
D.
Increases shear force
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Solution
Increasing the moment of inertia I of a beam decreases its deflection, as deflection is inversely proportional to I.
Correct Answer:
B
— Decreases deflection
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Q. What is the primary assumption made in the Euler-Bernoulli beam theory?
A.
Plane sections remain plane
B.
Material is isotropic
C.
Beam is perfectly elastic
D.
All of the above
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Solution
The primary assumption made in the Euler-Bernoulli beam theory is that plane sections remain plane after deformation, along with the material being isotropic and elastic.
Correct Answer:
D
— All of the above
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Q. What is the primary purpose of using the stiffness method in structural analysis?
A.
To find reactions
B.
To determine deflections
C.
To analyze indeterminate structures
D.
To calculate internal forces
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Solution
The primary purpose of using the stiffness method in structural analysis is to analyze indeterminate structures by relating displacements to forces.
Correct Answer:
C
— To analyze indeterminate structures
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Q. What is the relationship between shear force and bending moment in a beam?
A.
V = dM/dx
B.
M = dV/dx
C.
V = M/x
D.
M = V/x
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Solution
The relationship between shear force V and bending moment M in a beam is given by V = dM/dx, where x is the distance along the beam.
Correct Answer:
A
— V = dM/dx
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