Direct Integration Method for Deflection

In summary, the problem is to determine the slope and deflection of a 4m long beam fixed to a wall at one end and free on the other, with a 50KN*m clockwise moment acting on the free end. The solution involves using the equation d2y/dx2=M/EI and setting x=0 at the fixed support and x=4 at the free end. The answers are expected to be .0174rad for slope and 34.8 mm for deflection.
  • #1
craig22
5
0

Homework Statement


I'm given a 4m long beam that is fixed to a wall at the left end and is free on the other end. There is an external 50KN*m clockwise moment acting on the free end. I need to know the slope and deflection of the free end.


Homework Equations


d2y/dx2=M/EI



The Attempt at a Solution


I know that the reaction moment at the fixed support is 50KN*m. There are no x or y direction components, so all I have to work with are the moments. When I pass a section through the beam, how do I get my equation together from there?

The answers are supposed to be .0174rad and 34.8 mm
 
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  • #2
Presumably, you know E and I, or the product EI.
Let x=0 at the fixed support, and x=4 at the free end. Can you write down the function for M at x?
 
  • #3
I figured it out, thanks
 

FAQ: Direct Integration Method for Deflection

What is the Direct Integration Method for Deflection?

The Direct Integration Method for Deflection is a mathematical technique used to calculate the deflection of a beam or structure under a given load. It involves solving differential equations to find the equation of the deflected shape of the structure.

What are the advantages of using the Direct Integration Method for Deflection?

The Direct Integration Method for Deflection is a more accurate and precise method compared to other approximate methods. It also takes into account the varying load and support conditions along the length of the beam, making it more versatile.

How does the Direct Integration Method for Deflection work?

The method involves breaking down the beam into small segments and calculating the deflection at each point using basic principles of mechanics and differential equations. These deflections are then integrated to find the overall deflection of the beam.

What are the limitations of the Direct Integration Method for Deflection?

The Direct Integration Method for Deflection can become quite complex and time-consuming for structures with irregular shapes or varying cross-sections. It also assumes that the material of the beam is homogenous and isotropic, which may not always be the case.

How is the Direct Integration Method for Deflection used in engineering?

The Direct Integration Method for Deflection is commonly used in structural analysis and design to determine the deflection of beams and other structures. It is also used to optimize designs and ensure the safety and stability of structures under different loading conditions.

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