Structural Analysis — Part 1 MCQs with Explanations

To determine the degree of static indeterminacy (Ds) for a rigid-jointed plane frame, use the formula: Ds = (3m + R) - (3j + A) where: m = number of members, R = number of reaction components, j = number of joints, A = number of internal hinges (A = 0 in this case). Given: m = 15 (members), R = 3 (reaction components), j = 14 (joints), A = 0 (no internal hinges). Substitute these values into the formula: Ds = (3 * 15 + 3) - (3 * 14 + 0) Ds = (45 + 3) - (42) Ds = 48 - 42 = 6 Thus, the degree of static indeterminacy is 6.

The nominal maximum size of the aggregates in heavily reinforced concrete members is determined to ensure proper compaction and minimal voids in the structure. 1. To avoid interference with the reinforcement, the size of the aggregate should be restricted to 5 mm less than the minimum clear distance between the main bars. 2. Similarly, to maintain adequate cover, the size of the aggregate should also be restricted to 5 mm less than the minimum cover to the reinforcement. 3. Therefore, the nominal maximum size of the aggregates should be the smaller of these two criteria to satisfy both conditions. This ensures proper placement and compaction of the concrete mix around the reinforcement.

1. Wheel Load: When a train of wheel loads moves over a simply supported girder, the bending moment changes depending on the position of the wheel loads. 2. Influence Line: The influence line for bending moment indicates that the maximum bending moment occurs when the wheel load is at a specific point on the span. 3. Critical Position: For the maximum bending moment to occur, the critical position of the wheel load is generally at a distance from the support, calculated based on the span and the load distribution. 4. Conclusion: Hence, the maximum bending moment due to a train of wheel loads on a simply supported girder always occurs under a wheel load. Therefore, the correct answer is Option B: Always occurs under a wheel load.

The three-moment equation is used for the analysis of continuous beams. When one end of a continuous beam is fixed , an imaginary or fictitious span is introduced beyond the fixed end so that the three-moment equation can be applied. For a fixed end , this additional imaginary span is assumed to have zero length . This allows the fixed-end condition of zero rotation (zero slope) to be incorporated into the three-moment equation. Option A: Zero length Correct. A fixed end is represented by an imaginary span of zero length when applying the three-moment equation. Option B: Infinite length Incorrect. An infinite-length span is not used to represent a fixed end in the three-moment equation. Option C: Zero moment of inertia Incorrect. Zero moment of inertia would imply zero flexural stiffness and does not represent a fixed-end condition. Option D: None of the above Incorrect because Option A correctly represents the fixed end. Hence, Option A — Zero length is the correct answer.

Plastic Moment Capacity: This is the maximum bending moment a structural section can withstand before it starts to deform permanently. Shear Force: Shear force acts parallel to the cross-section of a structural member. Effect of Shear Force: When shear force is present, it reduces the area available to resist bending. Think of it like some part of the section is already 'busy' resisting shear, so it can't contribute as much to resisting bending. Therefore, the plastic moment capacity decreases . Axial Force: Axial force acts along the longitudinal axis of a structural member (either tension or compression). Effect of Axial Force: Axial force also reduces the area available to resist bending. If there's compressive axial force, some of the material is already stressed in compression, leaving less capacity for resisting compressive stresses from bending. If there's tensile axial force, it can similarly reduce the effective area for resisting bending. Therefore, the plastic moment capacity decreases . In summary, both shear force and axial force reduce the plastic moment capacity of a structure.

The correct answer is Option C: 3 . Here's why: In a rigid jointed plane frame, each member is subjected to three internal forces: * Axial Force: The force acting along the longitudinal axis of the member (tension or compression). * Shear Force: The force acting perpendicular to the longitudinal axis of the member. * Bending Moment: The internal moment that causes bending in the member. Therefore, there are three unknown internal forces in each member of a rigid jointed plane frame.

