How to rearrange to find the height of a hollow beam

In summary, the conversation discusses a problem with finding the vertical dimension of a new hollow rectangular beam with a reduced weight but the same maximum bending stress as a solid rectangular beam. The formula M=550 is given and the equation for maximum stress is mentioned. The solution involves solving for the ratio of c/I and setting it equal to c/I for the hollow beam, then solving for the height of the beam.
  • #1
bobmarly12345
27
0

Homework Statement


i had a solid rectangular beam of max stress equalling 1.65x10^6N/m²
a new beam, a hollow rectangular beam is made to reduce weight, it has the same maximum bending stress 1.65x10^6N/m² but this time has a horizontal dimension of 0.2m and a constant wall thickness of 0.02.
i need to find the vertical dimension but am really having trouble rearranging the formula

M=550


Homework Equations



I=B.D^3/12 - b.d^3/12

max stress = MY/I

The Attempt at a Solution



1.65x10^6 N/m²= 12X550/(BD^3-bd^3)
then
(BD^3-bd^3)=12x550/1.65x10^6

having trouble getting the D value to equal a calculation
 
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  • #2
You know M and you know the stress for each beam.

Sigma = Mc/I

Solve the above for the ratio of c/I, a number. Then set that number equal to c/I for the hollow beam taking the wall thickness into consideration. Solve equation for the height of the hollow beam.
 

Related to How to rearrange to find the height of a hollow beam

1. How do I find the height of a hollow beam?

To find the height of a hollow beam, you will need to use the formula: height = (moment of inertia * load) / (maximum stress * width). This formula takes into account the maximum stress the beam can handle, the load placed on the beam, and the width of the beam. It is important to have accurate measurements for each of these variables to get an accurate result.

2. What is the moment of inertia?

The moment of inertia is a measurement of an object's resistance to changes in its rotational motion. In the case of a hollow beam, it is a measure of how the beam's shape and size affect its ability to support a load. A larger moment of inertia indicates a stronger beam.

3. How can I determine the maximum stress of a hollow beam?

The maximum stress of a hollow beam can be determined by calculating the bending stress at the point of interest. This can be done using the formula: maximum stress = (M * c) / (I * y), where M is the bending moment, c is the distance from the neutral axis to the point of interest, I is the moment of inertia, and y is the distance from the neutral axis to the farthest point of the beam.

4. What if I don't know the load placed on the beam?

If you do not know the exact load placed on the beam, you can estimate it based on the type of load the beam is expected to support. For example, if the beam is supporting a uniformly distributed load, you can use the formula: load = (w * L) / 2, where w is the weight per unit length and L is the length of the beam.

5. Can I use this formula for any type of hollow beam?

This formula can be used for most types of hollow beams, as long as the beam is subjected to bending stress and the material properties are known. However, it is always best to consult a structural engineer for more accurate and specialized calculations for specific beam designs.

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