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Shear check for timber

According to EN 1995-1-1 §6.1.7 (1)P the shear check implies:

    \[ \tau_d \leq f_v_._d \]

with

  • \tau_d  the design shear stress
  • f_v_._d  the design shear strength (= a material property)

From any course on mechanics, you can find that the maximal shear stress in a rectangular section equals:

    \[ \tau_d=\frac{3 V_E_d}{2 A} \]

Combining both equations gives:

    \[ \frac{3 V_E_d}{2 A} \leq f_v_._d \]

or

    \[ V_E_d \leq \frac{2 f_v_._d A}{3} \]

The area A of a rectangular section equals b h:

    \[ V_E_d \leq \frac{2}{3}  b h f_v_._d \]

Yet EN 1995-1-1: 2004/A1:2008 §6.1.7 (2) states that the effective width b_e_f_f = k_c_r  should be used instead of the width b  to take the influence of cracks into account. k_c_r = 0,67 for solid and glued laminated timber, k_c_r= 1,0 for all other wood based products.

    \[ V_E_d \leq \frac{2}{3} b_e_f_f h  f_v_._d = \frac{2}{3}  k_c_r b h f_v_._d  = \frac{2}{3}  \frac{2}{3} b h f_v_._d = \frac{2}{3}  A_e_f_f f_v_._d \]

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