This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of Externally Redundant Trusses”.

1. Externally redundant truss can be solved by three equilibrium equations.

a) True

b) False

View Answer

Explanation: Redundant truss is solved by using equilibrium equations along with the displacement equilibrium.

2. Calculate the P value of the member AC for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 1kN

b) 3kN

c) 5.77kN

d) 2.89kN

View Answer

Explanation:

Va=Vb (Due to symmetry)

Va=Vb=5kN

At joint A,

∑V=Fac sin θ=5kN

Fac=\(\frac{5}{sin60}\)=5.77kN.

3. Calculate the P value of the member AC for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 1kN

b) 3kN

c) 5.77kN

d) 2.89kN

View Answer

Explanation:

Va=Vb (Due to symmetry)

Va=Vb=5kN

At joint A,

∑V=Fac sinθ=5kN

Fac=\(\frac{5}{sin60}\)=5.77kN

Fac cosθ=Fab=5.77*cos60=2.89kN.

4. Calculate the P value of the member BC for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 1kN

b) 3kN

c) 5.77kN

d) 2.89kN

View Answer

Explanation:

Va=Vb (Due to symmetry)

Va=Vb=5kN

At joint B,

∑V=Fbc sinθ=5kN

Fbc=\(\frac{5}{sin60}\)=5.77kN.

5. Calculate the k value of the member BC for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 0kN

b) 1kN

c) 2.89kN

d) 3kN

View Answer

Explanation: If the support reaction at support is considered 1kN rightward, the horizontal force at the joint will be balanced by horizontal force in member AB. Thus, member BC becomes a zero-force member.

6. Calculate the k value of the member AC for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 0kN

b) 1kN

c) 2.89kN

d) 3kN

View Answer

Explanation: If the support reaction at support A is considered 1kN leftward, the horizontal force at the joint will be balanced by horizontal force in member AB. Thus, member AC becomes a zero-force member.

7. Calculate the k value of the member AB for the given external redundant truss, considering the horizontal reaction of support B as a redundant force.

a) 0kN

b) 1kN

c) 2.89kN

d) 3kN

View Answer

Explanation: If the support reaction at support is considered 1kN leftward, the horizontal force at the joint will be balanced by horizontal force in member AB. Thus, member AC becomes a zero-force member.

8. Calculate the redundant horizontal forces at support B, for the given truss considering the horizontal reaction of support B as a redundant force.

a) 1kN

b) 5kN

c) 3kN

d) 2.89kN

View Answer

Explanation:

Member | P values | k values | Length of Member | \(\frac{P k L}{AE}\) | \(\frac{∑k^2 L}{AE}\) |
---|---|---|---|---|---|

AB | 2.89 | 1 | 3 | 8.67 | 3 |

BC | -5.77 | 0 | 3 | 0 | 0 |

AC | -5.77 | 0 | 3 | 0 | 0 |

Redundant horizontal force at support B=\(\frac{- ∑\frac{P k L}{AE}}{\frac{∑k^2 L}{AE}}\) = -2.89kN

9. Calculate the force in the member AB for the given truss.

a) 0kN

b) 2.89kN

c) 5.78kN

d) 10kN

View Answer

Explanation:

Member | P values | k values | Length of Member | \(\frac{P k L}{AE}\) | \(\frac{∑k^2 L}{AE}\) |
---|---|---|---|---|---|

AB | 2.89 | 1 | 3 | 8.67 | 3 |

BC | -5.77 | 0 | 3 | 0 | 0 |

AC | -5.77 | 0 | 3 | 0 | 0 |

Redundant horizontal force at support B=\(\frac{- ∑\frac{P k L}{AE}}{\frac{∑k^2 L}{AE}}\) = 2.89kN(leftward)

Considering, joint B

∑H=0

2.89-2.89+Fab=0

Fab=0 kN.

10. Externally redundant trusses are always internally determinate.

a) True

b) False

View Answer

Explanation: There is no dependency among the external and internal indeterminacy of a truss. If a truss is externally indeterminate, it can be either internally determinate or indeterminate.

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