Cantilever Beam: Shear Force and Bending Moment Diagram [SFD BMD Problem 2] By Shubham Kola

Summary

This tutorial explains how to analyze a cantilever beam by calculating support reactions, shear forces, and bending moments. The process involves three main steps: first, calculating the reaction force at the support using equilibrium conditions; second, determining shear forces across various points of the beam using sign conventions; and third, calculating bending moments, with sagging and hogging effects. The tutorial emphasizes the importance of sign conventions for accurate shear force and bending moment diagrams. The detailed step-by-step analysis provides a clear understanding of internal forces and moments in structural engineering problems.

Takeaways

• 😀 The problem involves solving for the reactions, shear forces, and bending moments in a cantilever beam.
• 😀 The first step is to calculate support reactions using equilibrium conditions, particularly the summation of vertical forces (Fy = 0).
• 😀 Upward forces are treated as positive, and downward forces are treated as negative when calculating support reactions.
• 😀 The reaction at support Ra is calculated as 3.5 kN by setting up the equation with forces acting on the beam.
• 😀 In the second step, shear force calculations are done using a sign convention where upward forces are positive and downward forces are negative.
• 😀 Shear force at various points along the beam is calculated by considering sections to the left and right of each point, starting from the left-hand side.
• 😀 Shear force remains constant between points if there are no external forces acting on the beam between those points.
• 😀 The shear force changes when a downward force is encountered, and the shear force value is updated accordingly.
• 😀 Bending moments are calculated in the third step, with sagging moments treated as positive and hogging moments as negative.
• 😀 The bending moment at the free end of a cantilever beam is zero, and moments are calculated starting from the free end to other points along the beam.

Q & A

What is the first step in solving the cantilever beam problem?

The first step is calculating the support reactions using the condition of equilibrium, specifically the summation of vertical forces (∑Fy = 0).

Why is the horizontal force equilibrium (∑Fx = 0) not used in this problem?

Horizontal force equilibrium (∑Fx = 0) is not used because there are no horizontal forces acting on the beam.

What is the value of the reaction force at support Ra?

The value of the reaction force at support Ra is 3.5kN, calculated by solving the equation Ra - 2 - 1.5 = 0.

How are shear forces calculated for this cantilever beam?

Shear forces are calculated step by step from left to right across the beam, using sign conventions where upward forces are positive and downward forces are negative.

What is the shear force at point A to the left of the beam?

The shear force at point A to the left is 0, as there are no forces acting on the beam to the left of point A.

What happens to the shear force as you move from point A to point C?

The shear force remains constant at 3.5kN between point A and point C because there are no forces acting between these points.

How does the downward force of 2kN affect the shear force at point C?

The downward force of 2kN reduces the shear force at point C from 3.5kN to 1.5kN, as it is treated as a negative force.

What is the shear force at point B after the downward force of 1.5kN is applied?

The shear force at point B becomes zero after the downward force of 1.5kN is applied, calculated as 1.5kN - 1.5kN = 0.

How do you calculate the bending moment at point C?

The bending moment at point C is calculated by multiplying the downward force of 1.5kN by the distance from the point of application (0.5m), resulting in a moment of -0.75kN·m.

What is the value of the bending moment at point A?

The bending moment at point A is calculated by considering the two downward forces (1.5kN and 2kN) and their distances, resulting in a moment of -4.25kN·m.

What is the significance of the negative values in the bending moment diagram?

The negative values in the bending moment diagram indicate a hogging effect, meaning the beam is bending downward at those points.

Why is the bending moment at point B considered to be zero?

The bending moment at point B is considered zero because it is the free end of the cantilever beam, where no moment is generated.