An RCC beam of cross-section 250 mm x 400 mm is subjected to a factored bending moment of 150 kNm and a factored torsional moment of 150 kNm. The longitudinal reinforcement provided on the compression face will be designed for the moment of______ kNm (round up to 2 decimal places)(take cover to both the reinforcements be 50 mm)Correct answer is between '79,80'. Can you explain this answer?

Question

Answer

Given Data:

Cross-section of RCC beam: 250 mm x 400 mm
Factored bending moment: 150 kNm
Factored torsional moment: 150 kNm

Solution:

To design the longitudinal reinforcement on the compression face, we need to calculate the moment for which the reinforcement will be designed.

Step 1: Calculate the effective depth (d)

The effective depth (d) of the beam is given by the formula:
d = Overall depth of the beam - Clear cover - Diameter of reinforcement

Given that the clear cover to both the reinforcements is 50 mm and assuming the diameter of reinforcement to be 10 mm, we can calculate the effective depth as follows:
d = 400 mm - 2(50 mm) - 10 mm = 290 mm

Step 2: Calculate the area of steel required for bending moment

To calculate the area of steel required for bending moment, we use the formula:
Ast = (M / (0.87 * fyd * d))

Where,
Ast = Area of steel required
M = Factored bending moment
fyd = Design yield strength of steel
d = Effective depth

Assuming the design yield strength of steel to be 415 MPa, we can calculate the area of steel required as follows:
Ast = (150 * 10^6) / (0.87 * 415 * 10^6 * 290) = 0.0116 m^2

Step 3: Calculate the area of steel required for torsional moment

To calculate the area of steel required for torsional moment, we use the formula:
Ast_torsion = (Mt / (0.87 * fyd * d))

Where,
Ast_torsion = Area of steel required for torsional moment
Mt = Factored torsional moment
fyd = Design yield strength of steel
d = Effective depth

Assuming the design yield strength of steel to be 415 MPa, we can calculate the area of steel required for torsional moment as follows:
Ast_torsion = (150 * 10^6) / (0.87 * 415 * 10^6 * 290) = 0.0116 m^2

Step 4: Total area of steel required

The total area of steel required is the sum of the areas of steel required for bending moment and torsional moment, which is:
Total area of steel required = Ast + Ast_torsion = 0.0116 m^2 + 0.0116 m^2 = 0.0232 m^2

Step 5: Calculate the moment for which the reinforcement will be designed

To calculate the moment for which the reinforcement will be designed, we use the formula:
M_design = (Ast / (0.87 * fyd * d)) * (0.36 * fck * b * d^2)

Where,
M_design = Moment for which reinforcement will be designed
Ast = Total area of steel required
fyd = Design yield strength of steel
d = Effective depth
fck = Characteristic compressive strength of concrete
b = Width of the beam

Assuming the characteristic compressive strength of concrete

Answer

M_e2 = 229.41 - 150 = 79.411 kNm

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