Calculating Section Modulus for Beam with UDL

In summary, the section modulus for a beam with a uniform distributed load can be calculated by dividing the moment of inertia by the distance from the neutral axis to the outermost fiber of the beam. The moment of inertia for a beam with a UDL can be calculated using the formula I = (b * h^3) / 12. A higher section modulus indicates a stronger beam, as it can withstand a greater bending moment. The section modulus can be negative if the neutral axis is outside of the cross-section, indicating that the beam will be in compression. The maximum bending moment for a beam with a UDL can be calculated using the formula M = wL^2/8 at the center of the beam.
  • #1
josh16
3
0

Homework Statement



I want to know the section modulus for a beam which has a UDL of 13.5 kn/m across 10 metres. Its simply supported at both ends. max allowable stress = 255 MPa

Homework Equations



Z= M / max allowable stress [cm^3]


The Attempt at a Solution



max bending moment = 13.5 x 10 ^2 / 8 = 168.75 kn/m

168.75 x 10^3 / 255 x 10^6 = 6.617647059 x 10 ^ -4 = 661 cm^3

Thanks,
Josh
 
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  • #2
The section modulus is a property of the geometry of the beam's cross-sectional area. What you are calculating is the minimum section modulus which a candidate beam must have in order keep the bending stresses below the max. allowable stress.
 

1. How do you calculate the section modulus for a beam with a uniform distributed load?

The section modulus for a beam with a uniform distributed load can be calculated by dividing the moment of inertia of the cross-section by the distance from the neutral axis to the outermost fiber of the beam. This can be represented by the equation Z = I / c, where Z is the section modulus, I is the moment of inertia, and c is the distance from the neutral axis to the outermost fiber.

2. What is the formula for calculating the moment of inertia for a beam with a UDL?

The moment of inertia for a beam with a uniform distributed load can be calculated using the formula I = (b * h^3) / 12, where b is the width of the beam and h is the height of the beam.

3. How does the section modulus affect the strength of a beam?

The section modulus is a measure of a beam's resistance to bending. A higher section modulus indicates a stronger beam as it can withstand a greater bending moment without failing.

4. Can the section modulus be negative?

Yes, the section modulus can be negative if the neutral axis of the beam is located outside of the cross-section. This indicates that the beam will be in compression rather than tension when subjected to a bending moment.

5. How do you determine the maximum bending moment for a beam with a UDL?

The maximum bending moment for a beam with a uniform distributed load can be calculated using the formula M = wL^2/8, where w is the magnitude of the UDL and L is the length of the beam. This occurs at the center of the beam, where the bending moment is at its highest.

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