Structural Engineering - Deflection

In summary, the formula for calculating the deflection of a simply supported beam with a load in the center of the span is \delta = (PL^3)/(48EI), where P is the load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. In this problem, the load is 6,000 pounds, the beam is 50 feet long, the modulus of elasticity is 29,000,000 psi, and the moment of inertia is 850 inches^4. The resulting deflection is 1.0953 inches.
  • #1
bbg5000
14
0
I'm not sure the formula to use to calculate the deflection of a beam. Here's the information I have got.

Steel beam is 50 feet long. There is a 6,000 pound load in the middle(all other loads are disregarded. The modulus of elasticity is 29,000,000 psi. Moment of inertia is 850 inches^4. There are simple pin connections at either end.

What would be the formula for calculating this?? :D An answer would be nice to :approve: lol
 
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  • #2
The beam deflection for a simply supported beam with a load in the center of the span (neglecting the beam's own mass) is:

[tex]\delta = (PL^3)/(48EI) [/tex]

Where:
[tex]\delta[/tex] = Deflection
P = Load
E = Modulus of Elasticity (Young's Modulus)
I = Moment of Inertia
 
  • #3
FredGarvin said:
The beam deflection for a simply supported beam with a load in the center of the span (neglecting the beam's own mass) is:

[tex]\delta = (PL^3)/(48EI) [/tex]

Where:
[tex]\delta[/tex] = Deflection
P = Load
E = Modulus of Elasticity (Young's Modulus)
I = Moment of Inertia

What's the L mean?! And the 48? Does the length of the beam have no place in the calculation?

So [tex]\delta = (PL^3)/(48EI) [/tex] would be:

6000^3 / 48 x 29,000,000 x 850^4 = 0.000000000297261601 ?
 
  • #4
The equation specified is for the maximum deflection (i.e. at mid point) of this simply supported beam.

L is the beam length between hinges.

48 is a value coming from the solution of the beam equation for this beam, load (pointwise at midpoint) and boundary conditions (hinges).

This problem has been asked in the Homework: College Level forum.
 
Last edited:
  • #5
My apologies for the omission.

Thanks for the cover Astronuc
 
  • #6
bbg5000 said:
What's the L mean?! And the 48? Does the length of the beam have no place in the calculation?

So [tex]\delta = (PL^3)/(48EI) [/tex] would be:

6000^3 / 48 x 29,000,000 x 850^4 = 0.000000000297261601 ?


You want your deflection in inches, so your length is 300", not 25'.
The way I read it, it would be (6000 x 300^3) / (48 x 29,000,000 x 850^4)
= (6000 x 27,000,000) / (48 x 29,000,000 x 522,006,250,000)
From there, it's simple math. My kid asked me how to do this. It's a
neopets.com "Lenny Conundrum" puzzle...
 
  • #7
deflection

I too am trying to work out the Lenny Conundrum. The length is 50 feet, so 600 inches :wink:
And after using all those calculations, I came up with a very incorrect answer! 1.78 inches as the deflection? I don't think I'm doing this correctly! :confused:
 
  • #8
The weight is at the center of the 50 foot beam, not the end...
 
  • #9
There seems to be some confusion regarding the moment of inertia (850^4)as reflected by the use in the forumula above.

FredGarvin posted the equation for the maximum deflection for this problem, which so happens to be at the location of the load, the midpoint of the beam.

P = 6000 lbf
L = 50 ft = 600 in
E = 29,000,000 psi (lbf/in2)
I = 850 in4

units must be consistent.

So sustituting the values into the equation above

[tex]\delta = (6000\,psi * (600\,in)^3)/(48*29,000,000\,lbf/in^2 * 850\,in^4) [/tex] = 1.0953 in

To the units should cancel with the result that the deflection [tex]\delta[/tex] is given in units of 'in' or inches.
 

1. What is deflection in structural engineering?

Deflection in structural engineering refers to the displacement or bending of a structural element under a load. It is a measure of the flexibility and stability of a structure and can affect its overall performance and safety.

2. How is deflection calculated in structural engineering?

Deflection can be calculated using various methods, depending on the type of structure and the type of loading it is subjected to. The most common method is using the Euler-Bernoulli beam theory, which considers the material properties, geometry, and applied loads to determine the deflection at a specific point on a beam.

3. What are the factors that can affect deflection in structural engineering?

There are several factors that can affect deflection in structural engineering, including the type of material used, the shape and size of the structural element, the magnitude and distribution of the load, and the support conditions. Other factors such as temperature and moisture can also play a role in deflection.

4. How does deflection impact the design of a structure?

Deflection is a critical factor in the design of a structure as it can affect its strength, stability, and overall performance. Excessive deflection can lead to structural failure, while insufficient deflection can result in a stiff and rigid structure that is not able to absorb and distribute loads effectively.

5. How can deflection be controlled in structural engineering?

There are various methods to control deflection in structural engineering, such as increasing the size or stiffness of the structural element, adding additional supports, or changing the type of material used. Computer-aided design and analysis tools are also used to optimize and minimize deflection in structural designs.

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