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In this article we will discuss about the behaviour of concrete when compressive stress varies.

When the compressive stress alternates between zero and a certain fraction of short term static strength the behaviour of concrete is very significant. As the stress increases from zero to a certain value of about 20 MPa, the strain also increases. On decreasing the load though strain decreases, but not fully regains its original value, that is there is some residual strain. The stress and strain curve is shown in Fig.13.14.

This fig shows that there is a change in the shape of the stress strain curve under increasing and decreasing load as the number of load cycles increase. Initially the loading curve is concave towards the strain axis, then straight at about 675 cycles and eventually concave towards the stress axis. The extent of the latter concavity is reflected by an increase in the elastic strain and a decrease in the secant modulus of elasticity. This feature is an indication that how near the concrete is to failure by fatigue.

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The area enclosed by two successive curves on loading and unloading is proportional to hysteresis (a continuous fig.) and represents the irreversible energy of deformation i.e., energy due to crack formation or irreversible creep. The area of the loop is affected by the rise of temperature of the specimen. It does not occur in specimens which do not fail in fatigue. On first loading to a high stress, the hysteresis is large, but then decreases as the number of cycles increases.

When fatigue failure is about to occur, the area of loop increases and an extensive cracking takes place at the interfaces of the aggregate and cement paste. Thus consequently hysteresis and non-elastic strain increase rapidly. As in static fatigue, the non-elastic strain at fatigue failure and the strain capacity are much larger than in short term failure. The fatigue cracking is extensive and the observed strain at failure is much larger than the static failure. The non-static strain increases with the number of cycles.

Cycling loading below the fatigue limit improves the fatigue strength of concrete. This shows that a concrete loaded a number of times below its fatigue limit will, when subsequently loaded above the fatigue limit exhibit, higher fatigue strength than the concrete which had never been subjected to the initial cycles. The former concrete also exhibits a higher static strength by 5 to 15%. This increase in the concrete may be due to the densification of concrete caused by the initial low stress level cycling, as in the case of under moderate sustained loading. This property is akin to strain hardening in metals.

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**Fatigue for a Constant Range of Alternating Stress:**

For a constant range of alternating stress, the fatigue strength decreases, as the number of cycles increases. This statement is illustrated by the S-N cures of Fig. 13.15. S is the ratio of the maximum stress to the short term static strength and N is the number of cycles at failure. The value of S is shown on y axis and N on x-axis. The maximum value of S below which no failure takes place is called as endurance limit. Mild steel has been found to have an endurance limit of about 0.5, which means that when S < 0.5 the value of N is infinity, whereas concrete does not seem to have such limit.

Thus it is necessary to define the fatigue strength of concrete by considering a very large number of cycles say one million (10^{6}) as shown in Fig. 13.15. Actually the S-N curves for concrete have a very large scatter due to the uncertainty of the short term strength of the actual fatigue specimen and also due to the uncertain nature of fatigue. Thus for a given cycle of stress, the precise determination of the number of cycles to failure is very difficult.

The effect of change in the range of stress on the fatigue strength can be represented by modified (Good man) diagram as shown in Fig. 13.16.

In the diagram, a line passing through the origin at an angle of 45° to the x-axis is drawn. The ordinate measured from this line indicates the range of stress to cause failure after one million (10^{6}) cycles. For practical purposes, the lower load is the dead load and the upper load is the sum of dead and live load. Fig. 13.16 shows the fatigue strength for various combinations of compressive and tensile stresses. For example when the stress is 0.1 of the short term static strength, the corresponding maximum stress and the range of stress expressed as ratio of the short term static strength are as shown in Table 13.4.

From the above, it can be seen that highest range of stress is tolerable in flexure (c) when the minimum stress is compressive and the maximum stress is tensile. This combination is very important as it takes place in a pre-stressed concrete beam in practice.

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As the strength of concrete increases with age, the fatigue strength also increases proportionately so that for a given number of cycles, fatigue occurs at the same fraction of the ultimate strength. A decrease in the frequency of the alternating load decreases the fatigue strength slightly, but only at very low frequencies less than 1 Hz. when the creep per cycle is significant. It has been observed that the moisture condition of the concrete affects the fatigue strength marginally except in case of very dry concrete, which has slightly higher fatigue strength than wet concrete.