Bending of Beams Questions

In summary, the conversation discusses the calculation of the maximum bending moment that a symmetrical section with timber flanges (50x100 c.s.a) can carry. The maximum stress is given as 1.0N/mm^2, and the dimensions of the central beam and flanges are provided. After working through the calculations, it is determined that the maximum bending moment is 4.3kNm. However, there is confusion over the problem and further clarification is needed to correctly interpret the question.
  • #1
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Calculate the maximum B.M the symmetrical section can carry Plyweb with timber flanges (50x100 c.s.a) The maximum stress = 1.0N/mm^2

The structure is essentially an I beam with dimensions as follows.

The central beam has a width of 25 and height of 500.

The four flanges which constitute the I shape have each a width of 50 and height of 100 and are flush with the top and bottom of the central beam.

Since no units are given I have assumed all dimensions are in mm.




B.M = W.L / 4 The Answer = 4.3kNm



Total force acting upon the beam is the udl of 1.0N/mm2.
Total width is 125mm therefore w = 125x1 = 125 N.

W.L / 4 = 125^2 / 4 = 3906.25 Nm which is clearly wrong with respect to the answer given.

Working backwards. 4300 N = W.L / 4 gives (4300 x 4) / L (where L = 125) gives a value of W = 137.6


Any help would be appreciated as I am majorly confused over such a simple problem.
 
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  • #2
I don't believe you are interpreting the problem correctly. It appears to be asking that given the allowable bending stress of the material is 1 N/mm^2, calculate the moment of inertia of the cross section and determine the maximum bending moment that the section is capable of supporting, without exceding the allowable bending stress in the flanges. It is not asking for loading, nor does it give a span length or support conditions.
 
  • #3


I would first clarify with the person who provided the question whether the dimensions given are in mm or some other unit. This is important in order to ensure accurate calculations and results.

Assuming the dimensions are in mm, the maximum bending moment (B.M) that the symmetrical section can carry can be calculated using the formula B.M = W.L/4, where W is the total force acting upon the beam and L is the length of the beam.

Given that the maximum stress is 1.0N/mm^2 and the total width of the beam is 125mm, we can calculate the total force acting upon the beam as 125mm x 1.0N/mm^2 = 125N.

Substituting this value into the formula, we get B.M = (125N x 125mm)/4 = 3906.25Nm. This is the maximum bending moment that the beam can carry.

However, the answer provided is 4.3kNm, which is equivalent to 4300Nm. This is significantly higher than the calculated value of 3906.25Nm. It is possible that there is an error in the given answer, or that the dimensions provided are not accurate.

I would recommend double-checking the dimensions and clarifying with the person who provided the question to ensure accurate calculations and results. Additionally, it may be helpful to consult with a structural engineer for a more detailed analysis and to ensure the safety and stability of the structure.
 

1. What is the definition of bending of beams?

Bending of beams refers to the deformation or curvature of a beam under the influence of external forces or loads.

2. What are the types of loads that can cause bending of beams?

The types of loads that can cause bending of beams include point loads, uniformly distributed loads, and moments.

3. What is the equation for calculating the bending stress of a beam?

The equation for calculating the bending stress of a beam is σ = (M * y) / I, where σ is the bending stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.

4. What is the difference between a simply supported beam and a cantilever beam?

A simply supported beam is supported on both ends, while a cantilever beam is supported only on one end, with the other end free.

5. How does the material of a beam affect its bending behavior?

The material of a beam can affect its bending behavior by influencing its stiffness and strength. Different materials have different elastic moduli and yield strengths, which can impact the amount of bending a beam can withstand before failing.

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