Beam equilibrium and shear force

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SUMMARY

The discussion focuses on calculating the transverse shear force and bending moment for a beam subjected to transverse loads at points A, C, and E, along with a concentrated couple at E. Specifically, it addresses the determination of shear force Vc and bending moment Mc just to the left of load C, and shear Vd and moment Md just to the left of support D. The loads are defined as P at A, 2P at C, and 2P at E, with the equations V=dM/dx and p(x)=dV/dx being central to the analysis.

PREREQUISITES
  • Understanding of beam mechanics and shear force analysis
  • Familiarity with bending moment calculations
  • Knowledge of free body diagrams in structural analysis
  • Proficiency in differential calculus as applied to mechanics
NEXT STEPS
  • Study the derivation of shear force and bending moment equations in beam theory
  • Learn how to construct and analyze free body diagrams for complex loading scenarios
  • Explore the effects of concentrated loads and couples on beam equilibrium
  • Investigate the application of the equations V=dM/dx and p(x)=dV/dx in practical examples
USEFUL FOR

Students in civil or mechanical engineering, structural analysts, and anyone involved in beam design and analysis will benefit from this discussion.

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Homework Statement


transverse loads are applied to the beam in the figure at A, C, and E, and a concentrated couple 3Pa is applied to the beam at E. Determine expressions for (a) the transverse shear force Vc and bending moment Mc at a section just to the left of the load at C, and (b) shear Vd and moment Md just to the left of the support at D. Express answers in terms of P and a.

The image is the same setup as this problem only the loads at A, C and E are P, 2P and 2P respectively
p5.2-03alt.gif


Homework Equations


I know that the derived equations are V=dM/dx and p(x)=dV/dx but I don't really know how to go about doing this. I have my free body diagram but other than that I don't know where to start. Can anyone give me a hand?


The Attempt at a Solution

 
Physics news on Phys.org
Start with point A. What's the shear force there? Does it change between points A and B? What happens to the shear force at point B?
 

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