Max Bending Stress: Find from Second Moment of Area

In summary, the problem involves finding the maximum bending stresses, both tensile and compressive, in a simply supported beam with a concentrated load at its midpoint. The second moment of area of the beam about the neutral axis is given as 4x10^6mm^4 and the overall height of the beam is 120mm. The equation M/I = E/R = σ/y is used to find the maximum bending stress, where y is the distance from the neutral axis and m is the maximum bending stress. The value of m is not given and needs to be calculated using the given equation and information. More understanding of the bending stress formula is necessary to solve the problem.
  • #1
Simon green
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0

Homework Statement



The second moment of area of the beam shown about the neutral axis X X is 4x10^6mm^4

Find the maximum bending stresses, tensile and compressive, set up in a beam of this section 2.6m long and simply supported at its ends and carrying a concentrated load of 4.8kn at its mid point, the weight of the beam may be ignored

Unable to load the picture of this beam, it is a t shaped beam with the neutral axis XX running through the centre of the beam horizontally and 40mm from the top of the beam, it also has an overall height of 120mm

Homework Equations



M/I = E/R = σ/y

The Attempt at a Solution



As far as I am aware I need to use σ/y = m/I to find the correct answer, y = 40mm (distance from neutral axis)
I= 4x10^6mm^4 (second moment of area)
I am unsure about which values or how to work out either σ or m
 

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  • #2
You have the right equation and you are trying to find the bending stress. The value of I is given. Please let us know what is your understanding of y and m in your equation.
 
  • #3
I believe that y is the distance from the neutral axis (40mm) and m is the maximum bending stress? But m is not given is it? Do I have to transpose the formula to find m?
 
  • #4
Simon green said:
I believe that y is the distance from the neutral axis (40mm) and m is the maximum bending stress? But m is not given is it? Do I have to transpose the formula to find m?
the bending stress formula is one of the most useful equations for beams, so it should be thoroughly understood. The max bending stress is a function of the max bending moment (M) in the beam. You should read up on it more and resubmit your thoughts and attempt.
 

FAQ: Max Bending Stress: Find from Second Moment of Area

What is "max bending stress"?

"Max bending stress" refers to the maximum amount of stress or force that a material can withstand before it starts to deform or break under a bending load. It is an important factor to consider in engineering and structural design.

How is max bending stress calculated?

Max bending stress can be calculated using the formula σ = (M * c) / I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the point of interest, and I is the second moment of area. It is important to note that different materials have different values for their second moment of area and therefore have different max bending stress limits.

What is the role of second moment of area in finding max bending stress?

The second moment of area, also known as the moment of inertia, is a measure of a cross-sectional shape's resistance to bending. It is used to determine the stiffness and strength of a material under a bending load. In the formula for calculating max bending stress, the second moment of area is in the denominator, meaning that a larger value for I will result in a lower bending stress.

How does the shape of a material affect its max bending stress?

The shape of a material's cross-section has a significant impact on its max bending stress. Materials with larger and more compact cross-sections, such as I-beams or tubes, have a higher second moment of area and therefore a higher resistance to bending. On the other hand, materials with smaller or irregular cross-sections, such as wires or rods, have a lower second moment of area and are more susceptible to bending stress.

What are some factors that can affect a material's max bending stress limit?

Aside from the material's shape and second moment of area, other factors that can affect a material's max bending stress limit include its composition, temperature, and loading conditions. Different materials have different strengths and weaknesses, and these must be taken into account when calculating max bending stress. Additionally, extreme temperatures or excessive loading can weaken a material and lower its max bending stress limit.

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