Test 7 - Doubly Reinforced Beams

Question 1 ప్రశ్న 1

Which situation most commonly requires a doubly reinforced rectangular RCC beam instead of an ordinary singly reinforced beam?

A The required factored moment exceeds the limiting moment of a singly reinforced section and the available beam depth cannot conveniently be increased. B The required factored moment is much smaller than the singly reinforced capacity. C The beam carries only its self-weight and no imposed load. D Concrete tensile strength is intentionally used as the principal tensile resistance.

Question 2 ప్రశ్న 2

In the usual IS 456 Limit State design approach for a doubly reinforced rectangular beam, how is the required ultimate moment conveniently treated?

A As the limiting moment of a singly reinforced section plus an additional moment resisted by a compression-steel and additional-tension-steel couple B As equal moments resisted independently by concrete in tension and concrete in compression C As a shear component and a torsional component only D As a moment resisted entirely by compression reinforcement

Question 3 ప్రశ్న 3

For an M25 rectangular beam with Fe415 reinforcement, b = 300 mm and effective depth d = 500 mm, what limiting neutral-axis depth is used as the basis of conventional doubly reinforced design?

A 200 mm B 230 mm C 240 mm D 265 mm

Question 4 ప్రశ్న 4

If compression reinforcement is located at depth d' from the compression face and the limiting neutral-axis depth is xu,max, which expression gives the compression-steel strain used in the conventional doubly reinforced design?

A εsc = 0.0035(1 - d'/xu,max) B εsc = 0.0035(d'/xu,max) C εsc = 0.002(d/xu,max) D εsc = fy/(1.15Es) + d'/d

Question 5 ప్రశ్న 5

For a limiting Fe415 section, xu,max/d = 0.48. If compression reinforcement is located at d'/d = 0.10, what is its compression strain approximately?

A 0.00125 B 0.00180 C 0.00277 D 0.00380

Question 6 ప్రశ్న 6

Why should the compression-steel design stress fsc not automatically be taken as exactly 0.87fy for every Fe415 or Fe500 doubly reinforced beam?

A Because fsc depends on the compression-steel strain, which depends on d' and the neutral-axis depth. B Because compression reinforcement is assumed to carry zero stress. C Because 0.87fy is a concrete stress rather than a steel stress. D Because compression reinforcement is always below the neutral axis.

Question 7 ప్రశ్న 7

According to the IS 456 Annex G design expression for a doubly reinforced rectangular section, what relation represents the additional moment M2 = Mu - Mu,lim?

A M2 = fsc Asc(d - d') B M2 = (fsc - fcc)Asc(d - d') C M2 = 0.87fy Asc(d - d') D M2 = 0.36fck Asc(d - d')

Question 8 ప్రశ్న 8

Under the same Annex G doubly reinforced design formulation, which expression gives the additional tensile reinforcement Ast2 required to balance the compression reinforcement?

A Ast2 = Asc fsc/(0.87fy) B Ast2 = Asc(fsc - fcc)/(0.87fy) C Ast2 = Asc fy/fsc D Ast2 = 0.36fck Asc/(0.87fy)

Question 9 ప్రశ్న 9

How is the total tensile reinforcement Ast obtained in the conventional Annex G design of a doubly reinforced rectangular beam?

A Ast = Ast1 + Ast2 B Ast = Ast1 - Ast2 C Ast = Asc only D Ast = 0.5(Ast1 + Ast2)

Question 10 ప్రశ్న 10

For an M25 rectangular beam with b = 300 mm, d = 500 mm and Fe415 reinforcement, what is the limiting singly reinforced moment capacity approximately?

A 187.4 kN·m B 206.9 kN·m C 258.7 kN·m D 350.0 kN·m

Question 11 ప్రశ్న 11

For the M25, b = 300 mm, d = 500 mm, Fe415 section in the previous question, what is the tensile reinforcement Ast1 associated with the limiting singly reinforced moment approximately?

A 1200 mm² B 1436 mm² C 1795 mm² D 2357 mm²

Question 12 ప్రశ్న 12

The M25-Fe415 beam with b = 300 mm and d = 500 mm must resist a factored bending moment of 350 kN·m. If Mu,lim = 258.68 kN·m, what additional moment must be resisted by the compression-steel and additional-tension-steel couple?

A 51.32 kN·m B 75.00 kN·m C 91.32 kN·m D 108.68 kN·m

Question 13 ప్రశ్న 13

For the beam in the previous question, take d' = 50 mm and compression-steel design stress fsc = 353 N/mm². What compression-steel area Asc is required approximately to resist the additional moment of 91.32 kN·m?

