ME 306 – Mechanics of Materials FINAL EXAM

05/12/06 Name __________________________

Page 1 12/12/2008

Problem 1 (## pts):

The uniform aluminum-alloy shaft is attached to a rigid wall at end A and is welded to a

rigid flange at end C.

(a) The holes in the flange were supposed to align with holes tapped in the wall plate, but

actually an initial external torque (TB)i must be applied in order to to perfectly align the

holes in the flange with the holes in the wall plate. By what angle (in degrees) are the

flange and the wall plate initially misaligned?

(b) While the initial torque (TB)i aligns the holes, bolts are

inserted at C and securely tightened. Subsequently an

external torque (TB)f is applied at B. Determine the

resulting maximum shear stress in segment AB and the

maximum shear stress in segment BC.

3

1 23.8 10 , 1.5 , 60 ., 40 .G ksi d in L in L in= × = = =

(TB)i=820lb in, (TB)f =7500lb in

Answers: (a) 1.493cφ = � ; (b) max,1 5.27ksiτ = , max,2 6.05ksiτ =

ME 306 – Mechanics of Materials FINAL EXAM

05/12/06 Name __________________________

Page 2 12/12/2008

Problem 2 (## pts):

Beam AB (beam 1) is cantilevered from a rigid wall at A. Through a roller at B, beam 1

supports one end of simply supported beam BC (beam 2). Both beams have the same

flexural rigidity, EI, and both have the same length, L. When there is no load on either

beam, the beams are both horizontal. For the two-beam system with a uniform load on

beam 2, as shown in Fig., determine expressions for the following:

(a) the common deflection at B, (v1)B =

(v2)B

(b) the slope of beam 1 at end B, (v’1)B

and (c) the slope of beam 2 and end C,

(v’2)C.

ME 306 – Mechanics of Materials FINAL EXAM

05/12/06 Name __________________________

Page 3 12/12/2008

Problem 3 (## pts)

A chair on a ski lift is supported by a steel pipe whose outer diameter is d0 = 60 mm and

whose inner diameter is di = 52 mm. The weight of the pipe may be neglected in

comparison with the weight of the chair and its occupants, which is W = 2 kN.

(a) Determine the stresses xσ , yσ , xyτ at point C,

which is on the front of the pipe at the indicated

cross section. The x axis is parallel to ilk 45o

section of pipe, AB.

(b) Using a Mohr’s circle, determine the principal

stresses and the maximum in-plane shear stress at

point C.

(c) Determine the maximum tensile stress in the

straight section of the pipe, DE.

ME 306 – Mechanics of Materials FINAL EXAM

05/12/06 Name __________________________

Page 4 12/12/2008

Problem 4 (## pts)

Rigid walls at each end of a solid slender rod AB provide fixed-fixed boundary conditions

for the member in Fig. At the reference temperature, T0, the rod is perfectly stress-free.

(a) Derive a formula that expresses the uniform increase in temperature, crT� , required to

cause elastic buckling of the compression member.

Express your answer in terms of the following material

and geometric parameters: the coefficient of thermal

expansion α , and the slenderness ratio, L./r.

(b) Determine the value of crT� in °F required to cause

elastic buckling of a stainless steel rod with a diameter of

d = 1 in. and a length of L = 4ft. The coefficient of

thermal expansion for stainless steel is 6 =9.6 10 /°Fα × .

ME 306 – Mechanics of Materials FINAL EXAM

05/12/06 Name __________________________

Page 5 12/12/2008

Problem 5 (## pts)

For the rod and sliding collar of Fig., (a) determine an expression for max∆ as a function

of W, A, E, h, and L.

(b) If the weight is dropped from a height of

40 sth = ∆ determine the value of the impact

amplification factor max / st∆ ∆ .

(c) Determine the maximum impact stress

maxσ in terms of the static stress stσ , the

drop height h, and the rod parameters.