# Slope and deflection of beam sample problem question

• Umayer
In summary, a student is struggling with a sample problem that requires using superposition to determine the slope and deflection of a beam. They have tried converting angles to degrees and using sine, but have not been able to find the correct solution. They are seeking an explanation for why the angle was multiplied by the length of the straight beam in the solution.

## Homework Statement

The sample question explains how I can use superposition to determine the slope and deflection of the beam. I have made a picture of the page. I know how to use the method as I've used it on other, much difficult problems. However, this sample problem has been stuck in my head for a quite long time. The problem starts by determining the deflection at the end of the beam. I've underlined the equation where I'm confused.

This is the sample problem.

https://www.dropbox.com/s/x025uvs253hne0f/Sample problem.jpg

I understand that by superposing the beam into two separate loadings, you can add the maximum deflection of those two in order to attain the maximum deflection of the original beam. In loading II, the beam goes straight half through so the angle is the same at the end of the beam. But in the book, they multiplied the angle with length of the part that goes straight. I have absolutely no idea why they did that. The angle is in radians and within my knowledge it made no sense to me.

## Homework Equations

Case 1

http://4.bp.blogspot.com/-wVZ-cJsAc...QgKKf2Q/s1600/beam+deflections+and+slopes.png

## The Attempt at a Solution

I converted the angle into degrees and then used sinus on that. Then I multiplied with the length of the straight beam but that didn't really gave me the answer I hoped for. I tried to look on the internet up if there was a relation between them but I couldn't find the answer.A huge thanks to anyone who can explain to me what they did!

Last edited:
For small angles (in radian measure), sin(theta) is approximately equal to theta.

1 person
Thanks alot!

## 1. What is the formula for calculating the slope of a beam?

The formula for calculating the slope of a beam is: S = (M x L^2) / (2EI), where S is the slope, M is the bending moment, L is the length of the beam, E is the elastic modulus, and I is the area moment of inertia.

## 2. How do you find the deflection of a beam?

The deflection of a beam can be found using the formula: D = (5WL^4) / (384EI), where D is the deflection, W is the load applied, L is the length of the beam, E is the elastic modulus, and I is the area moment of inertia.

## 3. Can slope and deflection be calculated for any type of beam?

Yes, the slope and deflection can be calculated for any type of beam as long as the beam is subjected to a load and has known properties such as length, elastic modulus, and area moment of inertia.

## 4. How does the load applied affect the slope and deflection of a beam?

The load applied has a direct impact on the slope and deflection of a beam. As the load increases, the slope and deflection also increase. This is because a higher load causes a higher bending moment, resulting in a larger slope and deflection.

## 5. What is the significance of calculating the slope and deflection of a beam?

Calculating the slope and deflection of a beam is important in structural engineering as it helps determine the stability and strength of a structure. It also helps in designing beams that can withstand the expected load without failing or causing excessive deflection.