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Aryam Design & Build <br />Project <br />1513 McFadden <br />Job Ref. <br />25073 <br />Section <br />(E) 6x12 CHK for ROOF DL+LL <br />Sheet no./rev. <br /> 3 <br />Calc. by Date Chk'd by Date App'd by Date <br />Modulus of elasticity, stability calculations;Emin = 580000 lb/in2 <br />Mean shear modulus;Gdef = E / 16 = 100000 lb/in2 <br />Member details <br />Service condition;Dry <br />Length of span;Ls1 = 20 ft <br />Length of bearing;Lb = 3.5 in <br />Load duration;Ten years <br />Section properties <br />Cross sectional area of member;A = N  b  d = 63.25 in2 <br />Section modulus;Sx = N  b  d2 / 6 = 121.23 in3 <br />Sy = d  (N  b)2 / 6 = 57.98 in3 <br />Second moment of area;Ix = N  b  d3 / 12 = 697.07 in4 <br />Iy = d  (N  b)3 / 12 = 159.44 in4 <br />Adjustment factors <br />Load duration factor - Table 2.3.2;CD = 1.00 <br />Temperature factor - Table 2.3.3;Ct = 1.00 <br />Size factor for bending - Table 4D;CFb = 1.00 <br />Size factor for tension - Table 4D;CFt = 1.00 <br />Size factor for compression - Table 4D;CFc = 1.00 <br />Flat use factor - Table 4D;Cfu = 1.00 <br />Incising factor for modulus of elasticity - Table 4.3.8 <br />CiE = 1.00 <br />Incising factor for bending, shear, tension & compression - Table 4.3.8 <br />Ci = 1.00 <br />Incising factor for perpendicular compression - Table 4.3.8 <br />Cic_perp = 1.00 <br />Repetitive member factor - cl.4.3.9;Cr = 1.00 <br />Bearing area factor - cl.3.10.4;Cb = 1.00 <br />Depth-to-breadth ratio;dnom / (N  bnom) = 2.00 <br /> - Beam is fully restrained <br />Beam stability factor - cl.3.3.3;CL = 1.00 <br />Bearing perpendicular to grain - cl.3.10.2 <br />Design compression perpendicular to grain;Fc_perp' = Fc_perp  Ct  Cic_perp  Cb = 625 lb/in2 <br />Applied compression stress perpendicular to grain;fc_perp = RA_max / (N  b  Lb) = 133 lb/in2 <br />fc_perp / Fc_perp' = 0.212 <br />PASS - Design compressive stress exceeds applied compressive stress at bearing <br />Strength in bending - cl.3.3.1 <br />Design bending stress;Fb' = Fb  CD  Ct  CL  CFb  Ci  Cr = 1350 lb/in2 <br />Actual bending stress;fb = M / Sx = 1264 lb/in2 <br />fb / Fb' = 0.936 <br />PASS - Design bending stress exceeds actual bending stress <br />Strength in shear parallel to grain - cl.3.4.1 <br />Design shear stress;Fv' = Fv  CD  Ct  Ci = 170 lb/in2