Homework for EAS 212

Spring 2004

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The following are homework assignments for EAS 212, section 001 (Carol Hasenberg's Class):

Homework 1 - Stress/Strain
due Tuesday April 6

Read all of Chapter 1

Homework Problems:

  • Section 1.2 - 3, 9
  • Section 1.3 - 6
  • Section 1.4 - 2
  • Section 1.5 - 1
  • Section 1.6 - 11
  • Section 1.7 - 8
  • Section 1.8 - 5

 Computer Homework 1

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW1.C1: click for instructions  User values for case one, h = L = 1m., EA = 10,000 N for both bars, P = 1,000 N.  For case 2 and graph, student selects the values.

HW1.C2:  Refer to text problem 1.7-9.  For user inputs
  • pin diameter,
  • spar steel tube inner and outer diameter,
  • connecting plate thickness,
  • allowable compressive stress in the spar,
  • allowable shear stress in the pin,
  • allowable bearing stress between the pin and the plates,
determine the allowable load P on the spar.  Submit two examples of the output - case one, the values given in the text, and case two, the same values except that pin diameter d = 0.75 in.

HW1.C3:  Refer to text problem 1.8-15 for the problem sketch.  For user inputs
  • angle theta
  • load P
  • length L between supports
  • bar area A
  • modulus of elasticity E
determine the displacement of point C under load P.  Disregard the instructions given in the text problem, and do not include the selfweight of the system. Determine the displacement for case one, theta = 45 degrees, P = 1 kN, L = 2.0 m, A = 4 cm2, E = 100 GPa., and case two, same except theta =  30 degrees.

Homework 2- Axial Loading
due Thursday April 15

Read Chapter 2 - 2.1- 2.6 (except prestrains and misfits of section 2.5)

Homework Problems:

  • Section 2.2 - 7, 8 13
  • Section 2.3 - 4, 8
  • Section 2.4 - 3, 10, 16
  • Section 2.5 - 8, 11
  • Section 2.6 - 3, 8

 Computer Homework 2

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW2.C1: click for instructions User values for submittal, for SI units, L = 1 m, Po = 1000 N/m, EA = 1,000,000 N; for US units, L = 1 ft., Po = 1 kip/ft, EA = 1,000 kip.

HW2.C2: click for instructions User values for submittal, a = b = c = 10 m., EA = 1,000,000 N for all cables, w = 500 N/m.  Conduct the comparisons requested in the results section of the problem statement.

HW2.C3: click for instructions User values for case one, L = 1m., EA = 100,000 N, W = 100 N, h = 0.2 m, change in T = 50oC to rod A, alpha = 10 x 10-6/oC.  For case 2, same values except rod B is heated.

HW2.C4: Refer to text problem 2.2-10.  For user inputs
  • spring constants k1, k2
  • spring lengths L1, L2
  • bar weight W
  • applied force P
determine the distance x needed to bring the bar to a horizontal position.  Submit two examples of the output - case one, the values given in the text, and case two, the same values except that k1 = k2 = 1200N/m, and W = 0.

HW2.C5:  Refer to text problem 2.4-13.  For user inputs
  • applied forces at springs P1, P2, P3. ( These are listed as 31 lb, 10 lb, and 7 lbs, respectively, in the text but you are to allow the user to change these values.)
calculate the displacements of the springs and determine the angle of rotation q of the rigid bar.  Plot the displacements on a graph.  Submit two examples of the output - case one, the loads given in the text (P1=31,P2=10, and P3=7 lbs), and case two, the opposite loads (P1=7, P2=10, and P3=31 lbs.)