All the given statements are correct definitions related to the gross sectional area of webs in different structural members . Option A: The gross section of the web of rolled I-beams is accurately calculated as the depth of the beam multiplied by the web thickness. Option B: For channel sections, the gross area of the web is indeed obtained by multiplying the depth of the web by its thickness. Option C: In the case of plate girders, the gross section of the web is correctly given by the product of the web plate depth and its thickness. Since none of the given statements are incorrect, the correct answer is Option D: None of these .

The principle of superposition is applicable when the deflections in a structure are linear functions of the applied forces. This principle holds when the relationship between force and displacement is directly proportional, meaning that the total displacement caused by multiple forces is the sum of the displacements due to each force acting individually. For this to be valid, the material must behave elastically and within its linear range, which is often governed by Hooke's law.

In the moment distribution method, the sum of distribution factors of all the members meeting at any joint is always 1 . Distribution factors are calculated for each member connected to a joint, based on their stiffness relative to the stiffness of all other members connected to the same joint. The distribution factors determine how the unbalanced moments at the joint will be distributed among the connected members. Since the total moment at the joint is distributed among the connected members, the sum of all distribution factors must equal 1, ensuring that the entire moment is accounted for.

Free end is the correct answer to “The fixed support in a real beam becomes in the conjugate beam a”. This question is standard in competitive examination syllabi for Structural Analysis.

The centre of span is midway between the centre of gravity of the load system and the wheel load under consideration is the correct answer to “When a series of wheel loads crosses a simply supported girder, the maximum bending moment under any given wheel load occurs when”. This question is standard in competitive examination syllabi for Structural Analysis.

The load position should be such that the section divides the load in the same ratio as it divides the span is the correct answer to “When a uniformly distributed load, shorter than the span of the girder, moves from left to right, then the conditions for maximum bending moment at a section is that”. This question is standard in competitive examination syllabi for Structural Analysis.

Displacements is the correct answer to “In the displacement method of structural analysis, the basic unknowns are”. This question is standard in competitive examination syllabi for Structural Analysis.

-5 mm to +5 mm is the correct answer to “If the specified thickness of a footing is 100 cm, the depth of the form work may be tolerated from”. This question is standard in competitive examination syllabi for Structural Analysis.

Sum of (A) and (B) is the correct answer to “For the stability of a structural part, the weight or anchorage should be”. This question is standard in competitive examination syllabi for Structural Analysis.

$$\frac{1}{{{\text{E}}I}}$$ is the correct answer to “The width of the analogous column in the method of column analogy is”. This question is standard in competitive examination syllabi for Structural Analysis.

(i) and (iii) is the correct answer to “For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal (i) Of a stiffness matrix must be positive (ii) Of a stiffness matrix must be negative (iii) Of a flexibility matrix must be positive (iv) Of a flexibility matrix must be negative The correct answer is”. This question is standard in competitive examination syllabi for Structural Analysis.

(ii) and (iv) is the correct answer to “Study the following statements. i) The displacement method is more useful when degree of kinematic indeterminacy is greater than the degree of static indeterminacy. ii) The displacement method is more useful when degree of kinematic indeterminacy is less than the degree of static indeterminacy. iii) The force method is more useful when degree of static indeterminacy is greater than the degree of kinematic indeterminacy. iv) The force method is more useful when degree of static indeterminacy is less than the degree of kinematic indeterminacy. The correct answer is”. This question is standard in competitive examination syllabi for Structural Analysis.

(i), (ii) and (iii) is the correct answer to “Muller Breslau’s principle for obtaining influence lines is applicable to i) trusses ii) statically determinate beams and frames iii) statically indeterminate structures, the material of which is elastic and follows Hooke’s law iv) any statically indeterminate structure The correct answer is”. This question is standard in competitive examination syllabi for Structural Analysis.

Only (i) is the correct answer to “In the slope deflection equations, the deformations are considered to be caused by i) bending moment ii) shear force iii) axial force The correct answer is”. This question is standard in competitive examination syllabi for Structural Analysis.

