me 270 – summer 2014 final exam name (last, first): · me 270 – summer 2014 final exam name...

ME 270 – Summer 2014 Final Exam NAME (Last, First): ________________________________

ME 270 Final Exam – Summer 2014

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: ______________________________________

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, i.e.

• The only authorized exam calculator is the TI-30IIS • The allowable exam time for 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.

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.

Instructor’s Name and Section:

Sections: J Jones 9:50-10:50AM J Jones Distance Learning

Problem 1 __________

Problem 2 __________

Problem 3 __________

Problem 4 ___________

Total _______________



PROBLEM 1 (25 points) – Prob. 1 questions are all or nothing. 1A. Sphere E has a weight of 100N and is supported by cable CBA and spring CD. Determine the magnitudes of the tension in cable CB (assume the pulley is ideal) and the tension in spring CD. (5 pts)

1B. Member AB has a 900N force and 500 N-m couple loading the member. It is held in static equilibrium by a collar at A and a roller support at B. The collar at A can freely slide in the y-direction but motion in the x-direction and any rotation about point A is resisted by the collar. Determine the magnitudes of the reactions at collar A and roller B. (5 pts)



1C. For the truss shown, identify all zero-force members and calculate the magnitudes of the loads in members CD and AE and specifiy whether each is in tension or compression. (6 pts)

1D. Frame ABC is designed as a compound beam which has a pin connection between members AB and BC. The beam is supported by a fixed support at A and a rocker support at C. For the loads shown, determine the forces acting at B and C in vector form on member BC. (Hint: Sketch the individual free body diagrams first.) (4 pts)



1E. Determine the total angle of wrap around pegs A, B, and C collectively and calculate the smallest force P required to lift the 100 N crate. Assume the coefficient of friction between the cable and each peg is sµ = 0.1. (5 pts)



PROBLEM 2. (25 points)

GIVEN: The sign has a weight of 1000N with a center of mass at G. The sign is held in static equilibrium by a ball and socket support at A and cables BC and BD.

FIND: a) On the sketch provided, complete the free body diagram

of the sign. (3 pts)

b) Write vector expressions for the forces in cables BC and BD in terms of their unknown magnitudes

and their known unit vectors. (4 pts)

D

D

2 m

2 m

D



c) Determine the magnitudes of the tensions in cables BC and BD. (10 pts)

d) Determine the magnitudes of the reactions at the ball and socket support. (8 pts)



PROBLEM 3. (25 points) 3A. A wood specimen is subjected to an average normal stress of 2 ksi during a tensile test. Determine the axial load P applied to the specimen. Also, find the average shear stress developed along section a-a of the specimen. (5pts)

3B. A static analysis of beam AB results in BCF = 12.5kN and A = -7.5 i + 20 j kN . Determine the average shear stress (in kPa) in the 20 mm-diameter pin at A and the 30 mm-diameter pin at B that support the beam. (Hint: Note the type of connection used on each end of the beam.) (5 pts)



3C. Determine the magnitude of the torque (in kN-m) pulleys A and B create in shaft AB and calculate the maximum shear stress (in kPa) due to this torsional load. Assume the shaft has a diameter of 40 mm. (5 pts)

3D. The cross-section of a beam is “T-shaped” with the dimensions shown. The location of the centroid is identified on the artwork. Determine the second-area moment of inertia about the x-axis (Ix). Based on the shape of the cross-section, which of these statements are true (Ix > Iy , Ix < Iy, Ix = Iy). No calculations are necessary. (5 pts)

x

y



3E. For the shaded area bounded by the y-axis, y = 1 and x = y2; determine the area and the second moment area of inertia about the y-axis (Ix). Hint:Use a horizontal differential element. (5 pts)

x = y2



PROBLEM 4. (25 points)

Given: Beam ABCDE is loaded as shown and is held in static equilibrium by a pin support at A and a roller support at D. The beam cross-section is “T-shaped” and has the dimensions shown and a second moment of inertia of -6 4

xI = 13.8 x 10 m . (Note – NA refers to the neutral axis.)