Homework 3- Torsional Loading
due Thursday April 22
Read Chapter 3 - 3.1-3.8

Homework Problems:

  • Section 3.2 - 1
  • Section 3.3 - 8 (hint on 8:  treat it like a particle equilibrium problem with torsional vectors)
  • Section 3.4 - 5, 12
  • Section 3.5 - 7
  • Section 3.7- 3
  • Section 3.8- 6
 Computer Homework 3

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW3.C1: click for instructions User values for submittal  shown in the table:
VALUE AXIAL
 CASE 1
 CASE 2
 VALUE TORSIONAL
 CASE 1
 CASE 2
L1
 0.1 m
 0.1 m
 L1
 0.1 m
 0.1 m
L2
 0.1 m
 0.1 m
 L2
 0.1 m
 0.1 m
L3
 0.1 m
 0.1 m
 L3
 0.1 m
 0.1 m
L4
 0.1 m
 0.1 m
 L4
 0.1 m
 0.1 m
P1
 0
 -1 kN
 T1
 0
 -1 kN-m
P2
 1 kN
 1 kN
 T2
 1 kN-m
 1 kN-m
P3
 0
 -1 kN
 T3
 0
 -1 kN-m
EA1
 1 E6 N
 1 E6 N
 GJ1
 1 E6 N-m2
 1 E6 N-m2
EA2
 1 E6 N
 1 E6 N
 GJ2
 1 E6 N-m2
 1 E6 N-m2
EA3
 1 E6 N
 2 E6 N
 GJ3
 1 E6 N-m2
 2 E6 N-m2
EA4
 1 E6 N
 2 E6 N
 GJ4
 1 E6 N-m2
 2 E6 N-m2
Note that you are to do either the axial or the torsional problem.  The method is similar.

HW3.C2: Refer to text problem 3.8-9.  For user inputs
  • max torque t0
  • bar length L
  • bar polar moment of inertia Ip (J)
  • shear modulus G
determine the fixed end torques Ta and Tb, and plot  the displacement of the bar at a minimum of  10 points evenly spaced along the bar.  Submit one case with values selected by the student.

Homework 4- Beam Statics
due Tuesday May 4

Read Chapter 4

Homework Problems:


Computer Homework 4

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW4.C1: click for instructions To demonstrate the effectiveness of the program, student to select  same L, c, M, P, and w values for all load cases.  Then print plots for the following load cases:
  • Case 1 - Point load only on the main span. (M and w are zero)
  • Case 2 - Point load only on the overhang. (M and w are zero)
  • Case 3 - M only on the main span.  (P and w are zero)
  • Case 4 - w only.  (M and P are zero)
  • Case 5 - All loads acting together.

HW4.C2: Refer to text problem 4.3-15.  For user inputs
  • foundation load q1
  • load width L1 (shown in the sketch as 8 feet)
  • total foundation width L (shown in the sketch as 3 + 8 + 3 = 14 feet)
Note:  soil reaction q2 is a derived unit, which can be computed from q1, L1, and L.
 
determine the shear force and bending moment at a minimum of 10 points evenly spaced along the bar.  Plot the values on a shear force diagram and a bending moment diagram.  Submit two examples of the output - case one, the values given in the text, and case two, q1 = 1000 lb/ft, L1 = 5 ft, L = 10 ft.

Homework 5- Beam Stress
due Tuesday May 11

Read all of Chapter  5 - 5.1-5.6, 5.8-5.11

Homework Problems:

  • Section 5.5 - 6, 19
  • Section 5.6 - 13, 23
  • Section 5.8 - 8
  • Section 5.9 - 1
  • Section 5.10 - 9
  • Section 5.11 - 6, 7

 Computer Homework 5

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW5.C1: Refer to text problem 5.4-5.  For user inputs
  • length L
  • thickness t
  • midpoint deflection delta
determine the radius of curvature rho and the normal strain at the top surface of the strip.  Hint:  find two equations that contain rho and curvature angle theta.  Use the solver feature to determine the rho in which the two equations intersect.  Submit two examples of the output - case one, the values given in the text, and case two, values selected by the student.

HW5.C2:  Refer to text problem 5.6-7.  For user inputs
  • span length L
  • joist spacing s
  • allowable bending stress fb
  • uniform floor load w
  • allowable shear stress fv
write a program that calculates the required size for the joists.  Submit two examples of the output - case one, the values given in the text, and case two, L = 8 ft., spacing s = 24 in., load w = 60 lb/ft2, and fb same as case one.

