MER311: Advanced StrengthSpring 2006

EXAM II Mechanical EngineeringUnion College

. SOL. ()TIQ NNAME:

~~

1 a. Detem1ine the minimum required thickness t of thecolumns if a factor of safety n=3 is required with respect toEuler buckling (P cr=3P).

~ - 'frt.e.IrGQ -

(a)

{b)

(.1 m- l.t.) 'I]~1~~~~.~~!9]~~~.lStr\~ = (.'3rf")~'

fJii3. 12)(.'10' ~""

-tIlt

1H\.t --

2.

-1-

Problem 1: A viewing platfom1 in a wild-animal park issupported by a row of aluminum pipe columns having lengthL=3.25m and outer diameter d=100mm. The bases of thecolumns are set in concrete footings and the tops of thecolumns are supported laterally (pinned) by the platfom1.The columns are being designed to support compressive

Mechanical EngineeringUnion College

EXAMllMER311: Advanced StrengthSpring 2006

1 b. Calculate the compressive stress in the column under maximum loading. Is the beam in the

Euler domain of buckling? Explain your answer.

(J~~--

--

A'tJOc.(;~UtJo~~5OtJ1#E

--~:

2.. '2...

T\i~ m)t})<.x ~uW"

E Q" ~ T ':f.CJ(\J

Ll.) ec, ~ ~TAN(jE~\T~ESI't'-.)CE.

5EE~A-PPl. y

ST(\.ESS

DGf"S

-~ - ~

Jo~~GV\'~ cGlRue

-1-

MER311: Advanced StrengthSpring 2006

EXAM II Mechanical EngineeringUnion College

PROBLEM 2: Using singularity functions,write expressions for the shear, bendingmoment, curvature, and deflection of thebeam shown. Be sure to calculate allintegration constants.

O.6m--. ?m OmORm

.2kN

1.5kN/m

~-.44kN om

';

1.2 ~N t

-.!:5.!)1T - -- ---~4~~~~~ ,

,-

i-.~A~t---,

-2.'A~t -1.5 ~\.1/m

~ A~ eQc..4\~ ~ T\.lc:. BE.t4- V)'\ c ~~ 13~ GcJCl.,:prI~

(!)

@

@

-4-

t L1J

Mechanical EngineeringUnion College

EXAM nMER311: Advanced StrengthSpring 2006

wto~ ppL.}E.~IS~CO) ::0.co ~ ot,"t:t.CJwfJQo t.J 'O~ ~~FI R ST ~cz=o,-::c-~>

T~r;. ~CO).)() &:>o'tJO~tt.., CONOt.llON fb~ ~I..S ~~EW\ :IS (.(.(3"r-') ~oSD~ 5~u~G 1'~:ts ~o~'O"4n y CO,J().t-Tror!J ~tON6- C.tJXT~ @ IWlV @

1 I f\' ( \ ~.' (\, ( . )~ ~ ( ! .LI

I -= 0 :: Ei -0. 'i33Sy:).N 3.'fr')J + O.2~W 3.0m 't" O. °'2 S VY'\ 3.0,...)

8E 'R'E (.,.J~ ~ \\J6)1-et

c.A'fJ~-.JDNoCc.)

u=

-5-

MER311: Advanced StrengthSpring 2006

EXAM II Mechanical EngilleeringUnion College

Ft.,!\.

Foa ,1

.G f).AI f '"

"- "

~

a Ii R

.:Iff III

:F

~

II tI\

,-CI

MI I ~

III: -J

--!'- :_1\: . ia..- ~

~ ja. ~

~

Fe.-" \...I

I,-.. IF

~'fEr

T sF Ft--Lt f't

- - ~1 .r '- : ..

r - '"- .'0,. ,'t I f

: ,II t

to. t

F+).)Qt~," TiE ~~T ~e:n.e T"'cvrz.V~6 Gc"n.~ cnos~E s ~Rt:~~ A))o U~f)eY\.~~~~,..~ o?T"tG R&t.A~S~t.P 8&7l,.JE;NT\t6~u-eG. W'Gnu e EQc,tA<..S 'l,En.a ~

(,..OI.fo)G- ~ 8t o...\tGn.E (..l ,~.MA~mGl'r1'. Tijr:. R~ of l'ij8 E:("~j'tc.. c.c..nue

fQc.Y)'\ ~A" ~ ~e m~~t.ml.m "*11\5"It> e;~~ 1~E: p~ F~ T-..G

{"}... ,...In A ~~W),,~ ~ rv.1 M" G.

. TU:ts h\e~N~ "l'~"r1~e ~~ UtJOE\"li\tE' e ,-",~CJe ~wEG~ ~y..IT A~~D -rhtZ ~~\En'~P7 IS c::~4t.."t) 1'ij~ AI1~ UNDER. -mE" e c.uRU'

Fuc;.rt\ T~G ~""iliR£.t:IlT 1CJ~Nr Co.~Q. --~- a ~r!

-~\ __1 ;:~-f~ -n

i.L~-G)c%

~-~

1--1- l-I I

':;::,.., .I

~ :.J:.:~ ~- -;I II II IIIe

-I,

ft,.ItI

-jI n: t..e

ir t

!-Jj=0-Q.'<1 LA-

-6- - "n '010.

MER311: Advanced StrengthSpring 2006

EXAM II Mechanical EngineeringUnion College

BONUS (lOpts): Using the moment area method, detemline the deflection of the free end, thecurvature of the free end, the curvature of the pinned end.-I t\£ cCJnVR-TLnE of'T\t£ eINJJ5t) E)J,1) :t s

T\\e \An~ O~OEn. .'fie. ~ ..

c.(,;y\."V~(,..1"t' D.t~6-n.'4W' I ~

foC)~'O

"Bt DETER..W\.1~"'; G

R2,cy)/\C"'\1.'tJ~

?:tlo

to WH-£n.E T\t£

F.a.. Q.-- .-E't. Lot6A'='

--

c.(;tl"\l~l'vttt::

E'tJ f) IS FoCi~"O'" "

~ 'tJ'P D

~=

-7.