7. Bending Stresses in Simple Beams
Bending stresses in simple beams are a fundamental aspect of structural analysis and design, as they impact the performance, safety, and longevity of various constructions, ranging from buildings and bridges to mechanical systems. Simple beams, often made of homogeneous materials with uniform cross-sectional shapes, experience bending stresses when subjected to external loads, causing the beam to deform. A thorough understanding of these stresses is crucial for engineers and architects, as it enables them to accurately assess a beam’s load-carrying capacity, determine appropriate material selections, and establish safe design limits.
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Example 1 |
A steel wire of \(4.5 mm\) diameter is bent into a circular shape of \(5.5 m\) radius. Using relevant formulas and sketches, determine the maximum stress induced in the wire. Take \(E=200 GPa\). |
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Solution:
Figure 28. Wire max stress.
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Example 2 |
A copper wire of \(2.5 mm\) diameter is required to be wound around a drum. Using relevant sketches and formulas, find the minimum radius of the drum, if the stress in the wire is not to exceed \(85 M P a\). Take modulus of elasticity for the copper as \(100 GPa\). |
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Solution:
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Figure 29. Wire max stress.
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Comments (7)
Ae we doing chapters 6, 7, 8 & 9?
No. That's for Solid II.
Kindly confirm for us the formula for volumetric strain
Hello, are the notes here all we will have for SSM2 or is there a possibility for addition?
Solid Mechanics II starts from chapter 6.
Could you confirm if in example 1 the shear force diagram is correct since from my shear force calculations the forces are positive meaning the diagram ought to be upwards
Yes, in example 1, the shear force diagram is correct. There are two point loads acting downwards, which tend to shear the bar in the negative direction.