Deflection by Moment Area Method

In summary, the conversation discusses a problem involving a cantilever beam with a triangular uniform load. The goal is to find the slope and deflection at the end using the moment area method. However, the solution obtained by the individual does not match the textbook solution. The conversation further mentions the use of the First and Second Moment Theorems to calculate the slope and deflection respectively. The individual suggests that the incorrect bending moment expression may be the reason for the discrepancy. They recommend drawing a shear force diagram and using it to develop the bending moment diagram.
  • #1
obrien040362
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0

Homework Statement


The problem is a cantilive beam of length L with a triangular uniform load or W. The solution is to find the slope and deflection at the end by moment area method. My solution is not matching the textbook solution of wl^3/8EI and 11wL^4/120EI

Homework Equations


First Moment Theorem - Slope equal to the area under the M/EI diagram
Second Moment Therorem - Deflection is equal to the moment of the moment area about the point you want the deflection.[/B]


The Attempt at a Solution


see uploaded file[/B]
 

Attachments

  • 20141030113155722.pdf
    85.8 KB · Views: 250
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  • #2
I think the reason your moment-area calculations aren't working is that your bending moment expression is incorrect.

I would draw the shear force diagram and develop the bending moment diagram from it.
 

1. What is the Deflection by Moment Area Method?

The Deflection by Moment Area Method is a structural analysis technique used to determine the deflection of a beam or structure subjected to a combination of loads and moments.

2. How does the Deflection by Moment Area Method work?

The method involves calculating the area under the bending moment diagram of the beam or structure, which represents the work done by the applied loads and moments. This area is then used to determine the deflection at any point along the beam.

3. What are the advantages of using the Deflection by Moment Area Method?

One advantage is that it can be used to analyze statically indeterminate structures, which cannot be solved using other methods such as the equations of equilibrium. It also provides a more accurate solution compared to other approximate methods.

4. Are there any limitations to using the Deflection by Moment Area Method?

Yes, the method can only be used for linearly elastic materials and assumes that the beam or structure is subjected to small deflections. It also does not take into account any effects of shear or axial forces on the deflection.

5. How is the Deflection by Moment Area Method different from other deflection analysis methods?

The Deflection by Moment Area Method is a more rigorous and accurate method compared to other approximate methods such as the double integration method. It also provides a more general solution that can be applied to a wider range of structures and loading conditions.

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