4. STRUCTURAL DESIGN OF LVL STRUCTURES Table 4.10. Example limiting values for beam deflection. Deflection due to bending moment and shear should be taken into account for all load-bearing timber products. As an example, the deflection of a single-span beam under uniformly distributed load is calculated from equation: w=(5 〖∙ q〗_(d,i,SLS) ∙ L^4)/(〖384 ∙ (4.74) and for a point load in the middle of the span w=(F_(d,i,SLS) ∙ L^3)/(〖48 ∙ E〗 (4.75) where qd,i,SLS is the design value of a uniformly distributed action in serviceability limit state [N/mm]; Fd,i,SLS is the design value of a point load in serviceability limit state [N/mm]; L is the span of the beam [mm]; I is the moment of inertia of the LVL cross section [mm4]; A is the cross-sectional area of the LVL beam [mm2]; ζ is the shear deformation factor, for rectangular cross section ζ = 6/5 Emean is the mean value of the modulus of elasticity of the LVL class [N/mm2]; and Gmean is the mean value of the modulus of rigidity of the LVL class [N/mm2]. Instructions for the deflection calculation of other loading and span configurations can be found, e.g, from general handbooks on mechanics or can be calculated with FEM calculation software. Note: In the EN standards modulus of elasticity E is defined as the local value, Elocal, which does not include shear deflection. Therefore shear deflection needs to be calculated separately, see equation (4.75) and (4.76). Another way to define modulus of elasticity is the global value, Eglobal, in which shear deflection is included. In edgewise bending of LVL the value of Eglobal is about 5-7% smaller than Elocal, but its use makes the calculation easier, because separate calculation of shear deformation is not needed. Eglobal is commonly used in e.g. Australia and USA. Another name for Eglobal is Eapparent and another name for Elocal is Etrue. Figure 4.28. Recommended range of and relationship between a and b. Performance improves in the arrow 1 direction and decreases in the arrow 2 direction (EC5 Figure 7.2). 4.3.14 Serviceability limit state design: Floor vibrations Eurocode 5, Section 7.3.3, gives requirements and some instructions for the design of residential floors. However, most national annexes deviate significantly from these. Wooden floor structures can be divided into high frequency floors and low frequency floors based on their lowest fundamental frequency. For residential floors with a fundamental frequency greater than 8 Hz (f1 > 8 Hz), the following requirements should be satisfied: w/F≤a [mm/kN] (4.76) (EC5 7.3) and v≤b^(〖(f〗_1 ξ-1)) [m/Ns2] (4.77) (EC5 7.4) where w is the maximum instantaneous vertical deflection caused by a vertical concentrated static force F applied at any point on the floor, taking account of load distribution; v is the unit impulse velocity response, i.e. the maximum initial value of the vertical floor vibration velocity (in m/s) caused by an ideal unit impulse (1 Ns) applied at the point of the floor giving maximum response. Components above 40 Hz may be disregarded; and ζ is the modal damping ratio. Values for factors a and b can be chosen from the diagram in Figure 4.28 depending on the desired performance level. ≤ [mm/kN] (4 ≤ ( 1 −1) [m/Ns2] (4 1 = 2 2 �( )l (4 ≤ [mm/kN] (4 ≤ ( 1 −1) [m/Ns2] (4 1 = 2 2 �( )l (4 winst wnet,fin Beam on two supports l/300 to l/500 l/250 to l/350 Cantilevering beams l/150 to l/250 l/125 to l/150 Figure 4.27 Components of deflection of LVL members (Kuva_98 deflection 190401) Note: LVL is not pre-cambered. Only in some very special cases LVL beams may be cut to a camber by special sawing from an LVL billet. The net deflection below a straight line between the supports, wnet,fin, should be taken as: net, fin = inst + creep (4.73) Note: The recommended range of limiting values of deflections for beams with span l is given in Table 4.10 depending upon the level of deformation deemed to be acceptable. Information on national limit values can be found in the National Annex for Eurocode 5. Table 4.10. Example limiting values for beam deflection. winst wnet,fin Beam on two supports l/300 to l/500 l/250 