Chat with us
Civil Engineering 2021 Paper I 50 marks Compulsory Solve

Paper I — Q1

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

(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

हिंदी में प्रश्न पढ़ें
(a)

नीचे चित्र में दर्शाए अनुसार भारित एवं आलंबित कैंची के AC, DE और GH अवयवों में बलों को निर्धारित कीजिए : (10 अंक)

(b)

160 mm चौड़े और 400 mm गहरे परिछेद की एक पूर्व-प्रतिबलित कंक्रीट धरन का उपयोग एक 8 m की प्रभावी विस्तृति पर एक 5 kN/m के एकसमान वितरित भार, जिसमें धरन का अपना भार शामिल है, को आलंब प्रदान करने के लिए किया गया है । धरन को, 200 kN के बल को वहन करने वाले और धरन के तल से 100 mm ऊपर स्थित सीधी केबल द्वारा पूर्व-प्रतिबलित किया गया है । धरन की विस्तृति के मध्य में परिछेद पर शीर्ष एवं तल के तंतुओं पर परिणामी प्रतिबलों को निर्धारित कीजिए । (10 अंक)

(c)

एक 12 mm मोटी ब्रैकेट प्लेट को एक स्तम्भ (आई.एस.एम.बी. 400) की फ्लैंज से लम्बवत् जोड़ा गया है । स्तम्भ के फलक से 250 mm पर लगने वाले 200 kN के उद्वधर भार को वहन करने के लिए, फिलेट वेल्ड का उपयोग करके, ब्रैकेट के लिए जोड़ की अभिकल्पना कीजिए । इसपात का ग्रेड E 250 है । कार्यशाला वेल्डिंग मान लीजिए । वेल्ड पदार्थ का चरम प्रतिबल, f_u = 410 MPa लीजिए । (10 अंक)

(d)

दो बड़े समतल पृष्ठों के बीच के 25 mm चौड़े स्थान को ग्लिसरिन द्वारा भरा गया है । पृष्ठों के बीच में 0·5 m/s की चाल पर 0·75 m² क्षेत्रफल वाली एक बहुत पतली प्लेट को विचलित करने के लिए कितने बल की आवश्यकता होगी : (i) यदि यह प्लेट दोनों पृष्ठों से समान दूरी पर रहती है, (ii) यदि यह एक पृष्ठ से 10 mm की दूरी पर है ? ग्लिसरिन की गतिक श्यानता μ = 0·785 N-s/m² लीजिए । (10 अंक)

(e)

एक मृदा का क्षेत्र घनत्व परीक्षण, मृदा में एक लघु छिद्र खोदकर, निकाली गई मृदा को तौलकर और छिद्र के आयतन को मापकर, किया गया । मृदा (नम) का भार 895 g, छिद्र का आयतन 426 cm³ था । सूखने के बाद प्रतिदर्श का भार 779 g था । शुष्क मृदा में से 400 g एक भांड़ में अति असंत अवस्था में डाली गई जिसमें 276 cm³ आयतन घेरा । इसी 400 g को 212 cm³ के आयतन तक के लिए कंपित किया एवं कुटा गया । क्षेत्र मृदा का आपेक्षिक घनत्व निर्धारित कीजिए । प्रदत : ठोसों का विशिष्ट घनत्व, G_s = 2·70 और जल का एकक भार, γ_w = 9·81 kN/m³. (10 अंक)

Q1 of the 2021 UPSC Mains Civil Engineering Paper I, as printed
The question as printed in the 2021 Civil Engineering paper
Evaluate your answer to this question → See all 2021 Civil Engineering questions

The figure this question refers to, in words

The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.

(a) A planar truss structure with top chord nodes A, C, D, G, H and bottom chord nodes B, E, F. The horizontal distance between adjacent top nodes (A-C, C-D, D-G, G-H) is 2 m each. The vertical distance between the top chord and bottom chord is 2 m. The bottom chord consists of members BE and EF, each 2 m long. Diagonal members connect A to B, C to B, C to E, E to G, and F to H. Vertical members connect C to B, D to E, and G to F. The truss is supported by a pin support at node A and a roller support at node H. Downward vertical point loads are applied at the top nodes: 5 kN at A, 10 kN at C, 10 kN at D, 10 kN at G, and 5 kN at H.

(b) A cross-sectional view of a T-beam. The top flange has a width of 1000 mm and a thickness of 100 mm. The vertical web has a width of 300 mm and a depth of 400 mm. The total depth of the beam is 500 mm. At the bottom of the web, there are 4 reinforcing bars, each with a diameter of 25 mm (labeled '25 phi ki 4 chode' in Hindi and '4 nos 25 phi bar' in English). The center of these bars is located 50 mm from the bottom edge of the beam. The text below the figure specifies: 'M 20 grade of concrete and Fe 415 HYSD bars'.

