Normal stress on cantilever beam

In summary, a cantilever beam is a type of anchored beam commonly used in engineering to support structures. Normal stress, or axial stress, is the force acting perpendicular to a surface and is calculated using the formula σ = (M*y)/I. The amount of normal stress on a cantilever beam is affected by factors such as the applied load, beam length and shape, and material properties. Engineers use normal stress in the design of cantilever beams to determine their maximum load capacity and avoid structural failure.
  • #1
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Homework Statement



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Homework Equations



[tex]\sigma_x = -\frac{M(x)y}{I}[/tex]

[tex]I = \frac{bh^3}{3}[/tex]

The Attempt at a Solution



For point A, I did the following:

[tex]I = \frac{t(2h)^3}{3}[/tex]

[tex]I = \frac{8th^3}{3}[/tex]

[tex]\sigma_x = -\frac{3\tau_0}{4th}[/tex]

[tex]\tau_{yx} = -\tau_0[/tex]

[tex]\sigma_y = 0[/tex]

Are my principal stresses correct for point A? Also, would these principal stresses be the same for Point B?
 
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  • #2
A principal stress state contains no shear. Also, it's hard to imagine why A and B would be equivalent when the applied traction is creating a moment around the fixed end of the beam.
 

1. What is a cantilever beam?

A cantilever beam is a type of beam that is anchored at one end and free to move at the other end. It is commonly used in engineering and construction to support structures such as bridges, balconies, and roofs.

2. What is normal stress?

Normal stress, also known as axial stress, is the amount of force per unit area that is acting perpendicular to a surface. In the case of a cantilever beam, it is the force acting on the beam in the direction perpendicular to its length.

3. How is normal stress calculated on a cantilever beam?

The formula for calculating normal stress on a cantilever beam is: σ = (M*y)/I, where M is the bending moment, y is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the cross-sectional area of the beam.

4. What factors affect normal stress on a cantilever beam?

The amount of normal stress on a cantilever beam is affected 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 yield strength.

5. How is normal stress used in the design of cantilever beams?

Normal stress is an important consideration in the design of cantilever beams, as it helps engineers determine the maximum load that a beam can withstand without failing. By calculating the normal stress at different points along the beam, engineers can ensure that the beam is strong enough to support the intended load and avoid potential structural failure.

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