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Structural Analysis [ Question No: 1 To 7 ] :
In the plastic analysis of beams, which of the following statements regarding the shape factor (also known as the shape factor for bending) is accurate?
A fixed beam AB of span 4 m is carrying a point load of 100 N at the centre. What is the fixed end moment at support A and B?
The distribution factor for the portion BC from the given beam is:
Which of the following statements is FALSE about the moment distribution method?
Which of the following statements is/are correct about the analysis of three-hinged arches?
A. Horizontal thrust may be found by using Castigliano's first theorem.
B. A three-hinged arch may have circular or parabolic shape.
Identify the INCORRECT statement about the conjugate beam theorem from the following.
Which of the following equations matches with the below-mentioned condition of truss?
Condition: The truss is internally stable and statically determinate space truss.
Total number of questions : 7
Number of answered questions : 0
Number of unanswered questions : 7
Structural Analysis [ Question No: 1 To 7 ] :
In the plastic analysis of beams, which of the following statements regarding the shape factor (also known as the shape factor for bending) is accurate?
Your Answer : (Not Answered)
Correct Answer : B
The shape factor is the ratio of the plastic moment capacity to the elastic moment capacity of the section, \(\frac{M_p}{M_y}\). It is always at least 1 (for a rectangle it is 1.5), so the statement that it is less than 1 is wrong. It is not the ratio of the maximum elastic bending stress to the yield stress, and it does not measure ductility, so the second option is the right one.
The shape factor is 1.5 for a rectangular section, about 1.7 for a solid circle and about 1.1 to 1.2 for rolled I-sections, always above 1.
A fixed beam AB of span 4 m is carrying a point load of 100 N at the centre. What is the fixed end moment at support A and B?
Your Answer : (Not Answered)
Correct Answer : C
For a fixed beam with a central point load W over a span L, the fixed-end moments are equal at both supports and equal to \(WL/8\), with a negative (hogging) sign:
\[ \begin{aligned} M_A = M_B = -\frac{WL}{8} \\ &= -\frac{100 \times 4}{8} = -50\ \text{N-m} \end{aligned} \]The values of 3, 12 and 6 N-m are not given by this formula. The formula \(WL/4 = 100\) N-m is the central bending moment of a simply supported beam, and the sagging moment at the centre of the fixed beam is also 50 N-m.
The distribution factor for the portion BC from the given beam is:
Your Answer : (Not Answered)
Correct Answer : A
Both far ends A and C are fixed, so the stiffness of each member at joint B is \(4EI/L\). For BA it is \(4E(3I)/L = 12EI/L\), and for BC it is \(4EI/L\). The distribution factor for BC is its stiffness divided by the total at joint B:
\[ \begin{aligned} DF_{BC} = \frac{4EI/L}{12EI/L + 4EI/L} \\ &= \frac{4}{16} = 0.25 \end{aligned} \]The factor for BA is 0.75, which is the third option, and the two factors add to 1. The value 0.5 would apply to equal stiffnesses, and 1.0 to a joint with a single member.
Which of the following statements is FALSE about the moment distribution method?
Your Answer : (Not Answered)
Correct Answer : D
It is false that the moment distribution method is not suited for plane rigid frames. The method is applicable to continuous beams and to plane frames, including rigid-jointed ones, which is what Hardy Cross devised it for. It is an approximate (iterative) method, since the fixed-end moments are distributed and carried over repeatedly, and the accuracy depends on how many successive cycles are carried out. The first three statements are therefore true.
Which of the following statements is/are correct about the analysis of three-hinged arches?
A. Horizontal thrust may be found by using Castigliano's first theorem.
B. A three-hinged arch may have circular or parabolic shape.
Your Answer : (Not Answered)
Correct Answer : C
Both statements are correct, as the key shows. The horizontal thrust of a three-hinged arch is found from the extra condition that the moment at the crown hinge is zero, and in principle an energy method such as Castigliano's theorem can also be used to find the unknown thrust. Both circular and parabolic arches are used, the parabolic one being the funicular shape for a uniformly distributed load. I follow the official key; the first statement is the one a reader may want to check.
Identify the INCORRECT statement about the conjugate beam theorem from the following.
Your Answer : (Not Answered)
Correct Answer : D
The statement that the conjugate beam theorem is derived from the unit load method is incorrect. The conjugate beam method comes from the moment-area theorems (the analogy between the load, shear and moment relations and the curvature, slope and deflection relations), so the first statement is true. It is used for finding slope and deflection and is applicable even where the beam has no point of zero slope, which is why it is more general than the moment-area method.
Which of the following equations matches with the below-mentioned condition of truss?
Condition: The truss is internally stable and statically determinate space truss.
Your Answer : (Not Answered)
Correct Answer : B
For a space truss, which is stable and statically determinate internally, the number of members m and the number of joints j satisfy \(m = 3j - 6\). Each joint in space has three equations of equilibrium, which give 3j equations, and six of them are used by the overall rigid-body motion in space (3 translations and 3 rotations). For a plane truss the matching condition is \(m = 2j - 3\). The options with an inequality (j < 2m - 3 and m > 2j - 3) describe unstable or indeterminate plane trusses, and m = 2j - 1 is not a standard condition.
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Total number of questions : 7
Number of answered questions : 0
Number of unanswered questions : 7