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NAME:
CLASS TIME (ch: one): INSTRUCTOR:
/./Consider the beam below with the concentrated load of 10 kN and the distributed load where MA
kN/m: '
)\ a. (2 points) Draw a free body diagram and determine the reactions at the suppo
Determine the forces exerted on member
ABC at A and C.
(To 10e it;
Solution: We start with the free-body diagram of the entire l'mme.
'I\vo or the equilibrium equations [or the whole frame are
2F, :A,+ so lb=0
2M5 : A, (2 n)A,. (4 n)
(so lb)(2/3 n)
(400I
MOMENT ABOUT AN AXIS
Todays Objectives:
Students will be able to determine the moment of a
force about an axis using
a) scalar analysis, and
b) vector analysis.
QUESTION
The triple scalar product u ( r F ) results in
A) a scalar quantity ( + or - ). B) a
Northeastern University
College of Engineering
MIE 2350 Engineering Mechanics and Design
Fall 2014
Instructor: B. Gommerstadt
Email: [email protected],neu.edu
Office hours: by appointment
Text : Bedford and Fowler, Engineering Mechanics Statics and Dynamics , 5
3) The10filadder shown below weighs 50 lb anditsoenter ofmass is located at the rnidpoint. The
coefficientofstatic ftiction betweentheladdei and the floor is 0.432,thewall exerts a negligible
friction force onthe ladder and theangle o=30". Thepainter \',/
Prof. Gonenmdt
Name:
I CZ/IZ#Z,a/5Iatz5.
Northeastern University
ent of Mechanical and Industrial Engineering
ENGINEERING MECHANICS & DESIGN
Indicator Question
Three loads are npialied to a beam as shown. The beam is supported by a roller
at A Ind by a
Pr. 3.32: The slider A is in equilibrium and the bar is smooth. What is
the mass of the slider?
F
N cos 45o T sin 20o
x
N
200 N sin 20
0
o
cos 45o
96.74 N
Actual surface force N between the slider
and the bar is in the opposite direction
Do not change di
Pr 2.96-S: The cable AB exerts a 32-lbf T, on the collar A. (a) Find the minimum and maximum extent of the
distance d. (b) Express T in terms of components as a function of d. (c) Plot components of T versus d.
distace d is limited by
0 d rDC
T e ABT (1
9/13/2016
EXAMPLES. CHAPTER 2 (CLASS 3) GROUP STUDY
Pr 2.87: (Modified) The magnitude of the axial force in one of the
beams of a geodesic dome is |P| = 10 kN, The cartesian
coordinates of the endpoints A and B of the straight beam
are (-12.4, 22.0, -18.4
Q1-A
a)
M C ? if
M
A
0
b)
M
B
? if M C 10 kN m
Moment arm lengths = shortest distance between Line of
Action (LOA) of Force to the point of which moment is
calculated. If LOA passes through the point then moment
due to that force is 0 at that particular
10/5/2016
Pr. 5.18* (Modified): (a) Draw the FBD of the structure by isolating its
supports at A and E. (b) Determine reactions at A and E. (c) Find
the sum of moments about point C.
2
4
Ax
Ay
200 ft lb
Ax
1
Ay
Ey
100 lb
Ey
4
M
1
Couple acts
everywhere
40
r
6
i
4
j
12
k
m
F 28 i 14 j 42k N
Quiz 2 Makeup 3 Solution
6 i 4 j 12k m
6 i 4 j 12k
0
.
429
0
.
286
0
.
857
e
i
j
k
a) unit direction vector parallel to r r
2
14
6 2 4 12 2 m
Given
b) Magnitude of component of
F parallel to r
12k
6i
4j
F/ r F e
Make these members 2x6
Add cross-bracing members (as shown). Use 2x4
BOTH SIDES
BOTH SIDES
Add cross-bracing members (as shown). Use 2x6
BOTH SIDES
Hardware
I recommend using SAE Grade 5 bolting hardware.
Bolts create a better joint due to the control o
Projectile Motion
Problem:
Tom fires his canon every year on July 6th. This year he fired the canon at an angle of
45 degrees and the cannonball flew for 400 yards. What was the initial velocity?
Key
g=Gravity
O= Angle projectil was fired at
x Distance pr
A
Moment of Inertia (in^4)
Beam Deflection (in)
B
20.796
0.4952
C
1.5469
6.6532
D
47.6347
0.2162
E
2.0391
5.051
Beam Deflection vs. Moment of Inertia
7
6
5
4
3
2
1
0
0
20
40
60
Axis Title
80
100
120
F
98.9317
0.1041
2.6016
3.9589
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Table 43b. Strength properties of some commercially important Woods grown in the United States (inch-poundFcon.
Static bending Corn
Com- pression Shear Tension
Modulus Modulus Work to pression perpen parallel perpen- Side
of of maximum Impact parall
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Activity 2.2.3 Recycling
Purpose
Have you ever filled a trash bag, poured cereal from a box, hammered a nail into wood, or
consumed a soda from an aluminum can? That trash bag, cereal box, nail, or aluminum can was most
likely made from recycled materials
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Projectile Motion
Projectile motion is a combination of horizontal motion and
vertical motion.
The horizontal motion of a projectile is constant because no
gravitational force acts horizontally
The vertical motion of a projectile is nothing more than free