Calculating maximum shear in a steel beam cantilever

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SUMMARY

The discussion focuses on calculating the maximum shear in a cantilever steel beam, emphasizing the importance of understanding shear stress and reaction forces. The maximum shear load for steel is noted as 14,000 lb/in². Key equations provided include V = dM/dx for shear and d²M/dx² = -w for load intensity. The process involves determining the resultant of the distributed load, calculating reaction forces, and analyzing the beam in sections to assess shear and bending moments.

PREREQUISITES
  • Understanding of cantilever beam mechanics
  • Familiarity with shear and bending moment diagrams
  • Knowledge of equilibrium conditions in structural analysis
  • Basic proficiency in calculus for applying differential equations
NEXT STEPS
  • Study the principles of shear and bending moment calculations in cantilever beams
  • Learn about the use of free body diagrams in structural analysis
  • Explore advanced topics in beam deflection and stress analysis
  • Review the application of the maximum shear stress theory in design compliance
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in the design and analysis of steel structures will benefit from this discussion.

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Problem:

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I do not know how to approach this problem. For a beam which has two reactions, the shear stress is equivalent to the reaction.

I suppose that the stress is calculated using moment some how. But how?

For seeing if the beam is allowable stress design compliant, you can use the maximum shear load of steel, which is 14,000lb/in^2
 
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maybe try using these equations: V = \frac{dM}{dx} and \frac{d^{2}M}{dx^{2}} = - w Where V is the shear, M is the moment, and w is the intensity of the load...
 
So I think you'll need to do something like this, find the resultant of the distributed load and where it acts (at the centroid of the beam), calculate the reaction forces, and then break the beam into sections to find the shear and bending moment...
 
It's a cantilevered beam. There is only one point on the beam which needs to be checked for shear and bending moment.

In any event, the first order of business is to solve for the reactions which keep the free body of this beam in equilibrium.
 

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