EM 319 - Mec

Name

EID

Unique Number

Instructions: Show all of your work. Free body diagrams are required for equilibriumanalyses. Place a box around your final answers and include units.

2d

Problem 2, The bar has length L, area,4, modulus E, and is subjected to a linear axial

load per unit length p(r): po@ I L) . (a) Determine the axial stress as a function of r,

(b) Determine the deflection of the bar at r : L, (c) Determine the deflection of the barat r : L/2 (20 points)

+k)= ?"?

Problem 1, The bars have area ,4,

Determine (a) the stress in each bar,and (c) the maximum load P that can(20 points) a

length -L, modulus E, and yield strength oy,

(b) the downward deflection of the load point,

be applied before one of the bars yields.

thermal expansion o,Determine the stress in

<----)

P

Problem 3.The bar oneach bar.

The bars have length L,, area A, modulus E, andthe right is subjected to a temperature change A 7 .(20 points) _

3L L.

r)

Sf-ry. fuI,Frwn

Tet!* */o{;ns

_Tcl l

'lrr vs 2//C

€

trr=a-)

, \D ) A L;rret Sr =,rL ? -JlJr--- --

So=trEf

kke\ /4",), 3s 8* = -Zh

So= # = -rh

-+ t? =+h.ft%

rnl4inz*tt- sl-*'^.g^rJrr/. .I

= PA + 2-C =€)

C=-/ f- P- BrC=a

+ g=-Zf

,^ (Sr)-tbF-+?25i- ?St

E eryipe tl.

l+l=.?f=7

=')to-*Zs,

?,o= 7qn

-3 f- -zA

rT-L

7

f ,B=

tr" --

c)

dJ)

)

-.-' -\ -+q(F +a-

3

t4= -B+C+

+k)

*f" t =o'c= B-**L

6_l -

4lc

zF*. u/*)-B , *f.f=o

-L7-flJCp>tr

@ tJk)= F

I t F-L*+ ,v, T4x

b--art 6T

(L & rlo dr *7

ao -o^-----\/ -

Vt2-

,./- L- -a Da

E

r , +c

b f"L- Lp+

:o= *t"L= -tpL

@+ N/x-)--

9L = 5/*=L)= o

6a= Lr+L L4L *b T-zTf

rtl(*)T

tgf=a

SE

t"

7o2 de-

2,t

2,t

'-P

=

I .

n1l

Pt /

./t

\LI

'=

&&

SIL*

L

BLaBT{*

5i--lb,

+

tc

f vv'o\, i c

tl+*u;al hrl :

tz

4 = * Eaal-

-?fc = -*EtxaT

= j ' f t + Ee=

h r i"or-L(Afur frdarL

+"'7-Lh EA-<aT

-+ Eu*zT

zil; = -lLc-3LE-c(= -79

L4

CLtr t a.ATL