5 mm is the correct answer to “A simply supported beam deflects by 5 mm when it is subjected to a concentrated load of 10 kN at its centre. What will be deflection in a 1/10 model of the beam if the model is subjected to a 1 kN load at its centre”. This question is standard in competitive examination syllabi for Structural Analysis.

The direction in which the deflection is required is the correct answer to “The deflection at any point of a perfect frame can be obtained by applying a unit load at the joint in”. This question is standard in competitive examination syllabi for Structural Analysis.

Two linear movements and one rotation is the correct answer to “Independent displacement components at each joint of a rigid-jointed plane frame are”. This question is standard in competitive examination syllabi for Structural Analysis.

The reduced diameter of the column is the correct answer to “The thickness of the rectangular plate for the cap or base of a solid round steel columns, is calculated from the formula $${\text{t}} = \sqrt {\frac{{9{\text{W}}}}{{16{{\text{f}}_{{\text{bct}}}}}} \times \frac{{\text{D}}}{{{\text{D}} - {\text{d}}}}} $$ where 'd' is”. This question is standard in competitive examination syllabi for Structural Analysis.

0.24 Wl is the correct answer to “A load W is moving from left to right support on a simply supported beam of span T. The maximum bending moment at 0.4 1 from the left support is”. This question is standard in competitive examination syllabi for Structural Analysis.

Internal as well as external forces is the correct answer to “The principle of virtual work can be applied to elastic system by considering the virtual work of”. This question is standard in competitive examination syllabi for Structural Analysis.

All the above is the correct answer to “Pick up the correct statement for the web stiffeners.”. This question is standard in competitive examination syllabi for Structural Analysis.

6 is the correct answer to “The number of independent displacement components at each joint of a rigid-jointed space frame is”. This question is standard in competitive examination syllabi for Structural Analysis.

12 times is the correct answer to “The slenderness effect of a wall is considered if the effective height of the wall exceeds the thickness”. This question is standard in competitive examination syllabi for Structural Analysis.

3 specimens is the correct answer to “The test strength of the sample is taken as the average of the strength of”. This question is standard in competitive examination syllabi for Structural Analysis.

2j - r is the correct answer to “Degree of kinematic indeterminacy of a pin-jointed plane frame is given by”. This question is standard in competitive examination syllabi for Structural Analysis.

m + r - 2j is the correct answer to “If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin-jointed plane frame is given by”. This question is standard in competitive examination syllabi for Structural Analysis.

All the above is the correct answer to “The effective length of lacing is the distance”. This question is standard in competitive examination syllabi for Structural Analysis.

Remains unchanged is the correct answer to “For a two-hinged arch, if one of the supports settles down vertically, then the horizontal thrust”. This question is standard in competitive examination syllabi for Structural Analysis.

Is decreased is the correct answer to “For a symmetrical two hinged parabolic arch, if one of the supports settles horizontally, then the horizontal thrust”. This question is standard in competitive examination syllabi for Structural Analysis.

60% is the correct answer to “If the main reinforcement of the slab is parallel to a T-beam, the transverse reinforcement at mid span of the slab is provided at least __________ of main reinforcement.”. This question is standard in competitive examination syllabi for Structural Analysis.

Flexibility is the correct answer to “The deformation of a spring produced by a unit load is called”. This question is standard in competitive examination syllabi for Structural Analysis.

3 is the correct answer to “The number of independent equations to be satisfied for static equilibrium of a plane structure is”. This question is standard in competitive examination syllabi for Structural Analysis.

A unit force is applied at coordinate j and the displacements are calculated at all co-ordinates is the correct answer to “To generate the j th column of the flexibility matrix”. This question is standard in competitive examination syllabi for Structural Analysis.

There is no discontinuity such as hinges within the span is the correct answer to “The three moments equation is applicable only when”. This question is standard in competitive examination syllabi for Structural Analysis.