Question

5. Fabricated box beam The simply supported beam is loaded by two forces as shown below. The beam is constructed from four 24 mm thick boards which are nailed together. Determine the maximum distance s between nails if each nail can carry a force of Fallowable = 275N. 1.5 KN 1.2 KN 24 mm 177 mm 24 mm 3.0 m 2.5 m 1.0 m 24 mm 24 mm 280 mm

Point loads are 1.2 kN and 1.5 kN respectively

Answer 1

Sigma M @ A = 0 R_B times 6.5 = 1.2 times 1 + 1.5 times 3.5 R_B = 0.9923 KN sigma V = 0 implies R_A + R_B = 1.2 + 1.5 R_A = 1.7077 KN Shear Force diagram: - V_AC = R_A = 1.7077 KN V_CD = R_A - 1.2 = 0.577 KN V_DB = 1.7077 - 1.2 - 1.5 = 0.9923 KN V_max = V_AC = 1.7077 KN = 1707.7 N I_ZZ = 280 times 25^3/12 - 232 times 177^3/12 = 158573412 mm^4 I_shaded = 280 times 24 times 100.5 = 675360mm^3 Now Force transferred to each pass lessthanorequalto followable 1/2 V_ma times Q_shaded times s/I_zz lessthanorequalto 275N 0.5 times 1706.7 times 675360 times s/158573412 lessthanorequalto 275 S lessthanorequalto 75.62mm