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

Shubham Kola
15 Jan 202106:08

Summary

TLDRThis 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.

Outlines

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Ähnliche Tags
Cantilever BeamStructural AnalysisEngineering TutorialShear ForceBending MomentSupport ReactionsSign ConventionsBeam DiagramEngineering BasicsMechanical Engineering
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