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The wire in figure 1 is pulled by the action of a mass attached to its lower end. In this condition the wire is in tension. Suppose the total load on the cross-section of the wire is P and the cross-sectional area of the wire is A, then the uniform tensile stress () in the wire is . This is called the intensity of force P over the cross-sectional areas A.

Figure 1

The stress is expressed in terms of or or etc.

When force P act at each end of a bar towards each other and if they tend to compress the bar, then the forces give rise to compressive stresses.

Tensile and compressive stresses are together referred as **direct stresses**.

**Practical situations of tensile force:**

a) Bolt when tightened, the bolt will be subjected to tension.

b) Cable when it sags under its self weight.

**Practical situations of compressive stresses:**

A column carrying a central axial compressive force.

**TYPICAL CASES OF AXIAL LOADING**

**(a) Circular tapering bar subjected to an axial pull** (figure 2)

Figure 2

Bar of circular cross-section with diameter at one end and at the other end of length L, is subjected to tensile force P.

Elongation over a small length

Where

Total elongation over the length AB =

**(b) Square tapering bar subjected to an axial pull** (figure 3)

If the bar is of length L and has a square cross-section measuring at one end and at the other end, the total elongation is

**(c) Bars of varying cross section subjected to an axial pull**

**Figure 3**

Axial pull = P

Material of the three parts is not uniform.

Total elongation =

In general, total elongation is given by

**(d) Bar of uniform strength** (figure 4)

Relationship in the variation of cross-section required to ensure that the strength is uniform throughout.

Figure 4

Bar is subjected to a tensile load in addition to its own weight

If is the stress in bar at any cross-section, then from consideration of an elementary strip dx,

Where is the specific weight of the bar.

In the limit,

Integrating

or,

when x = L,

**(e) Extension of a bar under its own weight (figure 5)**

Figure 5

Cross-section (uniform) = A

Consider a small element of length dx.

Extension of the strip =

Where is the specific weight of the bar

Total extension of the bar =

If W is the total weight of the bar, then total elongation =

*It may be observed that the total extension produced by self weight of the bar is equal to that produced by a load of half its weight applied at the lower end.*

**(f) Bar of varying cross-section subjected to a pull due to its self-weight (figure 6)**

Figure 6

Bar is hung from the top as shown in figure. If A is the variable cross-section, then weight of the bar upto the height x is

Stresses in the strip =

Elongation in the strip =

Total elongation =