Problem 1
Determine the reactions at A and B. Assume smooth surfaces.
Solution:
Free-body diagram
Equilibrium equations
3
0 Ax 500 N B
5
4
Fx 0 Ay 500 5 450
4
M A 0 500 5 1 4503 600 N B 4 sin 30
F
x
(i)
(ii)
(iii)
Solving:
N B 1175 lb
(ii) Ax 1475 lb
Energies 2011, 4, 582-598; doi:10.3390/en4040582
OPEN ACCESS
energies
ISSN 1996-1073
www.mdpi.com/journal/energies
Article
Evaluation of Lithium-Ion Battery Equivalent Circuit Models
for State of Charge Estimation by an Experimental Approach
Hongwen He *,
HW-6: Torsional Loading of Beams
(Only two problems will be graded for correctness, rest will be graded for completion)
1.
Also find the angle of twist in each case with the maximum Torque (use G = 26 GPa, L= 1m, or just leave your
answer in G and L)
2.
A
HW-7: Bending of beams
(Only two/three problems will be graded for correctness, rest will be graded for completion)
1.
2.
3.
4. For practice only
5. For extra credit
6.
7.
8.
If the shear yield stress is twice as large as the tensile
yield stress, then wi
HW-3: Strain
(Only two problems will be graded for correctness, rest will be graded for completion)
1.
2. Components of strain (strain tensor) along different axes.
A rectangular plate undergoes the deformation as shown by dashed lines. Find:
a. Normal st
HW-5: Axial Loading of Beams
(Only two problems will be graded for correctness, rest will be graded for completion)
1.
For practice only (you dont need to do it for completion or correctness) but it will help
EAl = 68.9 GPa
2.
Your answer will depend on v
HW-1
1. Let vector: A = (1, 0, -3) and B = (-2, 5, 1).
Draw the vector A and B in x-y-z axes.
Find the vector C = A x B (cross product).
Draw the vector C.
What is the angle between (A and C) and (B and C)?
2. Problem 1-2
The P=500-lb load is applied alon
HW-2: Stress and stress based design
(Only two problems will be graded for correctness, rest will be graded for completion)
1. Picturing stress
A bar of square cross-section is attached to a plate.
A normal force F is applied as shown on the right end of
P1. [Mechanical properties of materials]
A 500-mm-long, 6-mm-diameter rod made of a material having the stress-strain diagram shown
(a) Determine the length change x due to the load 15 kN.
(b) Determine the final length of the rod after the load has been
P1. [Internal loadings]
Determine the resultant internal loadings acting on the a-a cross section at C
Solution:
Free-body diagram of the beam (to find the reaction at B)
M
A
1
1
0 (9)(900)( )(9) Bx (9 sin 30) Bx 2700
2
3
Method of section
1
0 V ( )(3)(
P1. [Torsion]
The solid A36 steel shaft is subjected to the
loading shown. Determine the maximum shear
stress in the shaft.
Solution:
Internal torque in segments
T AB 35 100 20 5 40 kN-m
TBC 100 20 5 75 kN-m
TCD 20 5 25 kN-m
TDE 5 kN-m
Maximum shear stres
P1. [Distributed load]
Determine the reactions at supports A and B.
Solution:
Free-body diagram (with simplified forces in blue)
Equilibrium equations
F 0 A 20
F 0 A B 180 540
M 0 B 12 180(2 / 3)(3) 5403 20(2) 30
x
x
y
y
A
y
y
(i)
(ii)
(iii)
Ax 20 kip
P1. [Statically indeterminate systems]
The 6061-T6 aluminum shaft is fixed at the ends
and subjected to the uniform distributed torque as
shown.
(a) Determine the reactions at the ends.
(b) Determine the maximum shear stress in the
shaft.
Solution:
(a) Fr
MAE 213 Solid Mechanics
Midterm #1
October 5, 2016
P1. [12 pts]
Determine the resultant internal loadings acting on the cross section through point C.
Solution:
Free-body diagram
Equilibrium equation
M
A
1
0 FB 18 12 318 6 3 18 9
2
Method of sections
Eq
P1. [Statically indeterminate systems]
The 40-mm-diameter A-36 steel rod is fit securely
between its fixed supports when the temperature
is 20C. Then the uniform distributed load is
applied and the temperature has a distribution as
shown. Determine the re
P1. [Strain]
The rectangular plate deforms into the dashed shape shown.
(a) Determine the average normal strain along the side CD.
(b) Estimate y at point A.
(c) Estimate xy at point A.
(d) Estimate xy at point B.
Solution:
(a) Average normal strain along
P1. [Average stresses]
The frame is subjected to the triangular
distributed load with w = 200 N/m. Bar BC has a
square cross section of 40 mm on each side.
Determine the average normal and shear stresses
at section b-b.
Solution:
Free-body diagram of the
MAE 213 Solid Mechanics
Midterm #1
October 5, 2016
P1. [12 pts]
Determine the resultant internal loadings acting on
the cross section through point C.
Solution:
Free-body diagram
Equilibrium equation
M
A
1
0 FB 18 12 318 6 3 18 9
2
Method of sections
Eq
HW-4: Stress-Strain relationships
(Only two problems will be graded for correctness, rest will be graded for completion)
1. Draw the stress strain curve for a) ductile material b) steel c) a brittle material.
Label proportional limit, yield stress, ultima