(a) Determine the forces in members AC, DE and GH of the truss loaded and supported as shown in the figure below : (10 marks)

(b) A prestressed concrete beam of section 160 mm wide by 400 mm deep is used over an effective span of 8 m to support a un

Question

(a) Determine the forces in members AC, DE and GH of the truss loaded and supported as shown in the figure below : (10 marks)

(b) A prestressed concrete beam of section 160 mm wide by 400 mm deep is used over an effective span of 8 m to support a uniformly distributed load of 5 kN/m which includes the self-weight of the beam. The beam is prestressed by a straight cable carrying a force of 200 kN and located at 100 mm above the bottom of the beam. Determine the resultant stresses at the centre of the span sections at top and bottom fibres of the beam. (10 marks)

(c) A bracket plate of thickness 12 mm is connected perpendicular to the flange of a column (ISMB 400). Design a connection for the bracket using the fillet weld to carry a vertical load of 200 kN acting at 250 mm from the face of the column. The grade of steel is E 250. Assume shop welding. Take ultimate stress of weld material, f_u = 410 MPa. (10 marks)

(d) A space 25 mm wide between two large plane surfaces is filled with glycerine. What force is required to drag a very thin plate 0·75 m² in area between the surfaces at a speed of 0·5 m/s : (i) if this plate remains equidistant from the two surfaces, (ii) if it is at a distance of 10 mm from one of the surfaces ? Take dynamic viscosity of glycerine μ = 0·785 N-s/m². (10 marks)

(e) A field density test of a soil was performed by digging a small hole in the soil, weighing the extracted soil and measuring the volume of the hole. The soil (moist) weighed 895 g, the volume of the hole was 426 cm³. After drying the sample weighed 779 g. From the dried soil, 400 g was poured into a vessel in a very loose state which occupied a volume of 276 cm³. The same 400 g was then vibrated and tamped to a volume of 212 cm³. Determine the relative density of the field soil. Given : Specific gravity of solids, G_S = 2·70 and unit weight of water, γ_w = 9·81 kN/m³. (10 marks)

UPSC Answer Check · Accepted Answer

This is a multi-part numerical problem requiring systematic solution of five independent engineering calculations. Allocate approximately 20% time to each sub-part (a-e) as marks are equal. Begin each part with clear identification of the governing principle, show all formulae with standard notations, substitute values with units, and present final answers with proper sign conventions and units. No introduction or conclusion is needed; use clear sectional headings for each part.
- Part (a): Correct application of method of joints or method of sections to determine forces in members AC, DE and GH; identification of zero-force members if applicable; proper sign convention for tension/compression
- Part (b): Calculation of prestressing force eccentricity; determination of moment due to external UDL; application of P/A ± Pe/Z ± M/Z formula; correct stress values at top and bottom fibres
- Part (c): Design of fillet weld connection considering direct shear and torsional shear; calculation of throat thickness; weld length determination; check against permissible stress as per IS 800
- Part (d): Application of Newton's law of viscosity for parallel plate flow; calculation of shear stress and force for symmetric and asymmetric plate positions; correct gap dimensions for each case
- Part (e): Determination of field density, moisture content, and dry density; calculation of minimum and maximum dry densities from loose and compacted states; application of relative density formula as per IS 2720

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies and applies: equilibrium equations for truss analysis (a), prestressing stress combination principles (b), eccentrically loaded weld design as per IS 800 (c), viscous flow between parallel plates (d), and relative density determination per IS 2720 (e); no conceptual errors in any part	Minor errors in one or two parts such as wrong sign convention in truss members, incorrect eccentricity calculation in prestressing, or confusion between minimum/maximum density in relative density formula	Fundamental conceptual errors like using wrong method for truss analysis, ignoring self-weight in prestressing, designing weld for direct load only ignoring moment, or incorrect viscosity law application
Numerical accuracy	20%	10	All calculations accurate to appropriate significant figures; correct unit conversions (mm to m, g/cm³ to kN/m³); final answers with proper units and sign conventions; no arithmetic errors	Minor arithmetic errors in one or two parts (e.g., calculation errors in moment of inertia, weld throat thickness, or density conversions) but method fundamentally sound	Major calculation errors, wrong order of magnitude, missing units, or consistent arithmetic mistakes affecting multiple parts; no verification of reasonableness of answers
Diagram quality	20%	10	Clear free-body diagrams for truss with reactions and member forces labeled (a); cross-section diagram showing prestressing cable position and stress distribution (b); weld connection detail with dimensions and force/moment arrows (c); schematic of plate-fluid system with velocity profile (d); phase diagram or test setup sketch for density determination (e)	Diagrams present but lacking clarity or missing key labels; rough sketches without proper proportions; or diagrams for only 3-4 parts with some parts having no visual aid	No diagrams or extremely poor quality sketches; missing critical diagrams for truss, prestressing section, or weld connection; diagrams that misrepresent the physical problem
Step-by-step derivation	20%	10	Each part shows complete logical progression: statement of principle → formula with standard symbols → substitution of values with units → intermediate calculations → final answer; clear sectional separation between parts; proper referencing of IS codes where applicable	Some steps skipped or combined without clarity; missing intermediate steps in complex calculations; inconsistent presentation across parts; some formulae stated without derivation or reference	Disorganized working with no clear step sequence; missing formulae; values substituted without explanation; no logical flow making verification impossible; illegible or cramped presentation
Practical interpretation	20%	10	Correct interpretation of sign conventions (tension positive/compression negative for truss; compression/tension for prestressing); physical reasonableness check of answers; brief comment on practical implications such as adequacy of weld design, suitability of prestressing level, or soil classification based on relative density	Correct sign conventions but no physical interpretation; or brief interpretation for only 2-3 parts; answers stated without context of practical engineering significance	Wrong interpretation of results (e.g., calling compression tension), no sign conventions, or answers that are physically impossible (negative areas, stresses exceeding material strength) without comment; no engineering judgment demonstrated

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