to l/350 Cantilevering beams l/150 to l/250 l/125 to l/150 Deflection due to bending moment and shear should be taken into account for all loadbearing timber products. As an example, the deflection of a single-span beam under uniformly distributed load is calculated from equation: = 5 ∙ d,i,SLS ∙ 4 384 ∙ mean ∙ + ∙ d,i,SLS ∙ 2 8 ∙ mean ∙ (4.74) and for a point load in the middle of the span = d,i,SLS ∙ 3 48 ∙ mean ∙ + ∙ d,i,SLS ∙ 2 4 ∙ mean ∙ (4.75) where qd,i,SLS is the design value of a uniformly distributed action in serviceability limit state [N/mm]; Fd,i,SLS is the design value of a point load in serviceability limit state [N/mm]; L is the span of the beam [mm]; I is the moment of inertia of the LVL cross section [mm4]; A is the cross-sectional area of the LVL beam [mm2]; ζ is the shear deformation factor, for rectangular cross section ζ = 6/5 Emean is the mean value of the modulus of elasticity of the LVL class [N/mm2]; and Gmean is the mean value of the modulus of rigidity of the LVL class [N/mm2]. Instructions for the deflection calculation of other loading and span configurations can be found, e.g, from general handbooks on mechanics or can be calculated with FEM calculation software. Note: In the EN standards modulus of elasticity E is defined as the local value, Elocal, which does not include shear deflection. Therefore shear deflection needs to be calculated separately, see equation (4.75) and (4.76). Another way to define modulus of elasticity is the global value, Eglobal, in which shear deflection is included. In edgewise bending of LVL the value of Eglobal is about 5-7% smaller than Elocal, but its use makes the calculation easier, Figure 4.27 Components of deflection of LVL members (Kuva_98 deflection 190401) Note: LVL is not pre-cambered. Only in some very special cases LVL beams may be cut to a camber by special sawing from an LVL billet. The net deflection below a straight line between the supports, wnet,fin, should be taken as: net, fin = inst + creep (4.73) Note: The recommended range of limiting values of deflections for beams with span l is given in Table 4.10 depending upon the level of deformation deemed to be acceptable. Information on national limit values can be found in the National Annex for Eurocode 5. Table 4.10. Example limiting values for beam deflection. winst wnet,fin Beam on two supports l/300 to l/500 l/250 to l/350 Cantilevering beams l/150 to l/250 l/125 to l/150 Deflection due to bending moment and shear should be taken into account for all loadbearing timber products. As an example, the deflection of a single-span beam under uniformly distributed load is calculated from equation: = 5 ∙ d,i,SLS ∙ 4 384 ∙ mean ∙ + ∙ d,i,SLS ∙ 2 8 ∙ mean ∙ (4.74) and for a point load in the middle of the span = d,i,SLS ∙ 3 48 ∙ mean ∙ + ∙ d,i,SLS ∙ 2 4 ∙ mean ∙ (4.75) qd,i,SLS is the design value of a uniformly distributed action in serviceability limit state [N/mm]; Fd,i,SLS is the design value of a point load in serviceability limit state [N/mm]; L is the span of the beam [mm]; I is the moment of inertia of the LVL cross section [mm4]; A is the cross-sectional area of the LVL beam [mm2]; ζ is the shear deformation factor, for rectangular cross section ζ = 6/5 Emean is the mean value of the modulus of elasticity of the LVL class [N/mm2]; and Gmean is the mean value of the modulus of rigidity of the LVL class [N/mm2]. Instructions for the deflection calculation of other loading and span configurations can be found, e.g, from general handbooks on mechanics or can be calculated with FEM calculation software. Note: In the EN standards modulus of elasticity E is defined as the local value, Elocal, which does not include shear deflection. Therefore shear deflection needs to be calculated separately, see equation (4.75) and (4.76). Another way to define modulus of elasticity is the global value, Eglobal, in which shear deflection is included. In edgewise bending of LVL the value of Eglobal is about 5-7% smaller than Elocal, but its use makes the calculation easier, LVL Handbook Europe 137
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