Homework #7 Solution
ME 311-Winter 2016
Due Date 03/11/2016
1
5.10. Find the fully plastic moment MP and the location of the corresponding
neutral axis for the beam section of Figure P5.10, if the uni
1
4.3. A cantilever beam of rectangular cross section is loaded by a force F directed along the diagonal AC of the section as shown in Figure P4.3. Show that
the neutral axis in this case coincides wi
1
4.18. A beam of circular cross-section, radius 3a has two eccentric holes of radius a as shown in Figure P4.18.
y
a
3a
2
3a
a
x
O
3a
2
Figure P4.18
Find the centroid of the section and the second mo
1
6.9. The beam of Figure P6.1 is fabricated from a channel and two bars by
welding, details of the weld being shown in Figure P6.9. If the minimum weld
thickness t = 1 mm, find the shear stresses in
1
8.3. A cylindrical tank of height h, radius a and wall thickness t is supported
from the top, as shown in Figure P8.3. It is just full of oil of density . Find the
membrane stresses (i) at the top o
1
6.45. The T-beam of Figure P6.45 transmits a shear force of 20 kN with the line
of action shown. Find the maximum shear stress and the twist per unit length,
if the material is steel with G = 80 GPa
1
5.10. Find the fully plastic moment MP and the location of the corresponding
neutral axis for the beam section of Figure P5.10, if the uniaxial yield stress is
200 MPa.
25
25
25
5
M
5
20
5
all dimen
1
4.34. Make a copy of the beam section of Figure P4.17 and use the least squares
fit method to estimate the location of the principal axes. Label the stiff and
flexible axes 1 and 2 respectively.
Est
1
3.17. The pin-jointed structure of Figure P3.17 consists of three rigid links each
of length L constrained by two springs on the diagonals, whose stiffnesses and
original lengths are k1 , L1 and k2
1
1.4. A 1.5 m wooden beam of 25 mm square cross-section is built-in at one end.
If you put all your weight on the other end of the beam will it break? What is
the longest beam of this cross-section t
ME 311 Winter 2018
Problem Set #5 Due: Wednesday, February 7
Problem 1
The I - beam is subjected to a bending moment that is intended to be aligned with the y - axis,
but is actually inclined towards
ME 311
Winter 2018
Problem Set #1 Due Wednesday, January 10
Problem 1
The center rod CD of the assembly is heated from T1 = 30C to T2 = 180C using electrical
resistance heating. At the lower temperatu
ME 311 Winter 2018
Problem Set #4 Due: Wednesday, January 31
Problem 1
The bending moment of magnitude Mo = 1.5 kn-m is applied to a beam having the Z-shaped
cross section shown. Determine (a) the str
ME 311 Winter, 2018
Problem Set #8 Due: Wednesday, March 7
Problems 1 and 2
In the structures shown below, the bars are connected by smooth pins. The bars have the
same area A and elastic modulus E. T
ME 311 Winter, 2018
Problem Set #7 Due: Wednesday, February 21
Problem 1
In the structure shown below, all three bars have the same A, E, L. Using the Theorem of
Minimum Potential Energy, determine a
ME 311 Winter 2018
Problem Set #3 Due: Wednesday, January 24
Problem 1
A beam with a uniformly distributed load is supported by concentrated forces at A and B. The
crosssection is Tshaped, having the
ME 311 Winter 2018
Problem Set #6 Due: Wednesday, February 14
Problem 1
Consider a cantilever beam having the cross-section shown below, and having a force P acing at
its free end. The area properties
ME 360
Modeling, Analysis and Control of Dynamic Systems
W 2018
University of Michigan, Department of Mechanical Engineering
Section 1, Tu/Th 9:00am 11:00am, 2505 GGB
Section 2, Tu/Th 12:30pm 2:30pm 2
Point mass m at a distance .r from the axis of rotation.
A point mass does not have a moment of inertia around its own axisr lJut
_ _ . . . . I = rm2
usmg the parallel aXIS theorem a momen
Note: black, blue and red curves are the function itself, 3rd-order and 1st-order approximations, respectively.
(a)
(b)
Code:
function [] = HW03TK01()
clear all; close all; clc;
a = 1;
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f1 = @(x)
Homework #6 Solution
ME 311-Winter 2016
Due Date 02/26/2016
1
4.37. A beam with the cross section of Figure P4.37 is loaded by a bending moment about the vertical axis as shown. Show on the figure you
Homework #1 Solution
ME 311-Winter 2016
Due Date 01/15/2016
1
1.6. A wooden plank is 200 mm wide, 25 mm thick and 1.5 m long. It is simply
supported at the two ends. How far will it deflect if you sta
Homework #2 Solution
ME 311-Winter 2016
Due Date 01/22/2016
1
3.15. Figure P3.15 shows a mechanism consisting of a set of pin-jointed rigid
bars, constrained by a spring of stiffness k connecting the
Homework #8 Solution
ME 311-Winter 2016
Due Date 03/18/2016
1
6.28. Find the torsional stiffness K for the closed thin-walled beam section of
Figure P6.28. The wall thickness is everywhere equal to t.
Homework #3 Solution
ME 311-Winter 2016
Due Date 01/29/2016
1
3.27. A complete circular ring of radius R and flexural rigidity EI is subjected
to two equal and opposite forces F on a diameter, as show
Homework #5 Solution
ME 311-Winter 2016
Due Date 02/19/2016
1
4.5. The C200 20 channel section of Figure P4.5 has second moments of area
Ix = 15 106 mm4 , Iy = 0.637 106 mm4 . It is loaded by the bend
Homework #8 Solution
ME 311-Winter 2016
Due Date 03/18/2016
1
6.3. The wide flange I-beam of Figure P6.3 has second moment of area Ix =
7a3t/12 and is loaded by a vertical shear force Vy . Find (i) th
Homework #4 Solution
ME 311-Winter 2016
Due Date 02/05/2016
1
3.45. Figure P3.45 shows a beam of length L and flexural rigidity EI, which is
simply supported at B and supported by a spring of stiffnes
Homework #10 Solution
ME 311-Winter 2016
Due Date 04/01/2016
1
8.1. A spherical fuel oil tank of radius R sits on an annular ring support, as
shown in Figure P8.1. The oil density is and the oil level
Examples of modeling, analyisis, and control
Analytical solutions of differential equations and
stability
Analytical solutions of differential equations and
stability
Linearization, particle dynamics
ME 311
Winter 2018
Problem Set #2 Due Wednesday, January 17
Problem 1
The rigid bar CDE is attached to a pin support at E and rests on the 30 mm diameter brass
cylinder BD. A 22 mm diameter steel rod