# Deflection of Prismatic Beam With Fixed Ends and Single Load

• Satonam
In summary, the conversation discusses the process of solving statically indeterminate beam deflection problems and the challenges of achieving confidence in the solutions. The speaker attempted to recreate standard equations but encountered unexpected results. They also express their desire to have validation for their solutions in order to provide accurate results for their employer.
Satonam
I've been refreshing my mind with regards to solving statically indeterminate beam deflection problems. In an effort to achieve confidence over my solutions, I attempted to recreate the standard equations in Figure 1. In my problem, I changed it so that:

• a = b = L/2
• Ay = R1
• By = R2
• etc.
However, while I expected the equations to naturally spit out Ay = By = P/2 as one would expect, I got By = P and Ay = 0. Can you find Waldo in Figure 2 and 3?

Figure 1

Figure 2

Figure 3

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Why not use the equations as written with your numbers rather than try to refactor it?

Due to my inexperience in a real engineering environment, I don't feel confident using an equation I can't even derive. Since I won't have a professor to tell me I'm right after graduation, I'm trying to figure out how to create that validation on my own so that I can provide my employer with a solution I know will work.

## 1. What is the equation for calculating the deflection of a prismatic beam with fixed ends and a single load?

The equation for calculating the deflection of a prismatic beam with fixed ends and a single load is:
δ = (PL^3)/(48EI)
Where δ is the deflection, 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.

## 2. How do fixed ends affect the deflection of a prismatic beam?

Fixed ends restrict the movement of the beam, causing it to resist deflection more than if it had simply supported ends. This results in a smaller deflection for the same applied load.

## 3. What is the significance of a single load in the deflection of a prismatic beam with fixed ends?

A single load is significant because it allows for a simpler calculation of deflection compared to multiple loads. It also represents a common scenario in real-world applications.

## 4. Can the deflection equation be used for other types of loads?

Yes, the deflection equation can be used for other types of loads as long as the beam is prismatic and has fixed ends. However, the equation may need to be modified for non-uniform or distributed loads.

## 5. How does the moment of inertia affect the deflection of a prismatic beam with fixed ends and a single load?

The moment of inertia is a measure of a beam's resistance to bending. A larger moment of inertia results in a smaller deflection for the same applied load, meaning that beams with a larger moment of inertia will be stiffer and less likely to bend under load.

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