-forces on either side of the point.

Explanation:

Shear force is defined as the internal force that is exerted by one portion of a beam or structure upon an adjacent portion, across an imaginary plane called the section plane. The magnitude and direction of the shear force at any point on the beam depend on the distribution of all the external loads and moments acting on the beam, as well as the geometry and support conditions of the beam.

To calculate the shear force at a particular point on the beam, we need to consider the forces acting on either side of the section plane at that point. The algebraic sum of these forces gives us the net shear force at that point.

Factors affecting shear force:

The shear force at any point on a beam is influenced by several factors, including:

1. External loads: The magnitude and direction of the external loads acting on the beam, such as point loads, distributed loads, and moments, can affect the shear force.

2. Beam geometry: The cross-sectional shape and dimensions of the beam can also affect the shear force, as they determine the distribution of internal stresses and strains.

3. Support conditions: The type and location of the supports that the beam is resting on can affect the shear force, as different support conditions can result in different bending moments and internal stresses.

Calculation of shear force:

To calculate the shear force at any point on a beam, we need to follow these steps:

1. Draw a free-body diagram of the beam and identify all the external loads and moments acting on the beam.

2. Determine the reactions at the supports of the beam using the equations of equilibrium.

3. Cut the beam at the section plane where we want to calculate the shear force and draw a free-body diagram of the cut section.

4. Identify all the forces acting on either side of the section plane and determine their magnitudes and directions.

5. Sum up the forces on either side of the section plane and calculate the algebraic sum of the forces.

6. The result of step 5 gives us the shear force at that point on the beam.

Conclusion:

In conclusion, the shear force at any point on a beam is the algebraic sum of the forces acting on either side of the section plane at that point. It is influenced by several factors, including external loads, beam geometry, and support conditions. To calculate the shear force, we need to draw a free-body diagram, determine the reactions at the supports, cut the beam at the section plane, and sum up the forces on either side of the section plane.