Questions with solution

Transcription

1 Questions with solution Q 1: The rectangular beam of width, 250 mm is having effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is : (a) knm (b) knm (c) knm (d) knm (i) Characteristics strength of concrete, f ck =20 N/mm 2 (ii) Characteristics strength of reinforcing steel, f y =415 N/mm 2 (iii) Width, b=250 mm (iv) Effective depth, d=317 mm (vii) Neutral axis factor, x ub d = ɛc ɛ c+ɛ s = =0.48 Coefficient, Q ub x =k ub 1 (1 k d 2 x ub ) d = ( ) =0.138 Moment of resistance due to concrete, M ucb =Q ub fck b d 2 = = knm 1. (b) knm

2 Q 2: The width of a rectangular beam is 250 mm and the effective depth is 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The position of neutral axis from compression side is (a) 266mm (b) 228mm (c) 190mm (d) 152mm (i) Characteristics strength of concrete, f ck =20 N/mm 2 (ii) Characteristics strength of reinforcing steel, f y =415 N/mm 2 (iii) Width, b=250 mm (iv) Effective depth, d=317 mm Neutral axis factor, x ub d = ɛc ɛ c+ɛ s = =0.48 Position of neutral axis from the compression side, x ub = x ub d d = = (d) 152mm

3 Q 3: The rectangular beam of width, 250 mm is having effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. As per limit state method, the area of steel in a balanced section is : (a) 757mm 2 (b) 833mm 2 (c) 909mm 2 (d) 984mm 2 (iii) Width, b=250 mm (iv) Effective depth, d=317 mm Area of tensile reinforcement, balanced section, A stb = k 1 f ck ( x ub d ) b d 0.87 f y = =757.3 mm 2 3. (a) 757mm 2

4 Q 4: The rectangular beam of width, 250 mm is having effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. As per limit state method, the lever arm in a balanced section is equal to : (a) 152mm (b) 178mm (c) 203mm (d) 254mm (iii) Width, b=250 mm (iv) Effective depth, d=317 mm Lever arm, Z ub x =d(1 k ub 2 ) d =317.0 ( ) = (d) 254mm

5 Q 5: The rectangular beam of width, 250 mm is having effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The tensile reinforcement is provided by 2-16 mm dia bars. As per limit state method, the moment of resistance due to steel is equal to : (a) knm (b) knm (c) knm (d) knm (iii) Width, b=250 mm (iv) Effective depth, d=317 mm Area of tensile reinforcement, A st =n t π φ 2 t /4 = /4 =402.1 mm 2 Moment of resistance due to steel, M us =0.87 fy A st (1 k 2 x ud ) d = ( ) = knm 5. (c) knm

6 Q 6: The rectangular beam of width, 300 mm is having overall depth of 400 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The tensile reinforcement is provided by 4-20 mm dia bars. In the compression side, the reinforcement is provided by 2-12 mm dia bars. The clear cover is 25 mm. The moment capacity of the section due to concrete as per limit state method is : (a) knm (b) knm (c) knm (d) knm (iii) Width, b=300 mm (iv) Overall depth, D=400 mm Clear cover, cc=25 mm (vii) (viii) (ix) Effective depth, d =D cc φ t /2 = /2 =365 mm Area of tensile reinforcement, A st =n t π φ 2 t /4 = /4 = mm 2 Area of compression reinforcement, A sc =n c π φ 2 c/4 = /4 =226.2 mm 2 Moment of resistance due to concrete, M ucb =Q ub fck b d 2 = = kn m 6. (b) knm

7 Q 7: The rectangular beam of width, 300 mm is having overall depth of 400 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The tensile reinforcement is provided by 4-20 mm dia bars. In the compression side, the reinforcement is provided by 2-12 mm dia bars. The clear cover is 25 mm. The salient points of design stress-strain curve of Fe415 is given by (strain, stress, N/mm 2 ) ( ,288), ( ,306), ( ,324), ( , 342), ( , 351), ( , 360). The stress in steel at compression level is equal to : (a) N/mm 2 (b) N/mm 2 (c) N/mm 2 (d) N/mm 2 (iii) Width, b=300 mm (iv) Overall depth, D=400 mm Clear cover, cc=25 mm Effective depth, d =D cc φ t /2 = /2 =365 mm (vii) Strain in concrete, ɛ c = (viii) (ix) Effective cover in compression side, d c =cc + φ c /2 = /2 =31.0 Strain in compression steel, ɛ sc =ɛ c (1 ( d c d )/( x ub )) d = (1 ( 31.0 )/0.48) = (x) Stress in compression steel, f sc =353.1 N/mm 2 7. (c) N/mm 2

8 Q 8: The rectangular beam of width, 300 mm is having overall depth of 400 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The tensile reinforcement is provided by 4-20 mm dia bars. In the compression side, the reinforcement is provided by 2-12 mm dia bars. The clear cover is 25 mm. As per limit state method, the section will take additional moment of : (a) knm (b) knm (c) knm (d) knm (i) (ii) (iii) (iv) (vii) Effective depth, d =D cc φ t /2 = /2 =365 mm Area of tensile reinforcement, A st =n t π φ 2 t /4 = /4 = mm 2 Area of compression reinforcement, A sc =n c π φ 2 c/4 = /4 =226.2 mm 2 Area of tensile reinforcement, balanced section, A stb = k 1 f ck ( x ub d ) b d 0.87 f y = = mm 2 Additional tensile reinforcement available, A st2 =A st A stb = =210.3 mm 2 Addl. moment of res. due to tensile reinforcement, M ust2 =0.87 fy A st2 (d d c) = ( ) = knm Moment of res. due to comression steel, M ucs =f sc A sc (d d c) = ( ) = knm (viii) Addl. moment of res. for doubly reinf. section, M u_addl = knm 8. (a) knm

9 Q 9: A flanged beam is having the following dimension : width of flange, b f = 1000mm depth of flange, D f = 125mm, width of web, b w = 250 mm and overall depth of beam, D = 350 mm The concrete grade is M20 and the grade of reinforcing steel is Fe415. The clear cover is 25 mm. The moment capacity of the section due to concrete as per limit state method is : (a) knm (b) knm (c) knm (d) knm (iii) Flange width, b f =1000 mm (iv) Flange thickness, D f =125 mm Web thickness, b w =250 mm Overall depth, D=250 mm (vii) Clear cover, cc=25 mm (viii) (ix) Effective depth, d =D cc φ t /2 = /2 =215 mm Moment of resistance due to concrete, M ucb =Q ub fck b f d 2 = = kn m 9. (b) knm

10 Q 10: A flanged beam is having the following dimension : width of flange, b f = 1000mm depth of flange, D f = 125mm, width of web, b w = 250 mm and overall depth of beam, D = 350 mm The concrete grade is M20 and the grade of reinforcing steel is Fe415. The clear cover is 25 mm. The area of steel required in balanced condition is equal to (a) 1029 mm 2 (b) 1543 mm 2 (c) 2058 mm 2 (d) 2572 mm 2 (iii) Flange width, b f =1000 mm (iv) Flange thickness, D f =125 mm Web thickness, b w =250 mm Overall depth, D=250 mm (vii) Area of tensile reinforcement, balanced section, A stfb = k 1 f ck ( x ub d ) b f d 0.87 f y = = mm (c) 2058 mm 2