Tensile Test Pre lab Question
1. Determine the Young's modulus of elasticity for the tensile test data given. Assume that the sample has a circular cross section and the diameter is 2 cm. Use some rationale or clear criteria to establish the number of points selected. (Looks good is NOT an answer, use a clear mathematical criteria, remember EASC1112).
2. Determine the yield stress of the material by first solving for 1 then using a graphical line to intersect the stress-strain curve to determine the yield point. If the intersection is not near an existing value, estimate the value by plotted a limited range around the intersection. Use a 0.2% offset line.
3. Determine the total energy absorbed during the tensile test for this material. Discuss your integration technique and use units of kJ/m^3 for your answer.
|
Strain
|
Load, Newton
|
|
0
|
0
|
|
0.00075
|
0.9
|
|
0.0015
|
2
|
|
0.0025
|
2.93
|
|
0.003
|
3.21
|
|
0.0035
|
3.46
|
|
0.007
|
4.73
|
|
0.009
|
5.08
|
|
0.011
|
5.2
|
Torsion Test Pre lab Question
1. Determine the shear modulus of elasticity for the torsion test data given. Assume that the sample has a circular cross section and the diameter is 2.5 cm. Use some rationale or clear criteria to establish the number of points selected. (Looks good is NOT an answer, use a clear mathematical criteria, remember EASC1112).
2. Determine the shearing yield stress of the material by first solving for 1 then using a graphical line to intersect the stress-strain curve to determine the yield point. If the intersection is not near an existing value, estimate the value by plotted a limited range around the intersection. Use a 0.04 rad/gage length offset line, so if the sample is 1 meter long, offset 0.04 radians or the resulting shear strain.
3. Determine the uncertainty in the shear stress due to diameter if the diameter uncertainty is 0.05 cm. Report the value in MPa.
|
angle, deg
|
Torque, NM
|
|
0
|
0
|
|
1
|
2
|
|
3
|
5
|
|
4
|
6.5
|
|
5
|
7.2
|
|
10
|
8
|
|
20
|
8.1
|
|
40
|
8.2
|
|
70
|
8.3
|
Beam Bending with Stress Concentrations
1. The strain gages around the hole are used to estimate the strain on the surface of the hole using a simply polynomial curve fit. Use the three data points given to determine the strain at the hole by using matrix solution with Excel. Assume the hole has a diameter of 1 cm.
|
distance from center of hole, mm
|
microstrains
|
|
1.0
|
120
|
|
1.5
|
180
|
|
2.1
|
220
|
2. Determine the nominal stress at the hole if the stress concentration factor Kt =1 for the equation in the lab handout (c1) and the properties are:
|
Load =
|
200
|
grams
|
|
distance from load
to hole =
|
8
|
cm
|
|
beam width =
|
3
|
cm
|
|
beam thickness =
|
0.5
|
cm
|
|
diameter of hole =
|
0.25
|
cm
|
3. Determine the stress concentration factor Kt at the hole using the model from the lab handout and the geometric values from question 2 above.
Impact Testing/Shock Test Experiment
1. An impact hammer strikes the end of a rectangular beam which shows a maximum strain of 1500 microstrains at a distance of 5 cm from the impact. If the beam is made of steel and has a thickness of 0.2 cm, width of 1.0 cm, how much energy (or work) was used to bend the beam? Watch your units! Assume the beam is steel, 200 GPA)
2. Calculate the potential energy change for a hammer to rotate about a fixed center, starting at an angle of 15 degrees as measured from the vertical then rotating clockwise to 0 degrees. Assume the hammer weighs 1.75 kg and the length between the center of rotation and the center of the hammer head is 11.5 cm. Ignore the mass of the bar holding the hammer head.
3. The natural frequency of oscillation of a beam with a mass at the end is given in the handout, determine the value if the beam has: a modulus of elasticity of 70 GPa, a length of 5 cm, a width of 0.5 cm, a thickness of 0.1 cm,
|
Modulus
|
70
|
GPA
|
|
Length
|
5
|
cm
|
|
Width
|
0.5
|
cm
|
|
Thickness
|
0.1
|
cm
|
|
Beam Mass
|
0.2
|
kg
|
|
Mass on the end
|
0.5
|
kg
|
Pressure Vessel
1. If the internal pressure in a soda can is 80 psi, determine the value of the principal stresses around the can (theta) and up and down the can (z). (Hint: Convert to SI units, and then use the pressure vessel relations to calculate the stresses. Wall thickness = 0.5 mm, diameter = 5 cm, E = 70 GPa, Poisson = 0.3)
2. If the principal stresses are 100 kPa (longitudinal) and 200 kPa (hoop/circumferential) determine the value of the principal strains around the can (theta) and up and down the can (z). (Hint: Convert to SI units, and use the stresses in the biaxial equations to determine the strains. Wall thickness = 0.5 mm, diameter = 5 cm, E = 70 GPa, Poisson = 0.3)
3. You measure a circumferential strain of 200 microstrains on a pressure vessel. What is the internal pressure? (Hint: Use the biaxial strain equations and substitute the pressure vessel relationships for stress. Wall thickness = 0.5 mm, diameter = 5 cm, E = 70 GPa, Poisson = 0.3)
Mode Shapes/Beam Vibrations
1. Calculate the 3rd natural frequency for a beam with the dimensions given.
|
Modulus
|
70
|
GPA
|
|
Length
|
50
|
cm
|
|
Width
|
3
|
cm
|
|
Thickness
|
0.25
|
cm
|
|
Density of Beam
|
2.7
|
g/cm^3
|
2. The natural frequencies are determined by solving for the roots of the nonlinear equation cosh(bl)*cos(bl)+1 = 0, plot the function for (bl) = 0 to 20, the 6th root is visible. Determine the 6th value for (bl) to 4 decimal places.
3. Create a plot that shows the variation of natural frequency vs length for the first three vibrational frequencies. Show each mode (1,2,3) as a different curve with length on the horizontal axis. Even though (bl) includes the length, use the factors from the table.