材料学essay/report/assignments代写
Name __________________________________
E MCH 213
Strength of Materials
Sample Final Exam 1
INSTRUCTIONS:
1. Read the problems carefully !!! 2. Show ALL work in a neat and logical order. Partial credit will only be given if the work and reasoning are shown clearly and legibly. Begin each problem by clearly indicating what you are trying to FIND. 3. Your exam should contain 4 problems on separate pages and 1 page of short answer and multiple choice concept questions. If something is missing, notify a proctor immediately. 4. Every internal load used must be clearly shown on a Free Body Diagram. 5. Neatness counts. Points will be deducted for sloppy work. 6. Place answers in the answer blocks provided. Be sure to label your answer and include units. (write F = 45 lb, not just the number 45 as the answer) 7. Individual calculators only. Sharing of calculators is prohibited.
Score (out of 100%)
A stainless steel pipe with an outside diameter of 120 mm and a wall thickness of 2 5 mm is rigidly attached to fixed supports at A and B as shown. If the length of the pipe is 12 m, determine the minimum temperature increase that will cause the pipe to buckle.
End Effective Buckling
Supports Length
Both Pinned 1.
Both Fixed 0.
One Fixed/One Free 2.
One Pinned/One Fixed 0.
A
B
L
A thin membrane is subjected to the plane stress state shown below. (a) Draw the Mohrs circle for this stress state. (b) Identify the in-plane principal stresses and maximum in-plane shear stress on the Mohrs circle. Calculate the values for these stress quantities. (c) Sketch the in-plane principal stresses oriented with respect to the xy coordinate system. (d) Calculate the magnitude of absolute maximum shear stress.
160 MPa
300 MPa
150 MPa
x
y
a) Principal Stresses
________________
________________
b) Maximum in-plane
Shear Stress
________________
d) Absolute maximum
shear stress
________________
c) principal stress state sketch
x
y
A stepped 6061 – T6 aluminum shaft consists of a solid 4 in. diameter segment AB and a solid 3 in. diameter segment BC. The angle of rotation at C is limited to 8 0 and allowable shear stress for any point on the shaft is 16 ksi. Determine the magnitude of the largest torque T that may be applied at C as shown. A correct FBD showing internal torque is required for full credit.
A B (^) C
T
3 ft 2 ft
An aluminum 2014-T6 beam supported by a pin and a roller is shown below. The cross section
of the beam is a channel section as shown.
(a) Draw complete shear and moment diagrams in the space provided under the beam diagram.
(b) Determine the maximum values of the tensile and compression stresses in the beam.
To help you get started, the reactions at A and B are 250 lb and 300 lb respectively and the
distance from the base of the beam to the neutral axis is y = 1.17 inches.
10 lb/in 150 lb^
4000 lb-in
40 20 10^ 15^
A
B
Maximum Tensile Stress
_____________________
Maximum Compressive Stress
_____________________
y
4
3
3/4
3/4
Cross-Section
5.1 List the boundary conditions you would use if you were calculating the deflections for the beam in problem 4.
5.2 Calculate the normal strain in the x direction for the stress state in problem 2 if the membrane is made of Kevlar 49.
5.3 Given that for force applied to the bar is F = 40 lb, calculate the average shear stress in the pin holding the bar to the wall at A. The pin has a cross-sectional area of 0.25 in^2.
5.4 Calculate and sketch the internal loads acting on the beam at the centroid of section A-A.
10 lb/in 150 lb^
4000 lb-in
40 20 10^ 15^
A
B
x
_________________________________
_________________________________
F
160 MPa
300 MPa
150 MPa
x
y
A
A
20 lb
30 lb
4 in
10 in (^) 15 in