Student Code Number:

Ph.D. Qualifying Exam

SOLIDS & STRUCTURAL MECHANICS

Spring 2014

Prof. P. KwonProf. T. Reid-Bush

Directions: Closed book and notes, you may use a onepage (8.5x11) — one sided formula sheet..

Answer all four questions are weighted equally

Time: 3.0 hrs.

Determine the reaction forces in sections, AB, AC and AD and displacements at A, C and D of thebar shown below. Please indicate the direction of displacements (up or down). The section AB ismade of a tube with outer and inner diameters of 6cm and 3cm, respectively. The section B hasbeen mounted on rigid wall as shown. In the diagram, the sections AC and AD are made of a2cm diameter solid bar and connected by the rigid bar (shown at A). The elastic modulus is20G Pa.

e

150NC

Rigid A

D

lOON

B

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A cylindrical pressure vessel whose radius and thickness are 20cm and 2cm,respectively, is carrying 2MPa of pressure. The vessel is made with the material thathas E3OGPa and o0.3. A strain gage is mounted at 45° to monitor the pressure.Determine the reading on the strain gage.

44

For full credit, all work must be shown. Free Body Diagrams must also be includedfor full credit.

3, Several forces are applied to the pipe assembly shown. Knowing that the inner andouter diameters of the pipe are equal to 1.50 inches and 1.75 inches respectively1,determine a) the forces and moments acting at point H located at the top of the outsidesurface of the pipe , b) the principal planes and the principal stre~ses at H, b) themaximum shearing stress at the same point.

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4. For the beam and loading shown, determine the equation of the elastic curve, thedeflection at B and the deflection at C.

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Determine the reaction forces in sections, AB, AC and AD and displacements at A, C and D of thebar shown below. Please indicate the direction of displacements (up or down). The section AB ismade of a tube with outer and inner diameters of 6cm and 3cm, respectively. The section B hasbeen mounted on rigid wall as shown. the sections AC and AD are made of a 2cm diameter solidbar and connected by the rigid bar(shown at A). The elastic modulus is 2OGPa.

R =SON

c RAC=1SONR =100NAD

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D

lOON

—50r(0.032 _0.0152)

~AC 150 =477.5kPair(O.012)

~AD 100 =318.3kPa~r(O.O12)

t 2

~ t!~ 2~20~=10MFa2t 4

s9 =——v---1-—v--=-=———0.3—= 566.7,uE E F 30 30

oz a0 a. 10 20a =~—v.~-—v-~.-=———O.3-—=133.3p

- F F F 30 30

.133~.3 3S~r75Z~.7 Reading on Strain gage =3SOja

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