Calculating Combined Loading Stress: Neutral Axis and Bending Moment at Point A

In summary, the calculation of combined loading stress involves determining the neutral axis and bending moment at a specific point, referred to as Point A. The neutral axis is the line within a beam where the material experiences no tensile or compressive stress during bending. To find the bending moment at Point A, one must analyze the forces acting on the beam, considering both external loads and reactions at supports. By applying principles of static equilibrium and using the moment-area theorem, the combined stress at Point A can be accurately computed, allowing for a better understanding of the beam's structural integrity under varying loads.
  • #1
morpheus343
29
4
Left side is fixed and right side is held together by a non deformable plate. There are two members with space inbetween. My question is when i want to calculate the stress due to bending moment at point A, which is shown in the crossection, where is the neutral axis? Is it at the middle of the whole thing, where the dotted line is (at the height of the force P), or do i take each member (top and bottom) as individuals and assume the neutral axis at the middle of each beam (h/4*1/2).
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  • #2
To calculate the stress due to bending moment at point A in a structure with two members connected by a non-deformable plate, you should consider each member individually and determine the neutral axis for each member separately. rsdfgrgvfd
The neutral axis is the axis within a member where the stress due to bending is zero. In a symmetric cross-section, like the one you described, the neutral axis typically passes through the centroid of the cross-section.
For each member (top and bottom), you can assume the neutral axis to be at the centroid of that specific member's cross-section. This means that the neutral axis for the top member is at a distance of h/4 from the top surface, and the neutral axis for the bottom member is at a distance of h/4 from the bottom surface, where 'h' is the height of the entire cross-section.
So, you should analyze each member separately and calculate the bending stress at point A based on the neutral axis position for that member. The stress in the top member and the stress in the bottom member might be different, and you'll need to account for both in your calculations.
In summary, when calculating the stress due to bending at point A, treat each member as an individual beam and determine the neutral axis for each member separately, considering their individual cross-sections and dimensions. :)
 
  • #3
Thank you alot for your response. I have another question, i need to calculate the maximum shear forces and their planes at point B. Don't i need to be given the vertical force V that is causing the bending moment in order to find the transverse shear at point B using the τ=VQ/It formula and then use the general stress transformation formulas? I am only given the value of M and axial force P
 

FAQ: Calculating Combined Loading Stress: Neutral Axis and Bending Moment at Point A

What is combined loading stress?

Combined loading stress refers to the stress experienced by a structural element subjected to multiple types of loading simultaneously, such as axial load, bending moment, and torsion. This combined effect influences the overall stress distribution within the material.

How do you determine the neutral axis in a beam under combined loading?

The neutral axis in a beam under combined loading is determined by finding the location where the bending stress is zero. This involves calculating the centroid of the cross-sectional area and considering the effects of axial force and bending moments. The neutral axis shifts from the centroid if there are non-symmetric loads or non-uniform cross-sections.

What is the bending moment at a point, and how is it calculated?

The bending moment at a specific point in a beam is the internal moment that causes the beam to bend at that point. It is calculated by summing the moments about that point from all external forces and moments acting on the beam. This can be done using the principles of equilibrium and considering both the applied loads and the reactions at supports.

How do you calculate the combined stress at a point in a beam?

To calculate the combined stress at a point in a beam, you need to consider both the axial stress and the bending stress. Axial stress is calculated using the formula σ = P/A, where P is the axial load and A is the cross-sectional area. Bending stress is calculated using the formula σ = My/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. The total stress is the sum of these stresses.

Why is it important to consider the combined loading stress in structural design?

Considering combined loading stress in structural design is crucial because real-world structures are often subjected to multiple types of loads simultaneously. Ignoring the combined effects can lead to inaccurate predictions of stress distribution, which can result in structural failures, reduced safety margins, and inefficient use of materials. Proper analysis ensures that the structure can safely withstand the expected loads.

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