HW5.C3:  Refer to text problem 5.11-2.  For user inputs
  • design shear force V
  • beam web height h and thinkness tw
  • beam flange width w and thickness tf
  • weld allowable load fallow (shear force/length)
  • weld spacing s
write a program that calculates the required length for skip welds joining the flange plates to the web.  Submit two cases with values selected by the student.
Homework 6- Plane Stress
due Tuesday May 18

Read Chapter 7-7.1-7.6 except strain energy density section

Homework Problems:

For sections 7.2 to 7.4 problems, construct the Mohr's circle. Show position of given x- and y-face stress points on the circle.

  • Section 7.2 - 1, 12, 16
  • Section 7.3 - 3
  • Section 7.4 - 8, 11
  • Section 7.5 - 5
 Computer Homework 6

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW6.C1: Using the transformation equations for plane stress, and the following initial (theta = 0) values:
element
 sigma x
 sigma y
 tau xy
 comment
1
 50 MPa
 10 MPa
 30 MPa
 general element
2
 50 MPa
 0
 0
 uniaxial tension
3
 0
 0
 50 MPa
 pure shear
4
 50 MPa
 50 MPa
 0
 biaxial stress

Write a computer program to calculate the sigma x1 and tau x1y1 values for each element rotated between theta = 0 and theta = 180 degrees.  Plot the calculated values on a graph to show the Mohr's circle for each of the elements.
Homework 7- Combined Stress
due Thursday May 27

Read Chapter 8-8.1-8.3,5.12,8.4-8.5

Homework Problems:

  • Section 8.2 - 8
  • Section 8.3 - 2, 4
  • Section 5.12 - 6
  • Section 8.4 - 5
  • Section 8.5 - 7, 12
 Computer Homework 7

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW7.C1:  Refer to text problem 8.3-6.  For user inputs
  • modulus of elasticity E
  • Poisson's ratio nu
  • ultimate shear stress fvu
  • factor of safety n
write a program that calculates the maximum permissible strain in the gage.  Submit two examples of the output - case one, the values given in the text, and case two, values selected by the student.  By the way, the answer given in the back of the text is WRONG because they chose an element on the outside surface of the cylinder to determine the maximum shear stress, rather than the inside surface. The  correct answer (permissible strain) should be a bit less.

HW7.C2:  Refer to text problem 8.4-11.  For user inputs
  • beam length L
  • point load P at the midpoint
  • beam width b
  • beam height h
  • distance x from the left end of the beam
write a program that calculates the sigma x, sigma y and tau xy stresses for stress elements at the top, midpoint and bottom of the beam at any section at distance x from the left end of the beam.  Plot the Mohr's circles for the 3 elements.  Submit two examples of the output - case one, the values given in the text, and case two, any point x to the right of the point load on the same beam.

Suggestions for plotting Mohr's circles:
Run sigma, tau values of theta  between the angles 0<= theta <=180 degrees.  Plot sigma horizontal and tau vertical.  In Excel, suggest use theta intervals of 15 degrees with the "spline" lines between plotted points.  In Matlab, plot lots of points.

HW7.C3:  Refer to text problem 8.5-3.  For user inputs
  • generator power output in hp
  • shaft rotation speed in rpm
  • outer and inner diameters of shaft, d2 and d1
  • axial force P
write a program that calculates the sigma x, sigma y and tau xy stresses for a stress element on the surface of the shaft.  Plot the Mohr's circle for the element, and determine the maximum tensile, compressive, and shear stresses.  Submit two examples of the output - case one, the values given in the text, and case two, values selected by the student.

Homework 8- Beam Deflections
due Thursday June 3

Read  Chapter 9-9.1-9.5

Homework Problems:

  • Section 9.3 - Find the boundary conditions only for 12,15,18. Do the whole problem for 13.
  • Section 9.5 - 2, 15, 16

 Computer Homework 8

NOTE: Not all of the computer problems listed are required.  Refer to the syllabus for instructions on the computer problems, and the class calendar for due dates.

HW8.C1:  Refer to text problem 9.5-12.  For user inputs
  • load q in kN/m
  • distance a in m
  • beam length L in m
write a program that calculates the midpoint deflection and support rotation based on the superposition/integration technique described in the text on page 633.  Submit one case with values selected by the student.

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