Solve Cantilever Beam: End Load 20kN, EI=40KNm^2, Length 0.25m

In summary, the conversation discusses using integration to determine the slope at the free end of a cantilever beam with an end load of 20kN and an EI value of 40 KNm^2. The fundamental equation d^2y/dx^2 = M/EI is mentioned, but the speaker is unsure how many times it needs to be integrated. The hint given is to think of the slope as the first derivative, representing the rotation of the beam's cross section. The conversation ends with a suggestion to consult a mechanics of materials book to better understand the meaning of the y in the differential equation.
  • #1
johnboy14
22
0

Homework Statement



A cantilever beam carriers an end load of 20kN and has an EI value of 40 KNm^2. If the beam is 0.25m long, use intergration to determine

the slope at the free end of the beam?



Homework Equations



I know from a handout I have that the fudamental equation to use is

d^2y/dx^2 = M/EI

when I substitute this I get EI X d^2y/dx^2 = WU(l - x)

This is where I am stuck? Any help much appricated
 
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  • #2
Hint: the slope means 'first derivative', i.e. the rotation of the cross section of the beam.
 
  • #3
Not with you? I think you have to intergrate it but Not sure how many times though.
 
  • #4
Do you know what the y means in that differential equation? open up your mechanics of materials book and look it up, then you'll understand what radou said.
 

1. What is a cantilever beam?

A cantilever beam is a structural element that is supported at only one end, with the other end free to move. It is commonly used in construction and engineering to support roofs, bridges, and other structures.

2. How do I solve for the end load of 20kN?

To solve for the end load of 20kN, you will need to use the equation F = P x L, where F is the end load, P is the distributed load, and L is the length of the beam. In this case, the end load is given as 20kN, so you will need to solve for P by dividing 20kN by the length of the beam (0.25m).

3. What does EI=40KNm^2 mean?

EI is a measure of the stiffness of the beam, where E is the modulus of elasticity and I is the moment of inertia. In this case, EI=40KNm^2 means that the stiffness of the beam is 40KNm^2.

4. How do I calculate the deflection of the cantilever beam?

To calculate the deflection of the cantilever beam, you will need to use the formula δ = FL^3 / 3EI, where δ is the deflection, F is the end load, L is the length of the beam, and E and I are the modulus of elasticity and moment of inertia, respectively. You can plug in the given values to solve for the deflection of the beam.

5. Can I use this information to solve for other types of beams?

Yes, the equations and principles used to solve for the end load and deflection of a cantilever beam can also be applied to other types of beams. However, the specific values for load, length, and stiffness may differ depending on the type of beam. It is important to use the correct equations and values for the specific type of beam being analyzed.

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