Vs

Ib where t is the shear stress at the required level, V is the shear force at the position being considered, S is the first moment of the area above the shear stress level about the neutral axis, I is the second moment of area of the cross-section about the neutral axis, b is the width of the cross-section at the shear stress level.

Shear stress components

Shear force, V

(a) A shear component parallel to the grain

Shear force, V

Shear stress components

Shear force, V

Shear stress components

Shear force, V

(a) A shear component parallel to the grain

Shear stress components

(b) Both shear components perpendicular to the grain (rolling shear situation)

Fig. 4.9. Shear stress components in a member: (a) a shear component parallel to the grain; (b) both components perpendicular to the grain (rolling shear).

At any position along the beam the shear stress at the top and bottom faces of the cross-section will be zero and the maximum shear stress will arise at the neutral axis position. For a rectangular section of width b and depth h the maximum shear stress will occur at mid-depth and will be:

3V 2bh

The limit state for shear design is the ULS and the requirement in EC5 is that for shear with a stress component parallel to the grain or where both shear stress components are perpendicular to the grain (e.g. rolling shear), as shown in Figure 4.9b,

where /v,d is the design shear strength for the condition being investigated, i.e. Figures 4.9a or 4.9b.

When deriving the shear strength of members subjected to bending, the assumption is made in EC5 that the influence of cracks in members is ignored. In the proposed draft amendment summarised in Appendix C, 6.1.7, a revision is included to take account of the influence of cracks in timber, LVL (glulam) and wood-based products on shear resistance. The UKNA to EC5 will determine the requirements for this change.

4.5.2.1 Shear stress with a stress component parallel to the grain

For a rectangular cross-section beam of breadth b and depth h with a shear stress component parallel to the grain, as shown in Figure 4.9a, the validation requirement for the design shear stress, Td, will be as follows:

(a) For a beam without a notch (as shown in Figure 4.10a):

Td 2bh

(a) Without a notch

(a) Without a notch

Fig. 4.10. Rectangular beams without a notch at a support (a) and with a notch on the opposite side to the support (b).

b

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