Serial : IG1_CE_G_Concrete Structures_100818 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: E-mail: info@madeeasy.in Ph: 011-451461 CLASS TEST 018-19 CIVIL ENGINEERING Subject : Concrete Structures Date of test : 10/08/018 Answer Key 1. (a) 7. (b) 13. (a) 19. (c) 5. (a). (a) 8. (c) 14. (c) 0. (d) 6. (b) 3. (c) 9. (a) 15. (d) 1. (b) 7. (c) 4. (d) 10. (c) 16. (a). (a) 8. (c) 5. (a) 11. (b) 17. (b) 3. (c) 9. (b) 6. (b) 1. (c) 18. (b) 4. (b) 30. (c)
CT-018 CE Concrete Structures 7 Detailed Explanations 4. (d) Modulus of elasticity of concrete is dependent on its compressive strength. Lower w/c ratio,larger curing period, higher vibration will produce concrete of higher compressive strength. With increase in age, compressive strength increases and therefore modulus of elasticity of concrete increase with increase in E age. Also, Modulus of Elasticity, E c, where E 1 +θ c is intial Modulus of elasticity and θ is creep coefficient. θ decreases with age, so E increase with age. 5. (a) For isolated T-beam, b f l l 0 0 + 4 b + b w where, l 0 6m, b 1000 mm, b w 300 mm b f 6000 6000 + 4 1000 + 300 900 mm 6. (b) Strain distribution is linear and stress distribution is non-linear. 7. (b) Central dip, h 8. (c) Let us design a square section of size B B A B wl 8P 40 ( 10) 8 500 0.m 00mm A s 1 B 0.01 B 100 Now for a short column A A s B 0.01 B 0.99 B P σ cc + σ sc A s 30000 10 4 0.99 B + 130 0.01 B B 38.81 mm Hence, column is a long column L eff B 4000 1 38.81 >
8 Civil Engineering Now, C R 1.5 4000 48 B 4000 P 30000 1.5 ( 0.4 0.99B + 13 0.01B ) 0.6575 B 43.83 B 30000 0 B 49.5 48B Area ( 49.5 ) 100 6.60 mm 9. (a) For deformed bars value of bond stress is increased by 60%. For bars in compression the value of bond stress is increased by 5% Development length ( 0.87f y ) φ 4 1.5 1.6 τ bd ( ) 5 0.87 415 4 1.5 1.6 1.4 805.9 806 mm 11. (b) b f t f b w 1000 mm 100 mm 50 mm d 500 mm π 4 4 150 mm Assuming N.A. to lie within the flange and equating the forces of compression and tension, we get 0.36 f ck b f x u 0.87 f y x u 0.87f A y 0.36 f ck st b f 0.87 50 150 45.9 mm 0.36 0 1000 x u < t f (ok) x u max 0.53 d 0.53 500 65 mm x u < x u max, section is under reinforced ultimate moment of resistance, M u 0.87 f y (d 0.4 x u ) 0.87 50 150 (500 0.4 45.9) 158.93 KNm 1. (c) Area of concrete A g A s
CT-018 CE Concrete Structures 9 π 4 400 6 π 4 5 15664 945 1719 mm Ultimate load, P u 1.05(0.4 f ck + 0.67 415 945) 1890 KN Safe load 1890 1.5 160 KN 13. (a) σ max P + Pe A Z 3 3 400 10 400 10 100 6 + 00 400 00 400 5 + 7.5 1.5 N/mm 14. (c) According to IS: 456-000 Span Effective depth (A) value 10 Span in metres (for span > 10 m) Effective depth Span 10 (A) value Span in metres (A) value for simply supported beam is 0. effective depth > 1,15 mm 15. (d) P u 1.5 500 3750 KN A 460 600 76000 mm P u 0.4 f ck + 0.67 f y A sc 3750 10 3 0.4 0 (76000 A sc ) + 0.67 415 A sc A sc 5710 mm 16. (a) Applying the yield line theory with, R 1, µ i x i y 1 l x l y 4 m µ (3 + iy) K 1 R (1 i ) + x K 4(1 + i x ) 4 µ (1 + i ) y
10 Civil Engineering α 1 α 4 4+ 3K1.35 K 1 K 1 3K 1 0.651 M + uy wu ly (3 α 1) 6( iy +α1) w 6(1 ) 0.0338 wl uly α 0.0353 wu ly + ix (Greater) 17. (b) Loss of prestress, stress in concrete at level of steel M + + uy Mux Muy Mu σ m θ σ c x 0.0353 10 4 5.65 knm/m Loss of prestress, σ c P Pey A + I m 50 1000 50 1000 60 60 1 + 150 300 3 150 300 8.3 N/mm E 00 1000 E 30190 6.6 s c σ 6.6 8.3 109 N/mm Prestress P 50 1000 A π s 6 7 4 1083 N/mm Loss of prestress 109 100 10% 1083 19. (c) Loss of prestress due to anchorage slip L Es L 3 10 30 3.1 10 5 1 N/mm % loss of prestress 1 100 100 1.75 %
