Question

The beam, the cross section of which is given in the figure, consists of 25 mm thick boards. The slip safety stress for nails is given as tem= 100MPa. The diameter of the nails is 5 mm and the gap between the nails along the beam axis is 200 mm · (30P) according to this 50 200 a) Calculate the intensity of the maximum V shear force that can be applied to the cross section through the direction of the vertical symmetry axis. b) Calculate the intensity of the maximum V cutting force that can be sectioned through the horizontal symmetry axis direction.. 150 Note: All dimensions in the figure are given in mm.e

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Answer 1

Soli- = 100 MPa Tallow. Nail diameter, d=5mm i. Area of each nail = I d² ) A = 7 (25) mm² Calculate Shear force offered by a single nail as - V = Zallow A 100% T (25) 625 T N = 1963.495 N Considering vertical symmetry artis Calculate moment of gertia about verbal aics - 1 25 150(50 + 25+253 260 IN-A 2008 1503 12 12. 150 25 25 so INA = 43750000 mmu 25 1 calculate shear Force per 150- + 75mm s sparing using relation- V' VA ý , INA spacing blu nails Sheared Area = Shaded portion = 2(75% 25) = 3750 mm2 beos in one spacing, there are 2 nails s = 200mm - 37.5mm by symmetry, ý = 75/2 ý a distance ble centeroid of Sheared area and Neutral anis.

For sale design, Vinduced > Vallowable 2 x V & VAų xs IN. A X 200 2 x 1963.495 > V X 3750 x 37.5 43750060 V s 6108.65N Vmax < 6109 N F 6.1 UN • AB. Max, Shear Force by Vertical Axis Symmetry. (b) Considering horizontal aris symmetry - IN A = 150 x 2003 100x 1503 =7185000 mmu 12 12 For sale 150 + 25 150 25 87.5 mm s = 200 mm, A = 150x25 = 3750 mm² 2. For safe design x 200 2 x 1963.495 Z vX3750 X 87.5 718750oo 150 'Uman. <u301N F 4.3 UN LAS. S Max. Shear Force by horizontal axis symmety. as ICT Sheased area ý A