Calculation of Moment of Resistance of a Beam

To calculate the moment of resistance of a beam, the following factors need to be considered:

1. Formula for Moment of Resistance:

The formula for moment of resistance is given as:

M.R. = f_y * Z_x

Where, f_y is the yield strength of the material used in the beam and Z_x is the plastic modulus of the cross-section of the beam.

2. Calculation of Plastic Modulus:

The plastic modulus of the beam can be calculated using the formula:

Z_x = (bd^2)/6 * (1 - (d/2)/c)

Where, b is the breadth of the beam, d is the actual depth of the neutral axis, and c is the critical depth of the neutral axis.

3. Calculation of Moment of Resistance:

Substituting the values of f_y, Z_x, b, d, and c in the formula for moment of resistance, we get:

M.R. = f_y * [(bd^2)/6 * (1 - (d/2)/c)]

Calculation of Moment of Resistance for the Given Beam

Given that the actual depth of the neutral axis is 350 mm and the critical depth of the neutral axis is 400 mm.

Assuming that the material used in the beam has a yield strength of 250 MPa.

Therefore, we can calculate the plastic modulus of the beam using the formula:

Z_x = (bd^2)/6 * (1 - (d/2)/c)
= (300*350^2)/6 * (1 - (350/2)/400)
= 45,062,500 mm^3

Substituting the values of f_y and Z_x in the formula for moment of resistance, we get:

M.R. = f_y * Z_x
= 250 * 45,062,500
= 11,265,625,000 N-mm

Therefore, the moment of resistance of the given beam is 11,265,625,000 N-mm.