Tài liệu shi20396 chương 10 doc

Chapter 10

10-1

10-2 A = Sdm

dim(Auscu) = dim(S) dim(dm) = kpsi · inm

dim(ASI) = dim(S1) dim

dm

1

= MPa · mmm

ASI = MPa

kpsi ·

mmm

inm Auscu = 6.894 757(25.40)m Auscu

.

= 6.895(25.4)m Auscu Ans.

For music wire, from Table 10-4:

Auscu = 201, m = 0.145; what is ASI?

ASI = 6.89(25.4)0.145(201) = 2214 MPa · mmm Ans.

10-3 Given: Music wire, d = 0.105 in, OD = 1.225 in, plain ground ends, Nt = 12 coils.

Table 10-1: Na = Nt − 1 = 12 − 1 = 11

Ls = d Nt = 0.105(12) = 1.26 in

Table 10-4: A = 201, m = 0.145

(a) Eq. (10-14): Sut = 201

(0.105)0.145 = 278.7 kpsi

Table 10-6: Ssy = 0.45(278.7) = 125.4 kpsi

D = 1.225 − 0.105 = 1.120 in

C = D

d = 1.120

0.105 = 10.67

Eq. (10-6): KB = 4(10.67) + 2

4(10.67) − 3 = 1.126

Eq. (10-3): F|Ssy = πd3 Ssy

8KB D = π(0.105)3(125.4)(103)

8(1.126)(1.120) = 45.2 lbf

Eq. (10-9): k = d4G

8D3Na

= (0.105)4(11.75)(106)

8(1.120)3(11) = 11.55 lbf/in

L0 = F|Ssy

k + Ls = 45.2

11.55 + 1.26 = 5.17 in Ans.

1

2

"

4"

1" 1

2

"

4"

1"

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270 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design

(b) F|Ssy = 45.2 lbf Ans.

(c) k = 11.55 lbf/in Ans.

(d) (L0)cr = 2.63D

α = 2.63(1.120)

0.5 = 5.89 in

Many designers provide (L0)cr/L0 ≥ 5 or more; therefore, plain ground ends are not

often used in machinery due to buckling uncertainty.

10-4 Referring to Prob. 10-3 solution, C = 10.67, Na = 11, Ssy = 125.4 kpsi, (L0)cr =

5.89 in and F = 45.2 lbf (at yield).

Eq. (10-18): 4 ≤ C ≤ 12 C = 10.67 O.K.

Eq. (10-19): 3 ≤ Na ≤ 15 Na = 11 O.K.

L0 = 5.17 in, Ls = 1.26 in

y1 = F1

k = 30

11.55 = 2.60 in

L1 = L0 − y1 = 5.17 − 2.60 = 2.57 in

ξ = ys

y1

− 1 = 5.17 − 1.26

2.60 − 1 = 0.50

Eq. (10-20): ξ ≥ 0.15, ξ = 0.50 O.K.

From Eq. (10-3) for static service

τ1 = KB

8F1D

πd3



= 1.126 

8(30)(1.120)

π(0.105)3



= 83 224 psi

ns = Ssy

τ1

= 125.4(103)

83 224 = 1.51

Eq. (10-21): ns ≥ 1.2, ns = 1.51 O.K.

τs = τ1

45.2

30 

= 83 22445.2

30 

= 125 391 psi

Ssy/τs = 125.4(103

)/125 391 .

= 1

Ssy/τs ≥ (ns)d : Not solid-safe. Not O.K.

L0 ≤ (L0)cr: 5.17 ≤ 5.89 Margin could be higher, Not O.K.

Design is unsatisfactory. Operate over a rod? Ans.

L0

L1

y1 F1 ys

Ls

Fs

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