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End beam, (referred to as a U-beam in EC5)

7.3.2.1 Effective flange width

When the beam is subjected to bending, stresses are transferred between the web and the flange by shear stresses. Because of shear deformation, the stresses in each flange will reduce as the distance from the web increases and the departure from the uniform stress profile assumed to be generated when using simple bending theory is termed the 'shear lag' effect. To take this into account the concept of the 'effective width' of the flange is used. The effective width is that width of flange over which the stress is taken to be uniform and at the maximum stress value derived from bending theory such that the total force in the flange will equal that carried by the full width of the actual flange.

The effective flange width concept applies to flanges in compression and in tension, and unless a more detailed calculation is carried out, in accordance with the requirements of EC5, 9.1.2(3), the effective flange width, bef, as shown in Figure 7.5, will be as follows:

• For internal I-shaped sections:

bef = bc,ef + bw or bef = bt,ef + bw (EC5, equations (9.12)) (7.33)

• For U-beams (i.e. the end beams in Figure 7.5):

bef = 0.5bc,ef + bw or bef = 0.5bt,ef + bw (EC5, equations (9.13)) (7.34)

Taking shear lag effects into account, the values of bc,ef and bt,ef must not exceed those given in Table 9.1 of EC5, reproduced in Table 7.2.

The shear lag effect in structures has been investigated by several researchers and a comparison of the EC5 criteria with the theoretical solution developed by Mohler, Abdel-Sayed and Ehlbeck (referred to in STEP 1 [3]), applied to glued thin flange beams in which plywood is used for the flange material, is shown in Figure 7.6. For the majority of this type of beam, bf/l will be within the range 0.2-0.3 and as can be seen from Figure 7.6, the effective flange approach will generally give a conservative result.

Material used for the flange |
Plate buckling* |
Shear lag* |

Oriented strand board (OSB) |
25hf |
0.15 i |

Plywood: |

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