Question

Required information A 1.75-in. steel plate and a 1-in gray cast iron plate are compressed with one bolt and nut. The bolt is in-13 UNC. A V2 N American Standard plain washer is used under the head of the bolt and under the NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. nut. Determine the bolt stiffness. The bolt stiffness is Mib/in.

Answer 1

I in Solution •Steel plate thickness (t) = 1.75 in Crray cast iron plate thickness bolt specification # 2 in 13 UNC { d = 1 in Tensile stress area (At) washer 1 N Amesi.com og tandard, thickness of washer (tw) = 0.095 in . 0.1419 in 2 Modulus at Elasticity of stelle (fs) - 30 X 106psi Modulus of Elosticity of gray cast iron (EC) = 14,5X10psi - Frustum method :- 0.75in. 1.4225in Ky 0.4225 in K2 1 1.4225 in K3 K K * 2 . •The frusta extend haltway into the point distance 1 (0.095 + 1.75+1) = 1.4225 in The distance between the joint line and datted frusta line is 1.4225-1 - 0.4225 in. The top frusta consist of steel washer & Steel plate of 1.3275 inch. They can be considered a single frustum of 1,4225 in. thick.

• The outer diameter of the frustum of cast iron member at the point Interface is 0.75+2 (1) ton3o - 1. 2047 in The outer diameter at of the the midpoint entine point is 0.75 + 21.4225) tanzo" 2.3926 in The spring rate in steel (upper frustam: - ki 0.5774* (E)(d) In [1.155++D-d ] Totd] [1.155€ + Dfd] [ord] Ky = obt/in} 0.5774 * (30x106) (0.57 In [1.355(1.42254+2.3926-0.5] 2.3926 +0,5] [1.155(1,4225)+2.3926 +0,5) 2.3926 -0.5] {kt = = 155,36 X10€ in steel Clower freestum) :- Ke = 0.5774 T (30 X106) (0.5) in [1-3 rr(0.4295)+1.9047_0,5] [1.901740.5] [1.155(0.4225) +1.9047 +0.5 1.9047-0.57 The spring nate Kat Sky = 2.33.31 x105 lbfling The spring rate in cast iron (lower frustum) :- 0.5774 T (14,5X10G) (0.5) in [[1298615+ 0.45-0.5][0,75+0.5) 121.155 (1)+0.75+-0.5] [0,15-0,5) Įks Ks = 12.268 X106 lbt lins The material stiffness (km): - } + 1/km + I K3 K2

+ home 1 155.36X106 29, 91X106 12.968 X1 of km = 10.856 8106 ebt/in between d- thickness of all material squeezed face of bolt and face of nut I 1.75+ 1 + 0.095 2.845 in thickness - 1.25 in Nut H 7 inch 0.4375 in 16 • Fastener length (L) :- Ly It H L> 2.845+0.4375 L> 3.2825 suitable length {L = 3.4 inch? Threaded length :- LT ad + 1 2(0.5)+ Length of unthreaded position In grip: ld=L-LT Id=3.4-1.25 Add = 2.15 in Length of threaded partion in grip: ht=l-ld lt=20845-2.15 {$t = 0.695 in} Area of unthreaded portion (Ad) :- Ad = Yud? I (0.52 O. 19635 in 2 balt stiffness (A) Ad At Es Ad lt + Atld (kb) = (0.19633) (0.1419) (30%106) (0.1985) 0.695 +0.1419) (2.15) . Ik6 1,893 x 106 lbflin

Thank you.