Question

Learning Goal: To analyze two bullt-up members that have the same geometry but are fastened differently, determine the maximum applicable shear force on each cross section, and determine the adjustment in spacing between the weaker member's fasteners that would allow the member to support the equivalent maximum shear force of the stronger member, The two cross sections shown below, (a) and (b), are subjected to a vertical shear force as shown. The members are fastened by nails that can support a load of 23 00 kN each and are spaced perpendicularly to the page in increments of 8 = 125.0 mm. The geometries of the cross sections are given by a = 250.0 mm, b = 50.00 mm. c = 295.0 m, d = 150 mm, and e = 345 mm. Assume the cross sections are uniform along the entire lengths of ПП (a) L. the members. Part A - Maximum applicable shear force on the member (a) Determine the maximum applicable shear force on the member (a). Express your answer to four significant figures and include the appropriate units. View Available Hint(s) THIHA ? Value Units

Answer 1

250 mm 150 Spacing = 125 mm sol 345 2915 х n Я (a) (6) geometry is same, both have same area and *since Scome moment of inertia. Neutsal axis E ai Li Za a, - Sox295 -14750 mm Az =250XSO =12,500 mm a= -50x295 =14750 mm y = 205 = 147.5 mm 42=29575€ = 300 mm Ly = 147.5 mm 7= 14750 x147.5x2 +12500X320 2X14750+12500 ☺ = 198.834 mm Moment of inertia I - E (Isex.cG+Ah) Parallel axis theorem Ixx = 2x soxas 12 +14750X (198.834–1475 / + 250x503 +12500x (128.3-3 2. 12 Ixx =477.793 xlos momy past-A Shear flow at jonction of web & Alonge 17 q V.a.y Ixx a = VX295xsox (198.839-1475) 477.743x106 V qa 630.957 Shear forre in Fasteners =qxSpacing 23x103 Vmax 630.957 *125 Wal16.096 KN<-mace. Shear force allowed Past -B Shear flow @ Junction î 345 VAJ q= VX50X345(198839-345 477.793x106 A So q v los).6 Shear force in fasteners 23x63 = Vmax losl.6 Vmax = 193.49 kn *25 past-c ..@) geometoy is weaker Vmax = 193.49 kn Spacing required for weaker section 23x103 193.49x103 630.957 XS 15=75 mm Scanned with CamScanner

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