Question

PROBLEM 6.5 The American Standard rolled-steel beam shown has been reinforced by attaching to it two 16 x. 200 mm plates, using 18-mm-diameter bolts spaced longitudinally every 120 mm. Knowing that the average allowable shearing stress in the bolts is 90 MPa determine the largest permissible vertical shearing force. (see Hint table) -16 mm X 200 mm Part A(mm) d (mm) Ad? (109 mm) (106 mm) S310 X 52 Top plate S310x52 Bot. plate 6650 0 95.3 1 164.86 95.44 D

Answer 1

Solution 16x 200 Plate - 16 X 200 mm ICI J cliameter 18 mm $310752 뉜 Spacing - 120mm allowable shear stress = 90 mpa We get here Is and d from table we look for 2318852 d = 305mm and I, 95.3x180 mm first we will get here centroidal moment of Inertia. take for x asets Ixz Iz + E (I rad') Ix but 12 95.3 x10 t +List +b+ x[4+$)]*2 Put here value and we will get 2 Ix 95.3810**2 [ 2oc X/63 +260 X11305+ 16 12 solve it we get Ix = 260.99 Xios

As here we take on y oxis centroid is. 2 3 Put here value 7 305 2 Rolă 7 = 160,5 so abone section AA moment wir.t (N.Axis) of area. Q 2. ху, Put here value we get Q 900 x 16 x 160.5 513.5x103 3 and here Tav Axz 4 So Zar 2 IT X 182 goy 4 Car 45804.420 N

so Avg. allouable shearing force in the bolt is Var 458o4.420 N and TAA Van A Put here ralue TAA u58o4.490 120x200 TAA 1.9085 N/mm² So allowable shear stres will be TAA Ix b Put here value we get 3 1.9085 vx 513,6 x 103 260.99 X10' x 300 soke it we get V 193.5 kn ✓

Part A (mm) demm) Ad²(10 mm) I Cloénm) 160.5 82.43 Top plate 3200 0:07 o S310 x 5.2 6650 O 95.3 Bot. Plate 3200 0.07 160.5 89.43 164.86 95.44 W