(a) A cantilever beam ABCD, as shown in the above figure, is carrying a uniformly distributed load of 10 kN/m between B & C and a clockwise moment of 50 kN-m at free end D. Draw the free body diagram for A, D and for the member BC only. (10 marks)

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Question

(a) A cantilever beam ABCD, as shown in the above figure, is carrying a uniformly distributed load of 10 kN/m between B & C and a clockwise moment of 50 kN-m at free end D. Draw the free body diagram for A, D and for the member BC only. (10 marks)

(b) Cross-section of an axially loaded compression member is shown in the above figure. This compression member was to be loaded at centre 'O' of the Section. Due to mistake this was loaded at point 'P' by a concentrated load of 500 kN. Find out the stresses at points A, B, C and D of the Section. (10 marks)

(c) A uniformly distributed load of 20 kN/m intensity and 6 m length moves over a simply supported girder of 30 m span. What will be the maximum bending moment at a section 6 m from the left support A ? (10 marks)

(d) Determine the maximum permissible load (P) on the bolt A. Assume the Bolt value as 45·3 kN. (10 marks)

(e) What are the functions of transverse reinforcement in a reinforced concrete column ? (10 marks)

UPSC Answer Check · Accepted Answer

Solve all five sub-parts systematically, allocating approximately 20% time to each part since marks are equally distributed. Begin with clear free body diagrams for part (a), then proceed through numerical calculations for parts (b), (c) and (d) showing all steps, and conclude with a structured explanation for part (e). Present solutions in sequence (a) through (e) with clear headings and proper units throughout.
- Part (a): Correct free body diagrams showing reactions at fixed end A, equilibrium at free end D with applied moment, and internal forces/shear-moment distribution for member BC under UDL
- Part (b): Calculation of direct compressive stress (P/A) and bending stresses (My/I) due to eccentricity at point P, superposition of stresses at corners A, B, C, D using appropriate section properties
- Part (c): Application of influence line concept or moving load analysis to determine maximum BM at 6m from left support, correct positioning of UDL for maximum effect using influence line ordinates
- Part (d): Analysis of bolt group eccentricity, calculation of direct shear and torsional shear, vectorial combination to find resultant force on critical bolt A, comparison with given bolt value
- Part (e): Functions of transverse reinforcement including confinement of core concrete, prevention of longitudinal bar buckling, shear resistance, and ductility enhancement as per IS 456 provisions

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates correct application of static equilibrium for (a), superposition theorem for combined stresses in (b), influence line theory for moving loads in (c), eccentric bolt group analysis in (d), and IS 456 codal provisions for column transverse reinforcement in (e)	Shows generally correct concepts with minor errors in one or two parts, such as incorrect stress sign convention in (b) or approximate influence line application in (c)	Fundamental conceptual errors like treating eccentricity effects incorrectly in (b) or (d), or confusing transverse reinforcement with longitudinal reinforcement functions in (e)
Numerical accuracy	20%	10	All calculations accurate to appropriate significant figures: correct reactions and internal forces in (a), precise stress values at all four corners in (b), exact maximum BM value in (c), correct resultant bolt force within 2% of bolt value in (d)	Generally correct calculations with arithmetic slips or unit conversion errors in one or two parts, final answers within 10% of correct values	Major calculation errors, incorrect section property usage, wrong load positioning for maximum effect, or answers orders of magnitude incorrect
Diagram quality	20%	10	Clear, labeled free body diagrams for (a) showing all forces and moments; neat cross-section sketch with dimensions and loading points for (b); properly drawn influence line diagram for (c); bolt group layout with force vectors for (d); illustrative sketch of column reinforcement for (e)	Diagrams present but with minor labeling omissions, missing dimensions, or unclear force directions; adequate for understanding but not examination-standard	Missing diagrams, unrecognizable sketches, or diagrams that contradict the written solution; failure to provide required FBDs in (a)
Step-by-step derivation	20%	10	Systematic presentation: equilibrium equations → section properties → load calculations → final results; explicit statement of formulas used (e.g., σ = P/A ± Mx/Ix·y ± My/Iy·x for (b)), clear substitution of values, and logical flow across all parts	Some steps implied or skipped, formulas stated without derivation, or occasional logical gaps that require examiner inference to follow	Disorganized working with no clear derivation sequence, missing intermediate steps, or jumping directly to answers without showing methodology
Practical interpretation	20%	10	Interprets results meaningfully: discusses implications of stress distribution in (b) for column design safety, comments on critical load position in (c) for bridge girder design, relates bolt value check in (d) to IS 800 connection design, and connects transverse reinforcement functions in (e) to seismic detailing and ductility requirements as per IS 13920	Brief contextual mention of practical relevance without elaboration, or generic statements about structural safety without specific code references	Purely mathematical treatment with no engineering interpretation, or irrelevant practical comments showing misunderstanding of application context

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