Title Strength of Materials (MEEN204) - Notes.pdf ✅

1 STRENGTH OF MATERIALS (MEEN204) Introduction While selecting a suitable material for his project, an engineer is always interested to know its strength. The strength of a material may be defined as ability, to resist its failure and behavior, under the action of external forces. Under the action of these forces the material is first deformed and then its failure takes place. A study of forces and their effects, along with some suitable protective measures for the safe working conditions, is known as Strength of Materials. In other words, Strength of Materials can be defined as “the study of the behavior of structural and machine members under the action of external loads, taking into account the internal forces created and the resulting deformations. 1.0 STRESSES AND STRAINS 1.1 Direct Stresses Whenever some external forces act on a body, it undergoes some deformation. As the body undergoes deformation, its molecules set up some resistance to deformation. This resistance per unit area to deformation is known as stress. Mathematically stress may be defined as the force per unit area i. e., stress A P   1.1 where P = Load or force acting on the body and A = Cross-sectional area of the body. If the load or total force P is expressed in N and the area in m2, then the unit of stress shall be N/m2. Stresses which are normal to the plane on which they act are called direct stress, and are either tensile or compression. Tensile Stress: When a section is subjected to two equal and opposite pulls and the body tend to increase its length as shown in Fig. 1.1a the stress induced is called tensile stress.
2 Fig.1.1a Compressive Stress: When a section is subjected to two equal and opposite push and the body tend to decrease its length as shown in Fig. 1.1b the stress induced is called compressive stress. Fig. 1.1b 1.2 Strain Whenever a single force (or a system of forces) acts on a body, it undergoes some deformation. This deformation per unit length is known as strain. Mahematically strain may be defined as the deformation per unit length i.e., strain L x   1.2 where x = Change of length of the body, and L = Original length of the body. Since strain is the ratio of two lengths, it has no unit. We also have tensile and compressive strains in correspondence to tensile and compressive stresses discussed above. 1.3 Stress-Strain Curves for Tension The behaviour of materials subjected to tension is studied by plotting curves of stress and the corresponding strains observed by gradually increasing the axially applied load to the point of failure of the specimen. Such curves differ in shape for different materials. Fig. 1.3 shows the result of test obtained mainly for ductile materials, but other engineering materials show the same phenomena to a varying degree. The significance of the points indicated on Fig. 1.3 are explained below:
3 Fig. 1.3: Stress-Strain Relationship for Ductile Material A - Limit of proportionality: Up to point A strains are proportional to stresses. Beyond this point stress-strain curve does not remain linear. B - Elastic limit: Up to point B specimen returns to its original position when the load is removed. Elasticity is the property of materials to recover their original size on removal of loads Strain Energy in elastic extension is the work performed in stretching the material Permanent Set is a certain amount of strain retained by a specimen if the specimen is loaded beyond point B then on unloading. C – Yield Stress: This is the point beyond which there is increase in strain even though there is no increase in stress D – Ultimate Stress: This is the point where maximum stress is reached. E – Fracture point: Beyond D the specimen elongates even with decrease in stress and finally fails at stage corresponding to the point E 1.4 Hooke’s Law Hooke’s Law states that for materials subjected to simple tension or compression within elastic limit, the stress is proportional to the strain. Mathematically Cons t Strain Stress  tan 1.3a
4 or  E   1.3b where E = Young’s Modulus 1.5 Deformation of a body due to application of load on it Since A P   1.5a and  E   1.5b It follows that EA P E     1.5c From eq.(1.2), L x   , It follows that EA PL E L x  L   . .   1.5d 1.6 Factor of Safety and Load Factor Working Stress is the maximum permissible stress that a material is subjected to and is well within the straight-line portion of the stress-strain curve. Factor of Safety is the ratio of Yield Stress (or Ultimate Stress) to the Working Stress Working Stress Yield Stress orUltimate Stress SF _ _ ( _ )  Load Factor is the ratio of between the load at failure and the working load. Working Load Failure load LF _ _  1.7 Strain Energy, Resilience