A 500 mm² B 575 mm² C 594 mm² D 660 mm²

Question 14 ప్రశ్న 14

For the same 350 kN·m beam, what additional Fe415 tensile reinforcement Ast2 is required when Asc = 574.9 mm² and fsc = 353 N/mm²?

A 420 mm² B 562 mm² C 575 mm² D 795 mm²

Question 15 ప్రశ్న 15

For the M25-Fe415 doubly reinforced beam designed for 350 kN·m, if Ast1 = 1795 mm² and Ast2 = 562 mm², what total tension reinforcement is required approximately?

A 1795 mm² B 2210 mm² C 2357 mm² D 2587 mm²

Question 16 ప్రశ్న 16

An M25-Fe415 beam has d = 500 mm, d' = 50 mm and 600 mm² of compression reinforcement. If fsc = 353 N/mm², what additional ultimate moment can the compression reinforcement resist according to the Annex G expression?

A 61.5 kN·m B 75.0 kN·m C 92.3 kN·m D 95.3 kN·m

Question 17 ప్రశ్న 17

For the 600 mm² compression reinforcement in the previous question, what additional Fe415 tension reinforcement Ast2 is required approximately?

A 455 mm² B 568 mm² C 587 mm² D 600 mm²

Question 18 ప్రశ్న 18

An M20 rectangular beam has b = 250 mm, d = 450 mm and Fe415 reinforcement. What is its limiting singly reinforced moment capacity approximately?

A 107.7 kN·m B 139.7 kN·m C 167.6 kN·m D 220.0 kN·m

Question 19 ప్రశ్న 19

The M20 beam in the previous question must resist a factored moment of 220 kN·m. If d' = 45 mm and fsc = 353 N/mm², what compression-steel area is required approximately?

A 420 mm² B 500 mm² C 562 mm² D 795 mm²

Question 20 ప్రశ్న 20

For the same M20-Fe415 beam designed for 220 kN·m, Ast1 is approximately 1077 mm² and Ast2 is approximately 549 mm². What total tension reinforcement is required approximately?

A 1077 mm² B 1397 mm² C 1626 mm² D 2200 mm²

Question 21 ప్రశ్న 21

For an analysis exercise, a doubly reinforced M25 rectangular beam has b = 300 mm, d = 500 mm, d' = 50 mm, Ast = 2200 mm² and Asc = 500 mm² of Fe415 steel. Taking fsc = 350 N/mm², assuming the tension steel develops 0.87fy, and using the Annex G simplification that the concrete area displaced by compression steel is neglected, what neutral-axis depth satisfies force equilibrium approximately?

A 180.0 mm B 210.0 mm C 229.4 mm D 267.4 mm

Question 22 ప్రశ్న 22

For the doubly reinforced beam in the previous question with xu = 229.37 mm, what is its ultimate moment capacity approximately under the stated assumptions?

A 258.7 kN·m B 300.0 kN·m C 328.7 kN·m D 350.0 kN·m

Question 23 ప్రశ్న 23

Which statement about load reversal and doubly reinforced beams is most appropriate?

A Reinforcement near both faces can be beneficial when bending reverses, but the member must be checked separately for the demands in each bending direction. B Compression reinforcement automatically gives identical capacity in both directions without further analysis. C Load reversal makes concrete tension fully effective and eliminates the need for reinforcement. D A doubly reinforced beam cannot carry reversed bending.

Question 24 ప్రశ్న 24

Which statement concerning compression reinforcement in a doubly reinforced beam is correct?

A Compression reinforcement should be properly restrained by transverse reinforcement to maintain its position and provide lateral restraint to compression bars. B Compression reinforcement requires no transverse restraint because concrete cannot deform laterally. C Compression reinforcement must always be placed exactly on the neutral axis. D Compression reinforcement is provided only to increase the self-weight of the beam.

Question 25 ప్రశ్న 25

Consider the following statements about doubly reinforced beams under the IS 456 Annex G Limit State formulation:
1. A common design procedure first assigns Mu,lim to the limiting singly reinforced part of the section.
2. The additional moment is represented by Mu - Mu,lim = fsc Asc(d - d').
3. The additional tension reinforcement is obtained from Ast2 = Asc fsc/(0.87fy).
4. For Fe415 and Fe500 compression reinforcement, fsc may always be assumed equal to 0.87fy without checking the compression-steel strain.

Which statements are correct?

A 1 and 4 only B 1, 2 and 3 only C 2, 3 and 4 only D 1, 2, 3 and 4

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