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ME 270 – Final Exam, Sum 2020 NAME (Last, First):________________________________ Please PRINT) PUID #: __________________

ME 270 Final Exam – Sum 2020

Please review the following statement:

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Signature: ______________________________________

Instructor’s Name and Section: (Circle Your Section)

Sections: J Jones 11am-Noon (Synchronous) J Jones Distance Learning (Asynchronous)

Please review and sign the following statement:

Purdue Honor Pledge – “As a Boilermaker pursuing academic excellence, I pledge to be honest and true in all that I do. Accountable together – We are Purdue.”

Signature: ______________________________________

INSTRUCTIONS

Begin each problem in the space provided on the examination sheets. If additional space is required, use the white lined paper provided to you.

Work on one side of each sheet only, with only one problem on a sheet.

Each problem is worth 25 points.

Please remember that for you to obtain maximum credit for a problem, it must be clearly presented. Also, please make note of the following instructions.

• The only authorized exam calculators are the TI-30XIIS or the TI-30Xa.

• The allowable exam time for the Final Exam is 120 minutes.

• The coordinate system must be clearly identified.

• Where appropriate, free body diagrams must be drawn. These should be drawn separately from the given figures.

• Units must be clearly stated as part of the answer.

• You must carefully delineate vector and scalar quantities.

• Please use a black pen for the exam.

• Do not write on the back side of your exam paper.

If the solution does not follow a logical thought process, it will be assumed in error.

When handing in the test, please make sure that all sheets are in the correct sequential order and make sure that your name is at the top of every page that you wish to have graded.



PROBLEM 1 (25 points)

1A. (5 pts) A 2000 N crate (D) is suspended using ropes AB and AC and is in static equilibrium. If θ = 53.13˚, determine the tension in ropes AB and AC.

1B. (5 pts) Plate AB is supported by a pin support

at A and a rocker support at B and is in static equilibrium. For the loading shown (neglect the weight of the plate), determine the magnitude of the reaction force at B. If the 100 in-lb couple were shifted to point A, would FB increase, decrease or remain the same.

TAB = (2 points)

TAC =

(3 points)

FB = ___________ lbs (3 pts) FB = (Increase Decrease Remain the Same) (2 pts) (Circle one)

x

y

x

y



1C. (5 pts) Truss ABCDEFG is loaded with a single 600 lb force at joint C and is in static equilibrium. Determine the magnitude of the force in member BC and whether it is in tension or compression. List and circle all zero-force members.

1D. (5 pts) For the 50 lb chest shown, determine the force P needed to tip the chest, assuming the dimension d = 3 ft. If the 30˚ angle were increased, would it increase or decrease the probability of tipping the chest?

FBC = lbs T C or Zero (Circle one) (3 pts)

Zero-Force Members = (2 pts)

x

y

μs = 0.7

Ptip = _____ lbs (3 pts) Prob. of Tip = Increase Decrease Same (2pts)

(Circle One)

x

y



1E. (5 pts) The A-Frame shown is supported by a rocker support at A and a pin support at E and is in static equilibrium. On the schematics below, complete a free-body diagram of each member of the A-Frame. Assuming Ay = 250 j N, Determine the force FB on member BD in vector form).

(2 PTS)

( F B ) = _________i + ___________j N (3 pts)

x

y

B D

A

B

C

E

D

C



Extra Page (if needed)



PROBLEM 2 (25 points).

2A. (5 pts) A rigid beam (AC) is supported by thin circular rod (AB) and a square post (CD). The diameter of the rod is 20 mm and the square post is 30 mm a side. Determine the axial stress in rod (AB) and post (CD) in MPa if the load on beam AC is P = 2000 N. Remember 1MPa = 1x106Pa.

2B. (5 pts) A joint is fastened together with two bolts as shown.

a) If the failure shear stress for the bolts is

failτ = 800MPa , determine the minimum diameter in

mm of each bolt.

b) If the plates were glued together rather than bolted,

determine the maximum shear stress in MPa for the

loading shown.

𝜎AB = ________________________ (2 pts) 𝜎CD = ________________________ (3 pts)

mina) (d) = ____________mm (3pts) maxb) ( ) = ______________MPa (2 pts)



2C. (5 pts) Two shafts (one solid and one hollow) are made of

steel having an allowable shear stress of allowτ = 12 ksi.

If the diameter of the solid shaft is 1.5 in, determine the max torque TA that can be transmitted. What would be the max torque TB if a 1-in diameter hole is bored through the shaft? Express the torques in units of in-lbs. Sketch the shear-stress distribution along a radial line for the hollow shaft. Remember 1ksi = 1000 lbs/in2.

2D. (5 pts) From the T-beam cross section shown, determine ӯ using the coordinate system provided and then determine Ix

about this centroid.