(c) A horizontal bar ABCD is fixed at both ends A and D. The bar consists of three segments: AB, BC, and CD. Segment AB has a length of 300 mm. Segment BC has a length of 500 mm. Segment CD has a length of 300 mm. An axial load P_B is applied at point B, directed to the right. An axial load P_C is applied at point C, directed to the left. The labels A, B, C, and D mark the joints and supports along the bar.

A cross-sectional view of a gravity retaining wall. The wall is a trapezoidal concrete structure with a vertical back face and a sloping front face. The total height of the wall is 6 m. The top width of the wall is 1 m. The bottom width of the wall is 3 m. The unit weight of the concrete is given as gamma_c = 24 kN/m^3. The wall retains a deposit of granular backfill soil on its vertical back face. The soil surface is level with the top of the wall. The soil properties are: unit weight gamma = 17.5 kN/m^3, angle of internal friction phi = 35 degrees, and cohesion C = 0. The base of the wall rests on a foundation soil.

Model answer

Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.

(a) Forces in AC, DE and GH (10 marks)

Total load = 5 + 10 + 10 + 10 + 5 = 40 kN. The truss and loading are symmetric, so R_A = R_H = 20 kN and the horizontal reaction at A is zero.

Joint A: net upward force = 20 − 5 = 15 kN. Member AB is at 45° (2 m by 2 m). ΣF_y gives F_AB/√2 = 15, so F_AB = 21.2 kN (tension). ΣF_x gives F_AC + 15 = 0, so F_AC = 15 kN compression.

Joint H: by symmetry F_HF = 21.2 kN (tension) and F_GH = 15 kN compression.

Joint D: the only non-horizontal member is DE, and the load is 10 kN downward. ΣF_y gives F_DE = −10 kN, so DE carries 10 kN compression.

AC = 15 kN (C), DE = 10 kN (C), GH = 15 kN (C).

(b) Stresses at mid-span (10 marks)

Take a simply supported beam with no losses and linear elastic behaviour.

A = 160 × 400 = 64,000 mm². Z = bD²/6 = 160 × 400²/6 = 4.267 × 10⁶ mm³. The cable is 100 mm below the centroid, so e = 100 mm.

Prestress alone: P/A = 200,000/64,000 = 3.125 N/mm². Pe/Z = 200,000 × 100/(4.267 × 10⁶) = 4.6875 N/mm². The eccentric force gives compression at the bottom and relief at the top.

Load moment: M = wL²/8 = 5 × 8²/8 = 40 kN·m, so M/Z = 4 × 10⁷/(4.267 × 10⁶) = 9.375 N/mm² (compression at top, tension at bottom).

Top = 3.125 − 4.6875 + 9.375 = 7.81 MPa compression. Bottom = 3.125 + 4.6875 − 9.375 = 1.56 MPa tension.

(c) Fillet-weld design for the bracket (10 marks)

The figure gives no weld layout, so assume a 400 mm deep plate with fillet welds on both faces along the full depth, i.e. two vertical welds each 400 mm long, shop welded (γ_mw = 1.25).

M = 200 × 250 = 50 kN·m. The welds lie in the plane of the column flange, so the vertical load gives shear along the welds and the moment gives a force normal to the flange; these are perpendicular components.

Design stress f_wd = f_u/(√3 γ_mw) = 410/(1.732 × 1.25) = 189.4 N/mm².

Shear per mm of weld: q_v = 200,000/(2 × 400) = 250 N/mm. Weld-group modulus: Z_w = 2 × 400²/6 = 53,333 mm². Bending force per mm: q_b = 5 × 10⁷/53,333 = 937.5 N/mm. Resultant: q = √(250² + 937.5²) = 970 N/mm.

Throat required = 970/189.4 = 5.12 mm, so size s = 5.12/0.7 = 7.3 mm. Provide 8 mm fillet welds (throat 5.6 mm, capacity 1,061 N/mm > 970 N/mm). The size is above the 5 mm minimum and below the 12 mm plate thickness.

Diagram: Bracket plate welded to column flange: weld layout

(d) Force to drag the plate in glycerine (10 marks)

Newton's law gives τ = μV/h on each face. The plate is thin, so the force is F = μAV(1/h₁ + 1/h₂).

(i) Each gap = 12.5 mm = 0.0125 m. τ = 0.785 × 0.5/0.0125 = 31.4 N/m² on each face. F = 2 × 31.4 × 0.75 = 47.1 N.

