Question

For the tension member shown below, determino the maximum tenslon force Tu that ma applied and meet the following requirements of the AISC Manual: (s P a. Tensile Yielding 1. b. Tensile Rupture c. Bolt Shear d. Bearing at Bolt Hole 1-1'4 A35 GusseT L16 (ASTAM A30) L6XYK AS1M A36 MA1'L GAEE 31

Answer 1

GIVEN DATA Member Details Crade А 36 Grade of Steel Member designation L бx4x3/4 6.94 in 2 Gross area of section, AG = =0.750 in f member, Thickness Connection Details Member connected to one/two legs one leg Diameter of bolt, di 1 in = 1 Designation of bolt Threads included/excluded A 325 N Number of shear planes 1 Number of bolts across a section, 1 Number of bolts in line (in the direction of loading) 3 in (in the direction of loading) 7 Pitch of the bolts S End Distance, 1.5 in Edge Distance, 1.5 in Distance of centroid from edge 2.07 in CALCULATIONS DESIGN STRENGTH OF PLATE A 36 For grade steel, Yield stress, 36 ksi = 58 ksi Ultimate stress, F. = d Diamter of bolt hole. 1 + 1 1 8 in 1.125 Yielding in the gross section Design strength of gross section is obtained as T ,FyA 0.9 36 x 6.94 X 224.9 kips i) Fracture in the net section A Ag-n(dt) Net area, 1.125 x 0.750 6.94 1 x in2 6.096 - NOTE Shear lag Factor, when connected to two legs 1.0 when connected to one leg 1-xL 0.9 xis distance of centroid from edge and Lis the where length of connection loading, Length of connection in the direction

18 in Since the member connected to leg, 1-x/L one (with four fasteners-Case 8) Shear lag Factor U= 0.8 0.89 Thus 0.89 (Maximum of Case-2 & Case-8) U = Effective area, A. =UA 0.89 x 6.096 in2 5.395 Design strength of net section is obtained as: T FuA 0.75 58 x 5.395 kips 234.7 The design strength of the member is the smallest of the design strength of gross section design strength of net section and design rupture strength. Thus, T 224.9 kips BOLT STRENGTH Tensile strength of bolt material, 120 ksi d. Ab = Area of bolt, 2. in 0.785 Design strength of bolt in shear R 0.75 x 0.4 F mAb 0.75 x 0.4 x Design shear strength/bolt, 120x 1 x 0.785 - 28.26 kips Design strength of bolt in bearing in 1.5db L Checks: 1.50 in 1.5 in 3db in 3 3 dR Design bearing strength/bolt, p(2.4Fudt) 0.75 x2.4 x 58 x 1.000 x 0.750 78,3 kips Thus, the design strength of bolt, R 28.26 kips minimum of the two values] Total design strength of the bolted connection, 7 x 28.26 197.82 kips Therefore, design strength of the connection 197.82 kips
Thus, the maximum tension force that can be applied is 197.82 kips