Consider the singly reinforced beam section given below(left

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Consider the singly reinforced beam section given below(left figure). the stress block parameters for the cross- section from IS: 456-2000 are also given below (right figure). The moment of resistance for the given section by the limit state method is ______ kN-m.

1. 40.82
2. 42.12
3. 42.82
4. 44.82

Correct Option: C

A_st = 4 ×	π	d²
	4

= 4 ×	π	(12)²
	4

= 453 mm²
0.36 f_ck. b. x_u = 0.87 f_y. A_st

⇒ x_u =	0.87f_y.A_st
	0.36 f_ck .b

=	0.87 × 415 × 453	= 90.86 mm
	0.36 × 25 × 200

x_{u. max} = 0.48d
= 0.48 × 300 = 144 mm
∴ x_u < x_{u max}
∴ it is U.R section (under reinforced)
Moment of resistance,
M_V = 0.87 × f_y × A_st × (d – 0.42 x_u)
= 0.87 × 415 × 453 (300 – 0.42 × 90.86) = 42.82 kNm