(ii) The gaps are 10 mm and 15 mm. τ₁ = 0.785 × 0.5/0.010 = 39.25 N/m² and τ₂ = 0.785 × 0.5/0.015 = 26.17 N/m². F = (39.25 + 26.17) × 0.75 = 49.06 N.

(e) Relative density of the field soil (10 marks)

Only dry densities are needed.

Field: γ_d = 779/426 × 9.81 = 17.94 kN/m³, so e = G_sγ_w/γ_d − 1 = 26.49/17.94 − 1 = 0.477. Loosest state: 400/276 × 9.81 = 14.22 kN/m³, so e_max = 26.49/14.22 − 1 = 0.863. Densest state: 400/212 × 9.81 = 18.51 kN/m³, so e_min = 26.49/18.51 − 1 = 0.431.

D_r = (e_max − e)/(e_max − e_min) = (0.863 − 0.477)/(0.863 − 0.431) = 0.894, i.e. about 89.5%, a very dense soil.

How this answer will be evaluated

What earns full marks: Complete working with correct values, units, and clear presentation for all parts.

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Forces in members AC, DE, and GH of the truss. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Calculate support reactions at A and H
    • Apply method of sections or joints
    • State magnitude and nature (T/C) for AC, DE, GH
    • Carry units (kN) through all steps

    Loses marks

    • Omission of support reaction calculation
    • Failure to state tension or compression

    Earns more

    • Neat labelled free-body diagram
    • Correct identification of zero-force members

    Extra mark

    • Verification of results using a second method
  2. (b) Resultant stresses at top and bottom fibres at mid-span. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Calculate section properties (A, Z, e)
    • Compute bending moment due to UDL
    • Apply superposition of P/A, PeZ, and M/Z
    • State final stress values with units (MPa)

    Loses marks

    • Incorrect sign convention for eccentricity
    • Missing units in final stress values

    Earns more

    • Clear calculation of eccentricity (e)
    • Separate calculation of bending stress

    Extra mark

    • Check for tensile stress limits
  3. (c) Design of fillet weld connection for the bracket. 10 marks

    justify— claim → 3-4 reasons → evidence → conclusion

    Must cover

    • Determine allowable shear stress for weld
    • Calculate direct shear per unit weld length and the force from the 50 kN.m eccentric moment (perpendicular components, not torsion)
    • Determine required weld size (throat thickness)
    • State the assumed plate depth and the final weld size (about 8 mm fillet, 400 mm long on each face)

    Loses marks

    • Ignoring the eccentricity moment (200 kN x 250 mm) or treating it as torsion
    • Using wrong allowable stress value

    Earns more

    • Section modulus of the weld group
    • Reference to IS 800 code clauses

    Extra mark

    • Sketch of weld arrangement on bracket
  4. (d) Force required to drag the plate in glycerine. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Apply Newton's law of viscosity (F = μA dv/dy)
    • Calculate force for equidistant case (i)
    • Calculate force for 10mm offset case (ii)
    • State final force values in Newtons

    Loses marks

    • Incorrect calculation of velocity gradient
    • Confusing dynamic and kinematic viscosity

    Earns more

    • Correct identification of velocity gradient
    • Clear separation of calculations for (i) and (ii)

    Extra mark

    • Comparison of forces in both cases
  5. (e) Relative density of the field soil. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Calculate dry density of field soil
    • Determine void ratio of field soil
    • Calculate e_max and e_min from test data
    • Apply relative density formula (e_max - e)/(e_max - e_min)

    Loses marks

    • Incorrect calculation of dry density
    • Swapping e_max and e_min in formula

    Earns more

    • Step-by-step calculation of void ratios
    • Correct use of specific gravity (Gs)

    Extra mark

    • Interpretation of relative density value
What "Solve" is asking you to do

Choose the method, then carry it through to a final answer. Identifying what kind of problem this is and why that method applies is the first thing marked; a correct figure arrived at invisibly earns almost nothing.

Structure that answers it

Given data and what is required → method chosen, with the reason it applies → set-up (equation, circuit, free body, trial balance) → working, step by step → answer with units and any condition of validity

Where marks are lost

Doing the middle steps mentally and writing only the result. In mathematics papers, a further loss comes from giving a decimal where the exact value in surds or fractions was wanted, or from skipping the justification a part explicitly asks for.

All UPSC directive words, compared →

Practice this exact question

Write your answer and it is marked point by point against the model answer above — what you covered, what you missed, what you got wrong.

Evaluate my answer →

More from Civil Engineering 2021 Paper I

Write this answer and get it marked in about 20 seconds

Free account: 5 AI evaluations a month, marked against the rubric above.

Start free

Already have an account? Log in