DESIGN OF RECTANGULAR SECTION SUBJECTED TO B.M and S.F

To design a rectangular beam section subjected to bending moment (B.M.) and shear force (S.F.), you need to follow these steps:

Determine the design loads:

Obtain the values of the applied loads, such as dead loads and live loads, from the project specifications or relevant codes.
Consider any additional loads like wind or seismic forces if applicable.
Calculate the maximum bending moment (B.M.):

Analyze the structure to determine the maximum bending moment along the length of the beam.
Use structural analysis software or hand calculations to obtain the B.M. values at critical locations.
Determine the maximum shear force (S.F.):

Analyze the structure to determine the maximum shear force acting on the beam.
Identify the locations where the S.F. is maximum and consider these critical locations.
Select the beam dimensions:

Determine the effective depth (d) of the beam based on the maximum B.M. and S.F.
Consider factors such as the span, load conditions, and any specific design requirements.
Ensure that the selected depth is reasonable and practical for construction.
Calculate the section properties:

Calculate the moment of inertia (I) and section modulus (S) of the selected rectangular beam section.
For a rectangular section, the moment of inertia is given by I = (b * d^3) / 12, and the section modulus is given by S = (b * d^2) / 6.
Here, b represents the width of the beam and d represents the effective depth determined in the previous step.
Check for bending strength:

Determine the bending stress (σ) using the formula σ = (M * c) / I, where M is the maximum B.M. at the critical location and c is the distance from the neutral axis to the extreme fiber.
Ensure that the bending stress does not exceed the allowable bending stress for the chosen material.
The allowable bending stress depends on the material, such as steel or reinforced concrete, and is typically provided by design codes or standards.
Check for shear strength:

Determine the shear stress (τ) using the formula τ = (V * A) / (b * d), where V is the maximum S.F., A is the cross-sectional area of the beam, and b and d are the dimensions of the rectangular section.
Verify that the shear stress does not exceed the allowable shear stress for the chosen material.
The allowable shear stress depends on factors like the material, type of construction, and the presence of shear reinforcement, and is typically provided by design codes or standards.
Revise and optimize the design:

If the initial design does not meet the strength requirements, adjust the beam dimensions (b and d) or consider alternative sections.
Iterate the calculations and checks until a suitable design that satisfies both bending and shear strength requirements is achieved.