Question

Review An engineered wood beam (Figure 1) will replace a portion of a structural wall as part of a house renovation. The beam can be modeled as a simply supported beam with a span L = 18 ft and an uniform distributed load w = 810 lb/ft . The beam is to be constructed as an I-beam with nails securing the flanges to the web. The flanges are 6 in wide and 1 in thick. The web has depth 18 in and thickness 3 in. The maximum allowable shear stress in the web is 900 psi. To calculate the shear stress at the web/flange joint in a beam and use that stress to calculate the required nail spacing to make a built-up beam. A built up beam can be constructed by fastening flat plates together. When an I-beam is subjected to a shear load, internal shear stress is developed at every cross section, with longitudinal shear stress balancing transverse shear stress. If the beam is built up using plates, the fasteners used must be able to resist the shear at the joints. The loading resisted by the fasteners can be described in the force per unit length of the beam and is called the shear flow. The shear flow at some distance y from the neutral axis can be VQ calculated using the shear formula q= I , where V is the shear force, Q is the moment about the centroidal axis of the cross-sectional area above y, and I is the moment of inertia of the cross section. Part A - Maximum shear load Assuming the joints do not fail, what is the maximum shear load the beam can support? Express your answer with appropriate units to three significant figures. View Available Hint(s) μΑ ? Figure 1 of 1 Vmax = 25632.6 lb w Submit Previous Answers I y X Incorrect; Try Again; 5 attempts remaining L Part B - Shear flow at joint

Answer 1

Ques) 6x2 203 6 in 2 12 115x183 12 skileg frin T = 2542 in 4 N. AA. 3in gin Qi=A AY =(6x1)x9.5 = 57 in3 A Tui .6in Q2 = A ý 6x1x9.5 +9x3x4.5 = (6x1+9x3) 6 x1 +9x3 - = 178.563 ool a ) Vmex Tit Oz 900*2542 x 3 178.5 Vmax 38450.42 lb

b) Vmax = wil = 810 18 = 7290 lb 2 q= Vmes o 1 7290 x 57 2542 q = 163.465 lblin c) s= Vnaii q 8 250 163.465 S= 1.5293 in