4. STRUCTURAL DESIGN OF LVL STRUCTURES Normal stress from bending moment is calculated for composite cross sections according to the equation: σ_(i,d(z) )=(E_i 〖 ∙ e〗_(z)i ∙ M_d)/〖EI〗_eff (4.86) where σi,d is the design value of normal stress at coordinate z in the section [N/mm2]; Ei is the modulus of elasticity of a part i [N/mm2]; e(z)i is the coordinate z of the point i where the stress is analysed = distance to the neutral axis of the entire composite cross section [mm]; Md is the design value of the bending moment at the evaluated location of the member [Nmm]; and EIeff is the effective stiffness of the composite cross section [Nmm2]. Shear stresses at the glued joints of composite cross sections are calculated according to equation: τ_(z)d=E_i∙(S_((z) ) ∙ V_d)/(〖EI〗_eff ∙〖 b〗_((z) ) ) (4.87) where τ(z)d is the design value of the shear stress at coordinate z in the section [N/mm2]; Ei is the modulus of elasticity of a part i [N/mm2]; S(z) is the static moment at coordinate z [mm³]; Vd is the design value of shear force at the evaluated location of the member [Nmm]; EIeff is the effective stiffness of the composite cross section [Nmm2]; b(z) is the width of the section at coordinate z [mm]; S(z) =∑iAi∙e(z)i (4.88) Ai is the cross-sectional area of a part i [mm2]; and e(z)i is the coordinate z of the point i where the stress is analysed = distance to the neutral axis of the entire composite cross section [mm]. Figure 4.29. Composite cross section. In thin-flanged beams axial stresses are checked at points 1, 3 and 5. Shear stresses are checked at points 2, 3 and 4. 0 =∑ i ∙ i ∙ i i∑ i ∙ i i i,d(z) = i ∙ (z)i ∙ d eff (z)d = i ∙ (z) ∙ d eff ∙ (z) (z) =∑ i ∙ (z)i i 165 (255) Ii is the moment of inertia of a part i [mm4], for rectangular cross section I i = bi∙hi 3/12, where bi is the width [mm] of the part and hi is the height [mm] of the part; Ai is the cross-sectional area of a part i [mm2]; and ei is the eccentricity of the part i = distance between the centre of gravity of part i and neutral axis of the entire composite cross section [mm]. The location of the neutral axis of a composite cross section related to the bottom of the section is: 0 = ∑ i ∙ i ∙ i i∑ i ∙ i i (4.85) where ai is the distance between the centre of gravity of part i and the bottom of the entire composite cross section [mm]. Normal stress from bending moment is calculated for composite cross sections according to the equation: i,d(z) = i ∙ (z)i ∙ d eff (4.86) where σi,d is the design value of normal stress at coordinate z in the section [N/mm2]; is the modulus of elasticity of a part i [N/mm2]; e(z)i is the coordinate z of the point i where the stress is analysed = distance to the neutral axis of the entire composite cross section [mm]; Md is the design value of the bending moment at the evaluated location of the member [Nmm]; and EIeff is the effective stiffness of the composite cross section [Nmm2]. Shear stresses at the glued joints of composite cross sections are calculated according to equation: (z)d = i ∙ (z) ∙ d eff ∙ (z) (4.87) where τ(z)d is the design value of the shear stress at coordinate z in the section [N/mm2]; Ei is the modulus of elasticity of a part i [N/mm2]; LVL Handbook Europe 139
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