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Figure 6.27. Graphical representation of Eq. 16, with cut-off for cot 9 = 2,5

Measurements of the deformation of the web in shear loaded I-beams show typically a behaviour as shown in Fig. 6.28. The diagram shows lines numbered from 1 to 4.

Line 1 In the beginning of shear loading the beams is uncracked in shear so that the principal strain direction is 45°.

At the formation of inclined shear cracks the principal strain direction decreases After having reached the stabilized inclined crack pattern a new type of equilibrium is obtained. The behaviour is elastic: the (constant) principal strain direction depends on the "stiffness ratio'' in the cracked state.

When the stirrups start yielding the web searches for a new state of equilibrium. By rotating down to a lower inclination the beam activates more stirrups to carry the load. In the mean time the compressive stress in the concrete increases. When the crushing strength of the struts is reached the beam fails in shear.

Line 2 Line 3

Line 4

Figure 6.28. Rotation of the concrete struts as measured on the web of beams with shear reinforcement, schematically represented (Walraven, 1995 and 1999)

Figure 6.28. Rotation of the concrete struts as measured on the web of beams with shear reinforcement, schematically represented (Walraven, 1995 and 1999)

Fig. 6.29a shows the strut rotation as measured in three beams with different shear reinforcement ratio's (L = low, M = medium and H = High). It can be seen that for M and H the beams fail before the stirrups have yielded. Fig. 6.29b shows a similar diagram for a series of high strength concrete beams (fc « 90 N/mm2).

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