Structural Analysis

Step 1: Recall the definition of flexibility coefficients.
Flexibility coefficients represent the displacement at one coordinate due to a unit force applied at another coordinate.
Step 2: Meaning of the column.
The column of the flexibility matrix consists of displacements at all coordinates caused by a unit force applied at coordinate .
Step 3: Analyze the options.
(A) Correct, this exactly matches the definition of flexibility coefficients.
(B) Incorrect, this describes stiffness matrix generation.
(C) Incorrect, flexibility matrix relates forces to displacements, not forces to forces.
(D) Incorrect, again related to stiffness, not flexibility.
Step 4: Conclusion.
Hence, option (A) is correct.

Step 1: Formula for modular ratio.
In working stress method, the modular ratio is given by:

Step 2: Permissible stress for M20 concrete.
For M20 concrete, permissible compressive stress in bending is:

Step 3: Substitute the value.

Step 4: Conclusion.
Thus, the modular ratio to be used is approximately 13.3.

Step 1: Understand what “limit state of strength” means.
Limit state of strength refers to a condition related to collapse or failure of the structure, where the structure becomes unsafe.
It includes failures such as yielding, buckling, fracture, instability, or deformation leading to loss of load carrying capacity.
Step 2: Check each option with respect to strength (collapse) criteria.
(A) Fire: Fire is generally treated as an accidental/exceptional loading condition, not a normal strength limit state factor.
(B) Failure by excessive deformation: If deformation becomes excessive such that the member loses stability or load capacity, it is treated under strength/collapse considerations. Hence, this is the best match.
(C) Corrosion: Corrosion is mainly a durability issue and affects long-term performance, not directly a strength limit state factor in standard MCQ classification.
(D) Repairable damage or crack due to fatigue: Fatigue cracking is usually treated under fatigue/durability or service life criteria and is not taken as the primary “strength limit state” factor in such MCQs.
Step 3: Conclusion.
Therefore, the factor included in the limit state of strength (collapse-type consideration) is (B) Failure by excessive deformation.

Step 1: Recall working stress method provisions.
In the working stress method, permissible stresses are allowed to be increased when wind or earthquake loads are considered along with dead and live loads.
Step 2: Standard increase allowed.
As per IS codes, when dead load, live load, and wind load act together, the permissible stress can be increased by 40%.
Step 3: Convert percentage to decimal form.

Step 4: Conclusion.
Hence, the correct answer is (C) 0.4.

Step 1: Recall equilibrium equations for a plane pin-jointed frame.
Each joint in a plane truss provides two independent equilibrium equations:

Step 2: Total available equations.
For joints, total equilibrium equations available are:

Step 3: Count total unknowns.
Total unknowns in the structure are:

Step 4: Degree of static indeterminacy.
Degree of static indeterminacy is defined as:

Step 5: Conclusion.
Hence, the correct expression is .

Step 1: Understanding flexibility coefficients.
Flexibility coefficients represent the displacement produced at a point due to a unit force applied at another point.
Step 2: Relation with structural analysis methods.
In the force method (also known as the flexibility method), unknown forces are taken as redundants and compatibility conditions are written using flexibility coefficients.
Step 3: Analysis of options.
(A) Force method: Correct, flexibility coefficients are fundamental to this method.
(B) Displacement method: Incorrect, this method primarily uses stiffness coefficients.
(C) Both force and displacement method: Incorrect, as each method uses different coefficients.
(D) Virtual force method: Incorrect, this method is mainly used for deflection calculations.
Step 4: Conclusion.
Hence, flexibility coefficients are used in the force method.

Step 1: Understanding influence line diagrams.
An influence line diagram represents how a response function (reaction, shear force, bending moment, etc.) at a fixed point of a structure varies as a unit load moves across the structure.
Step 2: Key characteristic of ILD.
In ILD analysis:
- The structure and the point of interest remain fixed.
- Only the position of the load changes along the span.
Step 3: Analysis of options.
(A) Correct, because the load moves while the point remains fixed.
(B) Incorrect, points do not change in ILD.
(C) Incorrect, both do not change simultaneously.
(D) Incorrect, load position does change.
Step 4: Conclusion.
Hence, the correct answer is (A).

Step 1: Understanding the concept of a beam.
A beam is a structural member designed primarily to resist loads that act perpendicular to its longitudinal axis. These loads cause bending and shear stresses within the beam. Beams are commonly used in structures such as bridges, buildings, and frames.
Step 2: Analysis of the given options.
(A) Axial tension or compression: This type of loading is mainly associated with columns or tie members, not beams. Hence, this option is incorrect.
(B) Transverse loads and couples: Correct — Beams are subjected to transverse loads (loads acting perpendicular to the axis) and bending moments or couples, which cause bending of the beam.
(C) Twisting moment: Twisting moments primarily act on shafts, not beams, so this option is incorrect.
(D) No load, but its axis should be horizontal and x-section rectangular or circular: This statement does not define the loading condition of a beam and is therefore incorrect.
Step 3: Conclusion.
A beam is mainly subjected to transverse loads and bending moments (couples). Therefore, the correct answer is (B) Transverse loads and couples.