22-11-2012, 05:24 PM
Strength Of Materials/Mechanics of Solids
Strength Of Materials.pdf (Size: 485.65 KB / Downloads: 208)
Stress is proportional to strain within its elastic limit. This law is known as Hooke’s law.
The material will not return to original shape if the applied stress is more than E.
Stresses are three types tensile, compressive, and shear stress. Moment and torsion will
produced any of these stresses.
Strain is nothing but deformation (change in length, breadth, height, diameter, therefore
area or volume) of the body or material due to load. Therefore strain is change in dimension to
the original dimension. It may be length or volume.
This is the fundamental equation to find change in length of any type of section or step
section using principle of superposition method of varying load, length, area, and material. The
change in length due to compressive load is taken as negative and positive for tensile load.
Both ends are fixed (cannot expand or shrink) indeterminate structure:
Total change in length is zero because the ends are fixed which will not allow the
sections to expand or shrink. Load or stress is produced by expansion or shrinkage of the section
is taken by the ends. Therefore ends carry some load or stress.
Using principle of superposition the reactions at the end of each section is found from
free body diagram. Equate the direction of force in free body diagram to force applied for each
section, The equation shows that the section AB and BC is under tension and CD under
compression. The direction of load in each section can be chosen as we desire, but if the final
result is negative then the direction chosen is incorrect but the answer is correct. So in other
words tensile force is actually a compressive force vice versa.
Sum of change in length of each section due to expansion is equal to sum of change in
length of each section due to compression. The load P, length L, Area A, and Young’s modulus
E parameters may vary from section to section.