Question

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Question A cantilever box beam carrying a point load of 0.36 kN at its tip is to be constructed from 4 boards nailed together as shown in Fig 1. Assume that each Nail B can carry a maximum shear force of 0.13 kN. (a) Draw the SFD of the cantilever beam and determine the shear force at mid-span. (b) Draw the shear stress distribution across the section at mid-span and determine the maximum shear stress and its location. (c) Determine the maximum spacing of Nail B. 0.36 kN 38 152 38 152 38 Fig 1 A cantilever beam and its cross section (All dimensions are in mm)

Answer 1

It is pure shear case the shear force will be constant all over the beam

a)

Given Cantilever beam 0-361 10.36kN Shear force 1 So; Shear fosce at mid-spanis 10-36 kN / 38 Let's find the moment of bestia I= bid body = (152738) X (152+33)} 12. - (152 -3 84 B=(152+38 b=38 I= 94.526 x 100 mm We know shear stress formula

-> SAY = Ag, +(Any) + a[3R4 (152–32))x(15.2-22) = 1042568 MA? ta so; ama s V (Ay) - VAS + V (Ag) (1) V (Ay) = 0.36x188x (152-838 +38) x (152) 94.526 xix (152438) IX B = 0.01099 N/mm² IXQb) (in v(A2y) = 0.36x1032/38x (152-38)) x (152-3- 94.526 X166 x 2x38] ) = 0.02474 N/mm = new :0 0 1099 +0.02475 10 0357 N

b)

Shear Stoess distributions amax - - - 0-0357 Mpa So maximum Shear stress occurs at Nutral wis

c)

♡ for spacing of If force in nail - Shear force S-spacing of na?! momat Area. Sej 3= FI V(AY) = 0.13x 10 x (94.526x16 0 36X102x(38*(152+38)) 03021033|(33 (5243691333) S +32 3=82.94mm

So spacing of nail B is 82.94mm

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