Cantilever Beam - Maximum Strain @ Deflection

In summary, a rectangular beam with dimensions of 3mm width, 3.5mm height, and 40mm length is attached to a wall with a point load at 11mm from the wall. The required deflection at this point is 2.5mm. The maximum strain of the beam can be calculated using the material data sheet for the material. The attached image shows the beam held by a white body and a key used to deflect the beam to activate a snap at the end. Assistance is requested in calculating the maximum strain, and the individual regrets not having a BSC in Design for this task. Referencing Roark's "Formulas for Stress and Strain" may be helpful.
  • #1
mikesankey
1
0
Hello Folks,

I'm after a little help here, I've been asked to calculate the maximum strain a beam is under at a certain deflection, for a part we are planning to get Rapid Prototyped

It is a rectangular beam attached to a wall at one end

I have the material data sheet for the material, the beam is 3mm wide, 3.5mm high.

It is 40mm long, with a point load at 11mm from the wall

the required deflection is 2.5mm at this point

To explain the attached image, the beam is held by the white body, and the key deflects the beam to one side to activate the snap at the end of the beam

Would appreciate any help, I'm regretting doing a BA instead of a BSC in Design when it comes to things like this!.
 

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  • #2
See Roark: Formulas for Stress and Strain
 

1. What is a cantilever beam?

A cantilever beam is a structural element that is supported at only one end, while the other end is free to move. It is commonly used in construction and engineering projects to support loads and distribute weight.

2. What is maximum strain in a cantilever beam?

Maximum strain in a cantilever beam is the highest amount of deformation or elongation that the beam experiences under a given load. This can be calculated by dividing the change in length of the beam by its original length.

3. How is maximum strain related to deflection in a cantilever beam?

Maximum strain and deflection are directly related in a cantilever beam. As the beam deflects or bends under a load, the strain on the beam increases. The maximum strain occurs at the point of maximum deflection.

4. What factors affect the maximum strain in a cantilever beam?

The maximum strain in a cantilever beam is affected by several factors, including the material properties of the beam (such as its elasticity and strength), the magnitude and distribution of the load, and the beam's dimensions and geometry.

5. How is maximum strain @ deflection calculated in a cantilever beam?

The maximum strain @ deflection in a cantilever beam can be calculated using the formula ε = PL/3EI, where P is the applied load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the beam's cross-section. This formula is based on the assumptions of linear elastic behavior and small deflections.

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