Determine the absolute maximum bending stress of the beam.

• Sarah Henly
In summary, the conversation discusses determining the absolute maximum bending stress in a beam given a distributed load of 74 kN/m. It includes a calculation for the moment of forces on one side of a point, but notes that the calculation for the moment of inertia and the equivalent force at each end of the beam are incorrect. The conversation also suggests drawing a free body diagram of the beam and constructing shear force and bending moment diagrams to determine the maximum bending stress.
Sarah Henly

Homework Statement

If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa.

The Attempt at a Solution

I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6
F = 74*24*1000? [/B]

I assume that F is the upward force in Ns at each end, but it's 2.4m not 24m.
Pick a point at distance x <2.4m from one end. What is the moment of all the forces on one side of it about that point?

Sarah Henly said:

Homework Statement

If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa.

The Attempt at a Solution

I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6
F = 74*24*1000? [/B]
The calculation for I is wrong. This beam has an overall depth of 266 mm, not 256 mm.

The calculation of the equivalent force at each end of the beam is wrong. w = 74 kN / m and extends over a distance of 2.4 m at the ends. You can't ignore those pesky decimal points.

You should get in the habit of recording units with the results of each of your calculations. It eliminates confusion.

The first thing to do is to draw a free body diagram of the beam and find the reactions at each end which keep the beam in equilibrium.

Once you know all of the loadings on the beam, you can construct the shear force and bending moment diagrams to determine the max.bending stress.

1. What is the definition of absolute maximum bending stress?

Absolute maximum bending stress is the greatest amount of stress that a beam can withstand before it breaks or permanently deforms.

2. How is the absolute maximum bending stress calculated?

The absolute maximum bending stress is calculated using the formula σ = (M * c) / I, where σ is the stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the cross-sectional area of the beam.

3. What factors affect the absolute maximum bending stress of a beam?

The absolute maximum bending stress of a beam is affected by its material properties such as strength and elasticity, as well as its shape, size, and the magnitude and direction of the applied load.

4. Why is it important to determine the absolute maximum bending stress of a beam?

Determining the absolute maximum bending stress of a beam is important in ensuring the structural integrity and safety of the beam. It helps engineers and designers select the appropriate materials and dimensions for the beam to withstand the expected loads.

5. What are some common methods for reducing the absolute maximum bending stress of a beam?

Some common methods for reducing the absolute maximum bending stress of a beam include increasing its cross-sectional area, using a stronger material, adding support or reinforcement, and redistributing the load to multiple beams.

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