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At the limit state of collapse, an RC beam is subjected to flexural moment 200 kNm, shear force 20 kN, and torque 9 kNm. The beam is 300 mm wide and has a gross depth of 425 mm, with an effective cover of 25mm. The equivalent nominal shear stress ( τve ) as calculated using the design code turns out to be lesser than the design shear strength ( τc ) of the concrete. 
Q.The equivalent flexural moment (Mel ) for designing the longitudinal tension steel is
  • a)
     187 kNm
  • b)
     200 kNm
  • c)
     29 kNm
  • d)
     213 kNm
Correct answer is option 'D'. Can you explain this answer?
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The equivalent flexural moment (Mel) for designing the longitudinal tension steel can be determined by considering the limit state of collapse of an RC beam. The given information includes the flexural moment (M) of 200 kNm, shear force (V) of 20 kN, and torque (T) of 9 kNm.

1. Determining the Equivalent Nominal Shear Stress (ve):
- The equivalent nominal shear stress (ve) can be calculated using the design code.
- However, it is mentioned that the calculated ve is lesser than the design shear strength (c) of the concrete.
- This indicates that the shear stress is not the governing factor for the design of the longitudinal tension steel.

2. Determining the Flexural Moment (Mel):
- Since the shear stress is not governing, the flexural moment (Mel) needs to be considered for designing the longitudinal tension steel.
- The flexural moment (Mel) can be calculated using the equation: Mel = M - (Vd + Td)
- Here, Vd represents the design shear force and Td represents the design torque.
- The given values for V and T can be used directly, as they are already provided.
- The design shear force (Vd) can be calculated using the formula: Vd = V + ρvbd
- Here, ρv represents the shear reinforcement ratio and bd represents the effective width of the beam.
- The shear reinforcement ratio (ρv) can be determined based on the design code requirements.
- The effective width of the beam (bd) is given as 300 mm.
- The design torque (Td) can be calculated using the formula: Td = ρtbd^2fyt
- Here, ρt represents the torsional reinforcement ratio and fyt represents the yield strength of the torsional reinforcement.
- The torsional reinforcement ratio (ρt) can be determined based on the design code requirements.
- The yield strength of the torsional reinforcement (fyt) is usually provided in the problem statement or can be assumed based on the code requirements.

3. Calculation:
- Substitute the given values and calculated values of Vd and Td into the equation for Mel.
- Compare the calculated Mel with the given options.
- The correct answer is option 'D' which corresponds to the calculated Mel of 213 kNm.
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At the limit state of collapse, an RC beam is subjected to flexural moment 200 kNm, shear force 20 kN, and torque 9 kNm. The beam is 300 mm wide and has a gross depth of 425 mm, with an effective cover of 25mm. The equivalent nominal shear stress ( τve) as calculated using the design code turns out to be lesser than the design shear strength ( τc) of the concrete.Q.The equivalent flexural moment (Mel ) for designing the longitudinal tension steel isa)187 kNmb)200 kNmc)29 kNmd)213 kNmCorrect answer is option 'D'. Can you explain this answer?
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