Question

30 pt Select the lightest angular to support a live load LL- 50 Kips and a dead load DL30 Kips. The angular will be connected to a gusset plate through bolts. Use at least three bolts in one line and 3 in as the distance between bolts in the load direction. Use A36 The length of the angular is 28 ft. (ignore block shear) Angular wPlate

Answer 1

GIVEN DATA Member Details Grade of Steel Length of member A 36 28 ft Connection Details Diameter of bolt, 7 in assumed) Loads Service dead load Service live load 30 kips 50 kips CALCULATIONS A 36 For grade of steel Yield stress, Ultimate stress, 36 ksi 58 ksi Diamter of bolt hole, 1 in Factored Design Load i) T1.4D 42 kips ii)「 = 1.2 D + 1.6 L 36 80 116 kips 116 kips Hence, factored design load Yielding in the gross section Design strength of gross section is obtained as 0.9 x 36 x Ag 32.4 A Therefore 32.4 9116 3.58 in racture in the net section U08 (since the angle is connected to one leg Shear lag Factor with 4 fasteners) 0.8 xAn 0.8 A Effective area Design strength of net section is obtained as

0.75x 58x0.8 A 34.8 A A11634.8 Therefore, 3.33 in 2 A3.58n 2 Threfore, required area is Select L 4x4x5/8

GIVEN DATA Load Applied Factored design load, 116 kips Member Details Grade of Steel Member designation Gross area of section, Thickness of member, Minimum radius of gyration A 36 L 4x4x5/8 4.61 in 2 Ag 0.625 in 1.2 in Connection Details Member connected to one/two legs Diameter of bolt hole Number of bolts across a section, Number of bolts in line Pitch of the bolts Distance of centroid from edge one leg in 3 plus 3 in 1.22 in CALCULATIONS For grade of steel, A 36 Yield stress, 36 ksi 58 ksi Ultimate stress, DESIGN STRENGTH Yielding in the gross section Design strength of gross section is obtained as: 0.9 x 36 149.4 kips X 4.610 Fracture in the net section A Ag-n(d,t) Net area, 4.61 2 x 1.000 x 0.625 3.36 in NOTE Shear lag Factor, 1.0 when connected to two legs when connected to one leg where x is distance of centroid from edge and L is the length of connection Length of connection in the direction of loading 6 in

Since the member is connected to one leg, U1-x/L 0.6 (with three fasteners-Case 8) Shear lag Factor 0.797 Thus, U0.797 (Maximum of Case-2 & Case-8) Effective area UA e 0.797 x 3.360 2.678 in2 Design strength of net section is obtained as: 0.75 x58 x 2.678 116.5 kips Thus, design strength of the member is the smallest of the three values, that is 116 Tu] 9.7,-116.5 kips SAFE Slenderness ratio, ry28 x 2/ 1.2 280 < 300 Hence SAFE ,