Cantilever Beam subjected to shear stress

In summary, the problem involves determining a stress function psi for a cantilever beam with given dimensions and boundary conditions. The shear stress and boundary conditions can be expressed as equations, and the constants can be solved for using these equations.
  • #1
L.Richter
21
0

Homework Statement


A cantilever beam (length, L, height, 2h, thickness 1). The top surface is subjected to shear stress tsubxy = s. Determine the stress function psi. The boundary conditions at the end of the free end (x=L) can be satisfied by integration (e.g., traction free can be expressed by integral from -h to h of sigma x dy = 0).


Homework Equations



Y runs vertical along the wall. X entends to the right. The shear stress runs along the +x direction.

The Attempt at a Solution



The only thing I need are the boundary conditions. I can solve for psi and the constants as long as I have the starting equations found from the boundary conditions. I am terrible at boundary conditions!
 
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  • #2
Got the boundary conditions! And now I'm working on solving the constants from these equations:

-B - 2Dx + 2Eh = 0
2A + 6Cx - 2Dh = 0
-B - 2Dx - 2Eh = -sx/I
2A + 6Cx + 2Dh = 0

Odd system of equations.
 

FAQ: Cantilever Beam subjected to shear stress

1. What is a Cantilever Beam?

A Cantilever Beam is a type of structural element that is supported at one end and free at the other end. It is commonly used in construction and engineering projects to support loads and transfer them to the support structure.

2. How is a Cantilever Beam subjected to shear stress?

When a force is applied perpendicular to the length of the beam, it causes the beam to bend. This bending creates internal shear stress, which is the force that acts parallel to the cross-section of the beam. In a cantilever beam, the shear stress is highest at the fixed end and decreases towards the free end.

3. What factors affect the shear stress in a Cantilever Beam?

The shear stress in a Cantilever Beam is influenced by several factors, including the magnitude and direction of the applied load, the length and cross-sectional shape of the beam, and the material properties of the beam, such as its modulus of elasticity and shear modulus.

4. How is shear stress calculated in a Cantilever Beam?

The formula for calculating shear stress in a Cantilever Beam is τ = VQ/Ib, where τ is the shear stress, V is the applied shear force, Q is the first moment of area of the cross-section, I is the moment of inertia about the neutral axis, and b is the width of the beam. These values can be determined through mathematical calculations or by using specialized software or testing equipment.

5. How does shear stress affect the strength and stability of a Cantilever Beam?

Shear stress can significantly impact the strength and stability of a Cantilever Beam. Excessive shear stress can cause the beam to deform or fail, leading to structural failure. Therefore, engineers must carefully consider the shear stress when designing and analyzing Cantilever Beams to ensure they can withstand the intended loads and maintain their structural integrity.

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