Internal energy absorbed by rotation along the yield line is moment x rotation x length - moaL where e> « 2 - = —

hence internal energy = 4maA

thus equaling internal energy absorbed with external work done

Since the displacement A is eliminated, this will generally be set to unity in calculations of this type.

In the simple case of example 8.11. the yield line crossed the reinforcement at right angles and transverse steel was not involved in bending calculations. Generally, a yield line will lie at an angle 0 to the orthogonal to the main reinforcement and will thus also cross transverse steel. The ultimate moment of resistance developed is not easy to define, but Johansen's stepped yield criteria is (he most popular approach. This assumes that an inclined yield line consists of a number of steps, each orthogonal to a reinforcing bar as shown in figure 8.24.

Figure 8.24

Stepped yield line

Yield line m,

Yield line

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