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Load
In any engineering s t ru ct u r e or mechanism the i n d ividu al components will be subjected to external forces arising from the service c o n d iti on s or environment in which the c om pon en t w o rk s.
Types of loads
(a) Static or dead l o a d s , generally caused by gravity eff e c t s.
(b) Live l o a ds , as produced by, for example, cars crossing a bri d g e. ( c ) Impact or shock l o a d s caused by s u dd en blows.
(d ) F atig u e , fluctuatin g or alternating l o ad s , the ma g n i tu d e and s i g n of the l oad c h ang i n g with time.
Direct or normal stress
Is the force acting normal to the cross section area
Direct strain ( ๐บ )
If a bar is subjected to a direct load, and hence a stress, the bar will change in length. If the bar has an original length L and changes in length by an amount ๐น๐ณ, the strain produced is defined as follows
Elastic materials- Hooke's law and Modulus of Elasticity
A material is said to be elastic if it returns to its original, unloaded dimensions when load is removed. Since loads are proportional to the stresses they produce and deformations are proportional to the strains, this also implies that, whilst materials are elastic, stress is proportional to strain. Hooke's law, in its simplest form", therefore states that:
Within the elastic limits of materials, i.e. within the limits in which Hooke's law applies, it has been shown that this constant is given the symbol E and termed the modulus of elasticity or Young's modulus.
Tensile test
In order to compare the strengths of various materials it is necessary to carry out some standard form of test to establish their relative properties. One such test is the standard tensile test in which a circular bar of uniform cross-section is subjected to a gradually increasing tensile load until failure occurs. Measurements of the change in length of a selected gauge length of the bar are recorded throughout the loading operation by means of extensometers and a graph of load against extension or stress against strain is produced
material. This involves a measure of the permanent deformation produced by a loading cycle; the 0.1 % proof stress, for example, is that stress which, when removed, produces a permanent strain or "set" of 0.1 % of the original gauge length - see Fig. l.4(a).
Ductile and Brittle Materials
Ductility : The capacity of a material to allow large extensions or the ability to be drawn out plastically.
While, A brittle material is one which exhibits relatively small extensions to fracture so that the partially plastic region of the tensile test graph is much reduced.
Poisson's ratio
Consider the rectangular bar of Fig. 1.10 subjected to a tensile load. Under the action of this load the bar will increase in length by an amount โ๐ฟ giving a longitudinal strain in the bar of
The bar will also exhibit, however, a reduction in dimensions laterally, i.e. its breadth and depth will both reduce. The associated lateral strains will both be equal, will be of opposite sense to the longitudinal strain, and will be given by
shear stress will always be tangential to the area on which it acts; direct stresses, however, are always normal to the area on which they act.
Shear Strain
The angle of deformation ๐พ is the shear strain. Shear strain is measured in radians and hence is non-dimensional, i.e. it has no units.
For materials within the elastic range the shear strain is proportional to the shear stress producing it,
The constant G is termed the modulus of rigidity or shear modulus and is directly comparable to the modulus of elasticity used in the direct stress application.
