Calculating maximum shear in a steel beam cantilever

[KV-1]

Problem:

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

 

[_N3WTON_]

maybe try using these equations: [itex] V = \frac{dM}{dx} [/itex] and [itex] \frac{d^{2}M}{dx^{2}} = - w [/itex] Where V is the shear, M is the moment, and w is the intensity of the load...

 

[_N3WTON_]

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...

 

[SteamKing]

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.

 

[rezeew]

I would suggest approaching this problem by first understanding the basic principles of mechanics and structural engineering. The maximum shear stress in a cantilever beam can be calculated using the formula τ = VQ/Ib, where τ is the shear stress, V is the shear force, Q is the first moment of area, I is the moment of inertia, and b is the width of the beam.

To determine the shear force, you can use the basic principles of statics and equilibrium to analyze the forces acting on the beam. This would involve identifying all the external loads and reactions, and then using equations of equilibrium to solve for the unknown forces.

Once the shear force is determined, you can calculate the first moment of area and moment of inertia using the beam's cross-sectional properties. These can be found in a structural properties table for steel beams.

Finally, you can use the calculated values in the formula to find the maximum shear stress in the beam. If the calculated value is within the allowable stress limit for steel (14,000lb/in^2 in this case), then the beam would be compliant with the allowable stress design.

In addition, it is important to consider other factors such as the beam's material properties, loading conditions, and safety factors in order to design a safe and efficient structure. It may also be helpful to consult with a structural engineer for a more detailed analysis and to ensure compliance with building codes and standards.