University of Florida/Egm3520/s13.team1.r5

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Team 1: Report 5


R5.1: Problem 4.7[edit]

Figure P4.7.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

Two W4 x 13 rolled sections are welded together as shown. Knowing that for the steel alloy used, and and using a factor of safety of 3.0, determine the largest couple that can be applied when the assembly is bent about the z axis.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R5.1 Solution[edit]

Appendix C:Page A18
Term Desig Value
Area A 3.83 in2
Depth d 4.16 in
Width w 4.06 in
Moment of Inertiax Ix 11.3 in4
Moment of Inertiay Iy 3.86 in4
Problem Given
Yield Strength
Ultimate Stress
Factor of Safety 3


Determine Allowable Stress
Use Parallel Axis Theorem to determine the Polar Moment of Inertia
Determine the Couple Moment


R5.2: Problem 4.8[edit]

Egm 3520.s13.team1.wcs (discusscontribs) 07:27, 27 March 2013 (UTC)

Figure P4.8.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

Two W4 x 13 rolled sections are welded together as shown. Knowing that for the steel alloy used, and and using a factor of safety of 3.0, determine the largest couple that can be applied when the assembly is bent about the z axis.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R5.2 Solution[edit]

Appendix C:Page A18
Term Desig Value
Area A 3.83 in2
Depth d 4.16 in
Width w 4.06 in
Moment of Inertiax Ix 11.3 in4
Moment of Inertiay Iy 3.86 in4
Problem Given
Yield Strength
Ultimate Stress
Factor of Safety 3
Determine Allowable Stress
Use Parallel Axis Theorem to determine the Polar Moment of Inertia
Determine the Couple Moment


R5.3: Problem 4.13[edit]

Figure P4.13.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.
Contents taken from Page 238 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

Knowing that a beam of the cross section shown is bent about a horizontal axis and that the bending moment is 6 kN*m, determine the total force acting on the shaded portion of the web.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R5.3 Solution[edit]

The first step of the problem is to split the shaded portions into two separate portions.

Calculate each moment of inertia about the horizontal axis at the centroid.

Each portion is divided.
Thomas Burley


For section A the moment of inertia is :



For section B the moment of inertia is :


Next add both moments of inertia to calculate the total moment of inertia


Next we need to calculate the stress using the pure bending equation


The final step is to calculate the force on the beam's cross section. We know that force is equal to stress on an area.


Now input the values for the cross section of the beam into the equation

R5.4: Problem 4.16[edit]

Contents taken from Page 239 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

A "T" shapes beam that is made of nylon, the allowable stress is 24 MPa in tension and 30 MPa in compression. The largest couple M that can be applied to the beam is?

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R5.4 Solution[edit]

1)

2)

1+2) A = 1100 mm^2 A*y = 14500 mm^3 y = (14500)/(1100) = 13.18mm


I = (1/12)*b* h^3 + A * d^3

I_1 = (1/12) (40) * (15^3) + 600*(20^2) = 251250 mm^4

I_2 = (1/12) (20)* (25^3) + 500*(10^2) = 76041.66 mm^4

I = I_1 + I_2 = 327291.67 mm^4 = 3.27 *10^-7 m^4

M = σ* I/y

Top M_1 = (24 * 10^6)(3.27*10^-7) / 0.02682 = 292.617 N-m

Bottom M_2 = (30*10^6) (3.27 * 10^-7)/0.01318 = 744.973 N-m

the smaller value is correct couple... so M_1




R5.5: Problem 4.20[edit]

Figure P4.20.
Contents taken from Page 239 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.
Contents taken from Page 239 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

The cantilever beam with the trapezoidal cross-section has an allowable tension stress threshold, and allowable compressive stress, .


R5.5 Solution[edit]


What is largest couple moment that can be applied?

Given(s):


Relation between cross-sectional area, stress, and moment


Determine position of centroid in y direction

: height

Using composite area method

Figure 2 P4.20.

By similar triangles

Because of symmetry

Therefore, and

Determine 2nd moment of inertia

Find limiting constraint to the maximum couple moment, or




R5.6: Problem 3.53[edit]

Contents taken from Page 174 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Contents taken from Page 174 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Rod AB is made of aluminum, which has a Young's modulus of 3,700,000 pounds per square inch. Rod BC is made of brass, which has a Young's modulus of 5,600,000 pounds per square inch.

A torque T equal to 12,500 pound inches is applied at point B along the axis AC.

The figure shows that AB is 12 inches in length and 1.5 inches in diameter, and that BC is 18 inches long and 2 inches in diameter.

Find a) The max shear stress in rod AB and b) the max shear stress BC.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R5.6 solution[edit]

Formulas used:


Applied torque T is equal to the sum of the reaction forces at points A and C:

Total rod twist angle is equal to the sum of section AB and BC's twist angles; total twist angle is equal to zero because points A and C are held stationary:

Insert formula to relate rod twist to variables T, L, J, and G for their respective sections:

Rearrange, insert numerical values, and simplify to solve for T in section BC relative to A:

Solve for relative to applied torque , solve for numerical values of and



Find max shear stress in each section of rod using their respective torques:

Egm3520.s13.team1.scheppegrell.jas (discusscontribs) 19:18, 27 March 2013 (UTC)