# Calculate Tip Deflection of Beam Under Applied Loads

• wildleaf
In summary, the conversation discusses calculating the tip deflection for a given beam with various loadings. The equations for deflection under a uniform load are provided, and the use of superposition is mentioned. The conversation also mentions using deflection tables for cantilever beams and using specific equations for different portions of the beam. The end goal is to calculate the maximum deflection at the tip of the beam.
wildleaf

## Homework Statement

E = 30 * 10^6 psi
I = 60 * 10^3 in^4

http://i52.tinypic.com/990xef.jpg

## Homework Equations

deflection for the uniform load is: w= -p/ (24*E*I)* [(x^4) - (4*L*x^3) + (6*L^2*x^2)]

You use this to calculate the uniform load of 1000 lb/ft. I think you use this for the weight of the beam (2000 lb/ft) as well, but i am not too sure.
I have solved the deflection function by hand and have checked on sites and it is the correct case for uniform load.

## The Attempt at a Solution

I know we have to use superposition, we have to separate them by uniform load of
1000 lb/ft, the 4000 lb load, 5000 lb load, and the weight of the beam itself... After I separate them, I solved for the deflection function for the uniform load of 1000 lb/ft.
I know that I need to do this for all four loads and then add them together at the end but I don't know how to calculate the deflection for the 4000 lb load, and 5000 lb load since they are not evenly spaced.

Check your deflection tables for a cantilever beam with a single load applied away from the end. You can calculate the deflection of the 4000# load by itself, and the 5000# load by itself. The total deflection at the free end is obtained by superposition.

there are two equations for one load for 4000 and two equations for 5000, Do use all 4 of them.. The two equations have a limit, the first equation is from the left end to the Force/load and second is from the Force/load to the right end. Here is the link: Look at case 2:

So i will have to use all 4 equations, 2 of each force, and add them?

If you look at Beam Type 2 and the equations for deflection y, note that each equation is applicable for a certain portion of the beam:

Eq. 1 - x is between the load P and the fixed end of the beam 0 < x < a
Eq. 2 - x is between the load P and the free end of the beam a < x < L

However, your problem asks you to calculate the tip deflection, so use the eq. in the right hand column (Max. deflection) of the table for dmax.

Thanks bro :)

## 1. How is tip deflection of a beam calculated?

The tip deflection of a beam can be calculated using the following formula: D = (5 * PL^3)/(384 * EI), where D is the tip 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. What are the units of measurement for tip deflection?

The units of measurement for tip deflection are typically in meters (m) or millimeters (mm), depending on the length of the beam and the units used for the other variables in the formula.

## 3. How does the applied load affect the tip deflection of a beam?

The applied load has a direct relationship with the tip deflection of a beam. As the applied load increases, the tip deflection also increases. This is because the beam experiences greater stress and strain under increased loads, causing it to bend more.

## 4. What factors can affect the accuracy of the tip deflection calculation?

The accuracy of the tip deflection calculation can be affected by several factors, including the assumptions made in the calculation, the material properties of the beam, and any external factors such as temperature or humidity that may affect the behavior of the beam.

## 5. Can the tip deflection calculation be used for all types of beams?

The tip deflection calculation can be used for most types of beams, as long as the beam is subjected to simple bending and the material properties are known. However, for more complex beam designs or materials, more advanced calculations may be necessary.

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