FIND: a) Sketch a free-body diagram of the beam and determine the magnitudes of the reactions at A and D. (5 pts)

A B C D E 3 m 3 m 1 m

NA

4 kN

21 kN-m

2 kN/m

3 m 1 m

3 m

1 m

D C B A E 1 m

FBD (1 pt)



4b) On the axes provided, sketch the shear-force and bending-moment diagrams of the beam. (10pts)

V(kN)

M(kN-m)

x (m)

x(m)

4 kN

21 kN-m

2 kN/m

3 m 1 m

3 m 1 m

D C B A E



4c) In which segment(s) of the beam does pure bending occur (2 pts)

4d) In the segment of the beam where pure bending exists, determine the magnitudes of the maximum tensile bending stress and the maximum compressive bending stress. (8 pts)



Summer 2014 Final Exam – Equation Sheet Normal Stress and Strain

σ! =F!A

σ!(y) =−MyI

ε! =σ!E =

∆LL

ε! = ε! = − ϑε!

ε!(y) =−yρ

FS =σ!"#$σ!""#$

Shear Stress and Strain

τ =VA

τ(ρ) =TρJ

τ = Gγ

G =E

2 1+ ϑ

γ =δ!L!=π2 − θ

Second Area Moment

I = y!dA!

I =112 bh

! Rectangle

I =π4 r

! Circle

I! = I! + Ad!"!

Polar Area Moment

J =π2 r

! Circle

J =π2 r!! − r!! Tube

Shear Force and Bending Moment

V x = V 0 + p ϵ dϵ!

!

M x = M 0 + V ϵ dϵ!

!

Buoyancy

=ρBF gV

Fluid Statics

= ρp gh

( )=eq avgF p Lw

Belt Friction

µβ=L

S

T eT

Distributed Loads

( )= ∫L

eq 0F w x dx

( )= ∫L

eq 0xF x w x dx

Centroids

= ∫∫cx dAxdA

= ∫∫cy dAydA

=∑∑

ci ii

ii

x Ax

A =

∑∑

ci ii

ii

y Ay

A

In 3D, =∑∑

ci ii

ii

x Vx

V

Centers of Mass

ρ=

ρ∫∫

% cmx dAx

dA

ρ=

ρ∫∫

% cmy dAy

dA

ρ=

ρ

∑∑

%cmi i i

i

i ii

x Ax

A

ρ=

ρ

∑∑

%cmi i i

i

i ii

y Ay

A

ME 270 – Spring 2014 Exam 1 NAME (Last, First): ________________________________

[Type text]

ME 270 Final Exam Solutions – Summer 2014

1A. CBT = 115 N CDT = 57.5 N

1B. xA = 0 N yB = 900 N AM = - 1486 N-m

1C. Zero-Force Members: AF, EF, BC

CDF = 400 lbs C AEF = 667 lbs C

1D. onBCB = 4 j kN onBCC = 4 j kN

1E. oβ = 360 = 2 π rad. minP = 187 N

2A. FBD

2B. BC BCT = T (0.333 i - 0.667j + 0.667k) BD BDT = T (- 0.707 i - 0.707 j)

2C. BCT = 750 N BDT = 354 N

2D. xA = 0 N yA = 750 N zA = 500 N

3A. P = 4000 lbs = 4 kips ( )a-a avgτ = 250 psi

3B. ( )B avgτ = 17,684 kPa

3C. T = 0.60 kN-m maxτ = 47,770 kPa

3D. 4xI = 33.3 in x yI > I

3E. 2 2A = 1/3m = 0.333 m 4 4

yI = 1/5m = 0.20 m

4A. FBD yA = 4 kN yD = 6 kN

4B. Shear-force and bending-moment diagrams

4C. BC, CD

4D. ( )max Tτ = 136,522 kPa ( )max C

τ = 102,391 kPa

me 270 – summer 2014 final exam name (last, first): · me 270 – summer 2014 final exam name...

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