Quck answer
To calculate the maximum bending stress in a beam, you need to know the moment of inertia, the distance from the neutral axis, and the applied load. The formula to calculate maximum bending stress is:
Maximum Bending Stress = (Applied Load * Distance from Neutral Axis) / Moment of Inertia
The moment of inertia represents the beam’s resistance to bending. The distance from the neutral axis is the distance between the point where the bending stress is calculated and the neutral axis of the beam. The applied load is the external force or weight that is causing the beam to bend. By plugging in these values into the formula, you can determine the maximum bending stress in the beam.
When metal is bent, one surface stretches while the other compresses, leaving an area of zero stress between them known as the neutral axis. The farthest surface from the neutral axis experiences the maximum stress, called “maximum surface stress” and represented by the sigma sign. To calculate this stress, you need to know the bending moment, distance from the neutral axis to the outer surface, and moment of inertia.
Step 1
Find the bending moment, denoted as “M,” by using specific formulas for the object being bent.
Step 2
Calculate the moment of inertia, denoted as “I,” which depends on the cross-sectional shape and thickness and is not affected by length or material. For a rectangular solid, I = (b*h^3)/12, where “b” is the width of the cross-section and “h” is the measure in the direction of the force applied. For a round solid, I = (pi*r^4)/4, where “r” is the radius of the cross-section.
Step 3
Determine the distance, represented as “c,” between the neutral axis and the outer surface where maximum stress occurs.
Step 4
Compute the maximum surface stress, or MSS, using the formula: MSS = (M*c)/I.