Calculating Maximum Bending Stress of a Beam

In summary, a simply supported beam with a length of 5 m and a varying load from 0 to 20 kN/m needs to determine the position and magnitude of the maximum bending stress. The distance of the maximum load is 2.89 m from the left support and the maximum bending moment can be calculated as 11560. However, this calculation may not be correct according to the given second moment of area and distance from the neutral axis.
  • #1
MMCS
151
0
A uniform simply supported beam, 5 m long and having a cross-section as shown, is to support a load which varies linearly from zero at the left hand support to a magnitude of 20 kN/m at the right hand support. Determine the position and magnitude of the maximum bending stress.
ANS : 140 MPa, 2.89 m from left

Total load w*L/2 = 50,000
Load at distance x (w*x)/L

I know that distance of maximum load = L/sqrt3 = 2.89

So the maximum bending moment = (20,000*2.89)/5 = 11560

I have out this into the formula M*Y/I =σ but get an incorrect answer

Unfortunately the picture with dimensions is unable to upload but it is an I beam with a second moment of area as 0.00003813 and a distance from the neutral axis as 0.1

Thanks
 
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  • #2
It would be nice to know what your incorrect answer was.
 
  • #3
MMCS said:
So the maximum bending moment = (20,000*2.89)/5 = 11560
I agree with the 2.89 but not the 11560 (I get 32075). What's the rationale for that equation?
 

FAQ: Calculating Maximum Bending Stress of a Beam

1. What is maximum bending stress of a beam?

The maximum bending stress of a beam is the highest amount of stress that a beam can withstand before it starts to deform or break.

2. How is maximum bending stress calculated?

To calculate maximum bending stress of a beam, you need to know the beam's material properties, geometry, and the applied loads. The formula for maximum bending stress is: σ = (M * c) / I, where σ is the maximum bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost point of the beam, and I is the moment of inertia of the beam.

3. What are the units of maximum bending stress?

The units of maximum bending stress are Newton per square meter (N/m²) in the SI system and pounds per square inch (psi) in the imperial system.

4. How does the shape of a beam affect its maximum bending stress?

The shape of a beam directly affects its maximum bending stress. For example, a rectangular beam will have a higher maximum bending stress than a circular beam of the same material and length. This is because the moment of inertia (I) is larger for a rectangular beam, making it more resistant to bending forces.

5. Why is it important to calculate maximum bending stress of a beam?

Calculating maximum bending stress is important for ensuring the structural integrity and safety of a beam. It helps engineers and designers determine the appropriate size and material for a beam to withstand the expected loads and prevent failure. Additionally, knowing the maximum bending stress can help identify any potential weak points in the beam and allow for necessary reinforcements.

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