CT-018 CE Concrete Structures 11 0. (d) Initial prestressing force, P 500 588.4 kn 0.85 e 75 mm. Area of beam, A 50 300 75000 mm Top fiber stress P 6e 1 A d 3.9 N/mm Bottom fiber stress P 6e 1+ A d 19.6 N/mm 1. (b) For HYSD bars in compression, actual bond stress φσs L d 4 τ bd 1.6 1.5 τ bd 1.6 1.5 1.4.8 N/mm. (a) 1 (0.87 415) L d 386.84 mm 4.8 According to IS 456 : 000, the development length should be increased by 0% for three bars in contact. L d is to be increases by 0% for three bundled bars. L d 1. 386.84 464.1 mm b 0.0035 0.00 x u C 0.67 f ck B 0.45 f ck 0.36 fckbxu A 0.87 f y 0.87 f y Assumed IS : 456 000 AB AC 0.00 0.0035 AB AC 4 7 [from assumed stress diagram] AB 4 7 x u But BC AC AB x u 4 7 x u 3 7 x u Total compressive force 0.67 f ck 3 7 x u b + 0.67 4 x 7 u b 0.4786 f ck b x u f ck
1 Civil Engineering 3. (c) Total tensile force 0.87 f y For actual depth of neutral axis, Total compressive force Total tensile force 0.4786 f ck b x u 0.87 f y 0.4786 0 300 x u 0.87 415 3 4 π (16) x u 75.84 76 mm 1000 mm 675 100 mm 100 600 mm 570 mm 570 35 Given, X u > 100 mm and section is under reinforce 0.36 f ck (35)X u + 0.45 f ck (675) 100 0.87 f y (This expression is valid only when 3 X 7 u > D f, 3 34.13 100 7 > OK) 0.36 5 35X u + 0.45 5 65 100 0.87 415 4000 X u 34.13 mm Take, X u 36.3 mm Check, X u(l) 0.48 570 73.6 X u < X u(l) (OK) 4. (b) Ultimate design shear force, V u 10 kn Ultimate shear capacity of concrete, V uc τ c bd 0.48 30 400 44.16 kn Ultimate shear to be resisted by shear reinforcement, V us V u V uc 10 44.16 75.84 kn For vertical stirrups, spacing is given as S v 0.87 f A d V y us sv 0.87 50 π (8) 400 3 75.84 10 4 115.3 mm
CT-018 CE Concrete Structures 13 5. (a) V s 75 kn, τ c 0.48 N/ mm V c 0.48 50 380 45.6 kn Vertical stirrups to be designed for (75 45.6) 9.4 kn S v (spacing) Area of stirrups σ effective depth design value for vertical stirrups y π 8 30 380 4 3 9.4 10 98.857 mm 6. (b) Maximum spacing allowed for vertical stirrups (1) 0.75 d 85 mm, () 300 mm S V 85 mm C min 3000 400 + 19.33 < 0.05 D 500 30 therefore we can apply, P u 0.4 f ck + 0.67 f y A sc 1500 10 3 π 0.4 0 400 Asc + 0.67 50 A 4 sc 7. (c) on solving, A sc 818.75 mm x u,lim 0.48 d 0.48 330 158.4 mm Moment of resistance 0.36 f ck b x u,lim (d 0.4 x u,lim ) 0.36 0 150 158.4 (330 0.4 158.4) 45.07 kn-m 8. (c) Bending tensile strength, σ bt. N/mm Characteristic compressive strength, f ck 0 N/mm Maximum stress in concrete, σ cbc 0.45 f ck 0.45 0 9 N/mm P P L/3 L/3 L/3 PL/3 PL/3 BMD Section modulus, Z bd 00 (300) 6 6 3 10 6 mm 3 Maximum moment, M max Z σ bt 3 10 6. 6.6 10 6 6.6 kn-m
14 Civil Engineering PL M max 3 P 3 6.6 3 P 6.6 kn 9. (b) Effective width of flange, b f l l b 0 0 + 4 + b w 10000 + 300 10000 + 4 1000 1014.3 mm This is greater than b, which is not possible. So, effective width of flange is 1000 mm. 30. (c) Axial load 1400 kn 10% of column load 140 kn Total load 1540 kn Actual area of footing required 1540 100 15.4m Net earth pressure acting upward due to factored load is Punching shear w 1400 1.5 136.36kN/m 15.4 Critical section 400 d The critical section is taken at a distance d Two way shear force, V u Punching shear stress away from the face of column as shown in above figure. 136.36 15.4 (0.4 0.6) + 1963.58kN Factored shear force Perimeter effective depth of the the critical section 1963.58 1000 0.818N/mm 4(400 + 600) 600