Question

Mech Design

PROBLEM #1 (50 points) A bolt with a nut is used to clamp together a 1-in cast-iron plate and a 2-in steel plate. The bolt is in-13 UNC. (a) Determine a suitable length for the bolt, rounded up to the nearest in. (b) Determine the bolt stiffness. (c) Determine the stiffness of the members

Answer 1

Solution Given, thickness of Cast iron t = lin thickuens of Steel plate kg = 2 in Bolt is in 13 UNC (a)! Griplength lg = 2.+1 = tette - 3 in nuty the height te for nominal size in 0.4375 in From table A-31" Dimen Gons of hexagonal of 0.5 in is 1 - 1 Length of the bolt dy 3 +0.4375 +1 L = 3.4375 in ~ 3.5 in The Suitable length for the bolt [L= 3.5in Are Threaded length for metric series for a cupany (d: diameter of buit] (b) L = 20 +0.ar in -(2x+ 0.2s in [. d = 1/2 in LT = leasin diameters and arcas y Cocerse pitch and fine pitch for nomine diameter of 0.5in the value tensile + from lagle metric thoready 1 . sties area is 0.1419 in 2 Ay of anthreaded portion Ana Aa : T H 0.1963 in dength of unthreaded portion is L- 3.5-1.25 l = 2.25 in

Distance between joint line and dotted truster line length of threaded portion in grip 3-2.25 de = lg-ld 사 -0.75 in : 14,5 MPsi E = 14,5 Xlopsi of Cast hon - 30 MPsi Young's is modules Young's moduly : Stiftnes of threaded Steel of E : 30x166 psi part of bolt 0.1419 x 30 A E D-75 ht - 5676 MDbf K stiffness of unthreaded part of belt 0.1963 X 30 Kd = AE 2.25 بل d. 6173 Mest in " Stiftres of bolt - ko + + 1 Id 2.6173 5.676 16 1.7913 Mestlin Ave (0) Now , Compute the length of frusta considering the fact that it extends half way into the grip length f. (24) f = 1.5in The ob-f - 2-1.5 0=0.5 in outer diameter of trustrum of Steel member at joint interface $ 0,75 + 200 tan 30% = 1.904 in

Spring rate of Cast inn en . 0.5774 T Ed T(1,1554 +0-d) (0+d) [Croisst+o+d) (0-0). (0.5774) (0) (14.5) (0.5) en [crss (1) +0.76-0.5) (0.75 +0.5) (MUST(1)+0.75 +0.5) (0.75-0.5) 12.268 Meestlin ki of Smaller frustum of Steel Spring rate lul 01577418 (30) (0.15) [(14556015) +1.904 -0.5)(1.904+0.5) (loss (0.5) +1,90470.5) (1.904-005). 210.-11 M0bt lin Kr. Spring rate of larger frustum of steel ke 0.5774 0 (3.) (0.5) [Ch.155(7,5) + ooth-0.5) (0.75 +0.5) en (1,156 (1,5) + 0-75 +0.5) (0.75 -0.5) K3 = 22.6 Mebelin The mean Stiftness of members in series I + K₂ Kg kom + + 22-6 12.26+ 210.71 0.1305 7.662 Mistlin - km 7.662 Mibt lin ". Then Stiftness of the member Thank You