T = A _______________in-lbs (2 pts) T = B ________________in_lbs (2 pts)

𝐲 = _______________in (2 pts) 𝑰𝑿 =________________in4 (3 pts)

1 pt

TA

TB



2E. (5pts) Determine the area (A) and the moment of inertia of the area about the y-axis (Iy) for the

shaded area shown. (5 pts)

𝑨 = _______________in2 (2 pts) 𝑰𝒚 =________________in4 (3 pts)

dx

𝐲 = 𝒃

𝒂𝟐 𝒙𝟐



PROBLEM 3. (25 points)

3A. (5 pts) A solid circular shaft is loaded as shown and is in static equilibrium. Determine the magnitude of the maximum torque experienced on shaft AD and which segment of the shaft it occurs in.

3B. (5 pts) If a solid circular shaft has an applied torque is T = 2kN-m and the allowable stress is τAllow = 50MPa, what is the minimum diameter shaft that could be used and still insure the allowable stress was not exceeded. Also, express the minimum shaft size to the nearest whole mm.

𝑻 = N-m (4 pts) Segment = AB BC CD (Circle One) (1 pt)

𝐝𝐦𝐢𝐧 = _____________ mm (4 pts) (𝐝𝐦𝐢𝐧)nearest mm = _________________mm (1 pts)

T=2 kN-m



3C. (12 pts) If a tubular shaft has an outside diameter do = 200mm and an inside diameter di = 100mm, and if the applied torque is T = 2kN-m, determine the polar moment of inertia (J) and the shear stress at points A (𝛕𝐀) and B (𝛕𝐁) shown on the figure.

3D. (3 pts) If a solid circular shaft is replaced by a tubular shaft of the same outside diameter (do), will the maximum shear stress qualitatively increase, remain the same, or decrease given the applied torque is the same for both shafts? No work needs to be shown.

𝑱 = _____________________ m4 (4 pts)

𝛕𝐀 = _____________________ Pa (4 pts) 𝛕𝐁 = _____________________ Pa (4 pts)

𝝉𝒎𝒂𝒙 = Increase Remain the Same Decrease (Circle One) (3 pts)

T=2kN-m



PROBLEM 4. (25 points)

Given: Beam ABC is loaded as shown and is held in static equilibrium by a pin support at A and a

roller support at B. The beam cross-section is an inverted “L-shape” and has the dimensions shown

and a second moment of inertia of Ix = 2.00 in4.

FIND:

4A. (7 pts) Sketch a free-body diagram of the beam and determine the magnitudes of the reactions at

A and B.

Ay = (3 pts)

By = (3 pts)

FBD (1 pt)

50 lb/ft



4B. (8 pts) Draw the shear force and bending moment diagrams of the beam ABC. In order to

receive full credit, you must label the shear force and bending moment values on the diagram at

points A, B, and C, as well as the point(s) at which shear stress crosses zero and the point(s) at

which the bending moment is maximum. You may use the graphical method.

V(lbs)

M(ft-lbs)

x(ft)

x(ft)

50 lb/ft



Extra Page (if Needed)



Summer 2020 Final Exam – Equation Sheet Normal Stress and Strain

σx =FnA

σx(y) =−My

I

εx =σxE=∆L

L

εy = εz = − ϑεx

εx(y) =−y

ρ

FS =σfailσallow

Shear Stress and Strain

τ =V

A

τ(ρ) =Tρ

J

τ = Gγ

G =E

2(1 + ϑ)

γ =δsLs=π

2− θ

Second Area Moment

I = ∫ y2dA

A

I =1

12bh3 Rectangle

I =π

4r4 Circle

IB = IO + AdOB2

Polar Area Moment

J =π

2r4 Circle

J =π

2(ro4 − ri

4) Tube

Shear Force and Bending Moment

V(x) = V(0) + ∫ p(ϵ)dϵx

0

M(x) = M(0) + ∫ V(ϵ)dϵx

0

Buoyancy

=BF gV

Fluid Statics

= p gh

( )=eq avgF p Lw

Belt Friction

=L

S

Te

T

Distributed Loads

( )= L

eq 0F w x dx

( )= L

eq 0xF x w x dx

Centroids

=

cx dAx

dA =

cy dAy

dA

=

ci ii

ii

x A

xA

=

ci ii

ii

y A

yA

In 3D, =

ci ii

ii

x V

xV

Centers of Mass

=

cmx dAx

dA

=

cmy dAy

dA



=

cmi i ii

i ii

x A

xA

�̃� =∑ ycmiρiAii

∑ ρiAii

ME 270-Sum 2020 Final Exam NAME (Last, First): ________________________________

(Please PRINT) PUID #: __________________

ME 270 Final Exam – Summer 2020

please print) puid

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