Determine deflection and deflection angle using Unit Load Method

In summary, the deflection angle of a simply supported beam is given by the equation θ = 5EI/L3 x (L2 - 4x2) and the limit taken for calculating the deflection Yc is from 0 to L/2 due to the symmetry of the beam.
  • #1
Homework Statement
attached below
Relevant Equations
attached below
relevant equations:
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My questions:
(1)Not sure whether I did correct especially for the deflection angle
(2)The limit taken for calculating defection Yc , I didn't understand why is from 0 to L/2 instead of the sum of 0 to L/2 and 0 to L, how is the limit determined?

Kindly advise, thanks
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  • #2
!The deflection angle of a simply supported beam is given by the equation:θ = 5EI/L3 x (L2 - 4x2)where E is the elastic modulus, I is the moment of inertia, and L is the length of the beam.For your question (1), it looks like you have correctly calculated the deflection angle.For your question (2), the limit taken for calculating the deflection Yc is from 0 to L/2 because the deflection of a simply supported beam is symmetric about the midpoint, so only one-half of the beam needs to be considered. The limit from 0 to L/2 is valid for any simply supported beam.
 

1. What is the Unit Load Method?

The Unit Load Method is a structural analysis technique used to determine the deflection and deflection angle of a beam or structure under a given load. It involves breaking down the load into smaller, unit loads and calculating the deflection caused by each unit load. The deflection and deflection angle can then be determined by summing up the individual deflections.

2. How is the Unit Load Method different from other structural analysis methods?

The Unit Load Method is a simplified approach to structural analysis compared to other methods such as the Moment-Area Method or the Virtual Work Method. It is based on the principle of superposition, where the overall deflection of a structure is calculated by adding up the deflections caused by individual loads. This makes it a quick and easy method to use for simple beam structures.

3. What are the steps involved in using the Unit Load Method?

The first step is to determine the support reactions of the beam or structure under the given load. Next, the load is broken down into unit loads and their corresponding deflections are calculated using the beam deflection formula. The deflections are then summed up to determine the total deflection and deflection angle of the structure.

4. What are the assumptions made in the Unit Load Method?

The Unit Load Method assumes that the beam or structure is linearly elastic, meaning that it follows Hooke's Law and the deflection is directly proportional to the applied load. It also assumes that the beam is initially straight and that the deflections are small compared to the beam's length.

5. Can the Unit Load Method be used for all types of structural analysis?

No, the Unit Load Method is best suited for analyzing simple beam structures with concentrated loads. It may not be accurate for more complex structures or those with distributed loads. In those cases, other methods such as the Moment-Area Method or the Finite Element Method may be more appropriate.

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