Shear Force and Bending Moment Diagrams

Engineers need SF and BM diagrams because:

• They help in understanding the internal forces and moments in a structure.

• They are used to calculate the cost of materials.

• They provide aesthetic value to the design.

• They are required for environmental analysis.

Answer explanation

The correct choice highlights that SF (Shear Force) and BM (Bending Moment) diagrams are essential for understanding the internal forces and moments acting on a structure, which is crucial for safe and effective design.

What happens to the shear force at the midpoint of the beam?

• It is at a maximum

• It is zero

• It is at a minimum

• It is negative

Answer explanation

At the midpoint of a simply supported beam, the shear force is zero due to the balance of forces. This is where the load is symmetrically distributed, resulting in no net vertical force acting at that point.

What is the difference between positive shear force and negative shear force as shown in the diagram?

• Positive shear force causes clockwise rotation, while negative shear force causes counterclockwise rotation.

• Positive shear force causes counterclockwise rotation, while negative shear force causes clockwise rotation.

• Positive shear force and negative shear force both cause clockwise rotation.

• Positive shear force and negative shear force both cause counterclockwise rotation.

Answer explanation

Positive shear force induces clockwise rotation, while negative shear force induces counterclockwise rotation. This distinction is crucial in understanding how forces affect structural elements.

In the diagram, which type of shear force is depicted on the left side?

• Positive shear force

• Negative shear force

Answer explanation

The left side of the diagram shows a positive shear force, which is indicated by the upward direction of the force acting on the beam. This type of shear force tends to cause the material to shear in a positive manner.

A bending moment diagram is a graphical representation of the bending moment along a beam. How is it drawn?

• By plotting the bending moment at various points along the beam

• By measuring the deflection of the beam

• By calculating the shear force at different sections

• By determining the axial force in the beam

Answer explanation

A bending moment diagram is drawn by plotting the bending moment values at various points along the beam, which visually represents how the moment varies, making the first choice the correct one.

What happens to the bending moment (BM) at the ends and midpoint of a beam under load?

• A) BM is maximum at the ends and zero at the midpoint.

• B) BM is zero at the ends and maximum at the midpoint.

• C) BM is zero at both ends and midpoint.

• D) BM is maximum at both ends and midpoint.

Answer explanation

In a simply supported beam under load, the bending moment is zero at the ends due to the support conditions and reaches its maximum at the midpoint where the load is applied, making option B the correct choice.

The moment of a force is the product of force multiplied by the shortest distance between the force and the ________.

• pivot point

• center of mass

• axis of rotation

• line of action

Answer explanation

The moment of a force is calculated as the force multiplied by the shortest distance to the pivot point, which is the point about which the object rotates. Thus, 'pivot point' is the correct answer.

What happens to bending when the shear force diagram crosses zero?

Answer explanation

When the shear force diagram crosses zero, it indicates a point of inflection in the bending moment diagram, leading to a change in the curvature of the beam. This is where bending starts to decrease or increase.

Fill in the blank: Maximum slide at the ends produces maximum shear and ______ bending.

• bending

• torsion

• compression

• tension

Answer explanation

Maximum slide at the ends leads to maximum shear forces, which in turn cause maximum bending moments. Therefore, the correct term to fill in the blank is 'bending', as it directly relates to the effects of shear.

What type of bending is shown in the first diagram on the left?

• A) Positive bending in a simple beam

• B) Negative bending in a simple beam

• C) Positive bending in a cantilever beam

• D) Negative bending in a cantilever beam

Answer explanation

The first diagram shows a simple beam experiencing positive bending, where the top fibers are in compression and the bottom fibers are in tension. This is characteristic of positive bending in a simple beam.