Lecture 4: Equilibrium (2D) (Chapter 4)
Equations of equilibrium; reaction forces & couples at
supports (2D); free-body diagram
Equations of equilibrium
1. Sum of all forces equals zero 2. Sum of moment about any point
equals zero
EF 0
=
① [Fx
② EFy
=
=
0
③
EMo
can
solve for
=
O
O
3
the
-
>
"reactions"
Force
In
equations
order
f
to
at
moment
do5o,
3
unknowns
supports
inside
we
parts of
use
the structure
free-body
diagrams /FBD)
1
Free body diagrams
i) Known (applied) forces and couples
ii) Unknown reaction forces and couples (from supports)
Common supports in 2D
supports
* if see external forces include
-
cantilever
↓ Aller
Support)
T
(
fee to rotets
Copy structure
#
+
remous
support
dirches
-
↑
L doesn't matter
vertical
up
=
horizontal right
⑭known
-
>
-
of arows
Y
6-
↑
positi (t
=
puntin (t)
knowns
Knowns
3
2
Ax
,
Ay
BytO
,
unknowns
are
By
=
0
,
Mr
,
=
Ma
=
O
O
Cunknownd
3
Remove
↓
supportsa
couples
# add
replace
key
shows
external
forces
nothing
intend
should
show
be
forces
dimensions
only
FBD
reaction
with
them
A
↑
Ax
>
-
T
+
4
By
Ay
F
3
equations
3
unknowns
> can
-
solls
If you
for
know
all
Unknowns
dimensions
+ F
4
on exch
talked
Free-body diagram:
draw
* can
moment
#
Will
at
84
-x)
semester
* can
only
be
negative
(1 moment
I moment
wall
be talked obt at end
beam ,
of
moment
4
(t)
all
-or
&
9 G
not
one
aids
Never draw the supports with the reaction forces & couples on
neschu
the same free-body diagram
,
Positiv +
one side
Always remove the supports and replace by reaction forces and
ION
couples
↓
MA
G
Example:
>
-
4
Ax
B
Im
Ay
10 N
wall
to EFX
+↑ [Fy
0
=
=
;
0
Ax
On
=
Ay-10 ; Ay
=
=
100
moment
&
A
5m
# Emrall
B
M
>
(shownnat
Ay
shows is
=
8
=
Ma-10
.
5
Ma
=
50 N
flor
EMral
=
O
=
-
MA-10-5
Go N-m
negche-7
Ma
=
5
-
m
d
Ax
-
4
Example:
FBC
Ay
[My
cond
[Fx
[Fy
=
0
=
Fac
=
0
↓
Frc
=
x
* 1
x
5722 5 d
=
=
=
5
-
700
.
.
98
.
-
d
Fx
Ax
+
Ax
-3933 5dN
=
98N
·
N
.
0
.
700
.
Ay + Fac
-
-
-
700
-
98
-
vertica fore
down from weight
-
5
4(2 2)
x
3
(1 5 2)
+
.
two
force
member
can
Ay
=
-
4598d + 6867N
A
FA =
Ayz
+
only have
tension +
lecture
6
Clicker question:
Select the equation that represents
the equation of force equilibrium
in the x direction
A) Pcos45 – Fcos45 + 100cos30 = 0
B) -Pcos45 + Fcos75 + 100cos30 = 0
C) 100cos30 + Fcos75 – Pcos15 = 0
D) -Pcos45 + Fcos75 + 100 = 0
E) None of the above
7
Clicker question:
The force of 100 N acts at point A.
Calculate the force developed in cable
AC.
A) 70.71 N
B) 100 N
C) 141.42 N
D) 0 N
E) None of the above
8