2.5. The potential deformation energy in tension

Under the static specimen tension, the tensile force F increasing slowly from zero up to some significance, lengthens the specimen by the value, simultaneously accomplishing work W. This work is accumulated as a potential deformation energy U in the deforming specimen; ignoring insignificant energy losses (for example, heat), we conclude that

W = U

If the tension diagram is drawn in the (F, ) coordinates, then the diagram area, expresses the deformation work. Before the proportional limit the work is expressed by the OAK triangle area (see Fig. 2.3). So, the potential deformation energy of tension for the bar with the length with the constant cross section A and the same normal force N = F will be equal to

The total work spent on the specimen rupture is given by the OABDN figure area of the tension diagram, the NMD triangle area corresponds to the strain work vanishing at the specimen rupture.

The deformation work per a unit bar volume is the specific potential energy of deformation:

2.6. Strength calculation in tension and compression

To secure the details strength it is necessary that the stresses arising in the function process should be lesser than the limit stresses.

The safety factor is called the relation of the limit stress to the stress arising during the details work process. It is denoted by S:

where

It is evident that the insufficient safety factor will not ensure the construction reliability while the excessive safety factor leads to the material over-consumption and the material increase of the construction weight.

The allowable working stress is called the relation of the limit stress to the safety factor. It is denoted by

The strength condition of the construction details is provided by the fact that the maximum working stress does not exceed the allowable working stress:

The guide values of the allowable working stresses in tension and compression for some materials are given in table 2.1.

If stresses in tension and compression are different, they are denoted by and accordingly.

The calculation formula in tension and compression is

Tabl. 2.1.

Material	МPа	МPа
	tension	compression
Grey cast iron Carbon steel constructional Alloy steel constructional Copper Brass Bronze Duraluminium Textile laminate Oak (along the grain) Laying brick Concrete	28...80 60...250 100...400 and above 30...120 70...140 60...120 80...150 30...40 9...13 up to 0,2 0,7…1	120...150 50...90 13...15 0,6...2,5 1...9

There are three problem types distinguished by the calculation formula form application:

1). The project calculation to determine the dangerous section dimensions by the formula

2). The checking calculation to determine the working stress and to compare with the allowable one by the formula

3). To determine the allowable load the formula is applied