Three aspects to strength of materials


Производство и промышленные технологии

There are three main aspects to this general problem of the Strength of Materials: 1 stress analysis 2 mechanical properties 3 theories of failure. A first course in Strength of Materials deals mainly with elementary stress analysis.



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Three aspects to strength of materials

The main object of the science of Strength of Materials is to develop principles for the safe and economical design of structures and machines. Given a definite structure it may be necessary to determine the limiting loads which it can withstand without producing failure, or given definite loads we may have to design the members of the structure to withstand these loads.

There are three main aspects to this general problem of the Strength of Materials: (1) stress analysis, (2) mechanical properties, (3) theories of failure.

A first course in Strength of Materials deals mainly with elementary stress analysis. The student must, however, realize that the knowledge or stresses is only a means to the end, and not the end itself. It is important to understand the significance and usefulness of stresses in problems of design. For this purpose certain fundamental mechanical properties of materials are determined experimentally. The most important among these are: (1) modulus of elasticity, (2) yield point, (3) ultimate strength.

The tension test

The mechanical properties used in design as a basis for working stresses are in the case of ductile materials obtained from the tension test. This test is the most commonly made.

A specimen is made of the material to be investigated and its load-Deformation curve is obtained. The specimen may be cylindrical or flat. The distance between two fixed centre marks on the specimen is know as the gage length. During the application of the load the change in the gage length is recorded by means of a sensitive instrument know as the extensometer. In American practice the standard gage length are 2 in. and 8 in. In order to eliminate bending and to assure axial loads, the ends of the specimen are fixed in a special manner.

Stress concentration in tension or compression members

In the discussion of simple tension or compression it has been assumed that the bar has a prismatical from. Then for centrally applied forces, the stresses at some distance from the ends are uniformly distributed over the cross-section. Abrupt changes in cross-section give rise to great irregularities in stress distribution. These irregularities are of particular importance in the design of machine parts subjected to variable external forces and to reversal of stresses. Irregularity of stress distribution at such places means that at certain points the stress is far above the average and under the action of reversal of stresses cracks are likely to start gradually from such points. The majority of fractures of machine parts in service can be attributed to such progressive cracks.

Stress concentration is a factor which is frequently overlooked by engineers. That the neglect of this factor has not led to more frequent disasters is due to the use of a large safety factor in stress analysis and to the beneficial effect of local yielding upon stress distribution. This does not justify, however, our neglecting stress concentration in those cases where it does occur.

A simple example of stress concentration occurs in a rectangular plate with a small circular hole at the centre when subjected to tension. Investigation has show that in this case there is a high stress concentration at the edges of the hole.

Small semi-circular grooves in the edges of a plate subjected to tension also produce hight  . stress concentration. Experiments show that at the edges of the grooves the stresses are about twice the average stress at the ends  of the plate. The standard tensile test specimen for cement is another example of a tension variation in

that the maximum stress at concentration points is about 1 3/4 times the stress over the cross-section.

Customary conclusions concerning stress distribution assume that the maximum stresses are within the proportional limit of the material. A ductile material can be subjected to considerable stretching beyond the yield point without great increase in load. Due to this fact, the stress distribution beyond the yield point becomes more and more uniform as the material stretches. This explains why, with ductile materials, holes do not lower the ultimate strength when the specimen is tested statically. Moreover, in testing a mild steel specimen with deep grooves, a certain increase in the ultimate strength is usually obtained due to the fact that the grooves prevent necking of the specimen at the cross-section of fracture. However, in the case of brittle material such as glass, the high stress concentration remains up to the point of breaking. This causes a considerable weakening effect as demonstrated by the decrease in ultimate strength of any grooved bar of brittle material.

In the case of ductile structural steel, high stress concentration is not dangerous provided there is no reversal of stress. In the case of brittle material, such as high carbon steel, points of stress concentration may have a great weakening effect and such places should be eliminated or the stress concentration must always be taken into consideration as progressive cracks are likely to start even if the material is ductile.


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