ef 202, module 3, lecture 3 frames ef 202 - week 11

EF 202, Module 3, Lecture 3

FramesEF 202 - Week 11

2


Multiforce Member

• A multiforce member has either

• three or more forces acting on it,

• or two or more forces and one or more moments acting on it.

3


Frames

•A frame

•has at least one multiforce member,

•is stationary,

•and is designed to support/resist loads.

4


Machines

•A machine

•has at least one multiforce member,

•is not stationary,

•and is designed to transmit loads from one thing to another.

5


Why?

•By definition, a truss is not a frame, because ....

•a truss has only two-force members and a frame must have at least one multiforce member.

6


Frame Examples

Example 6.9, p. 288

7


Frame Examples

PS 2-2, Problem 4

8


Frame Examples

PS 2-2, Problem 5

9


Frame Examples

Online Homework 2-2-3

10


Frame Examples

Test Two, Problem 2

11


Analysis of Frames•Because some forces are not

directed along members,

•the method of joints is not sufficient;

•the method of sections is not sufficient.

•But Newton’s first and third laws are still sufficient

12


x

y

+

Ax

Ay

Dx

Dy1000 lbStatically indeterminate:3 equations4 unknowns

Let’s try to solve without recognizing that BD and ABC are a 2-force and a 3-force member, respectively.

13


Ax

Ay

Dx

Dy

1000 lb

Bx

By

By

Bx

x

y

+

Statically determinate:6 equations6 unknowns

lbDlbDlbBlbBlbAlbA

y

x

y

x

y

x

250033332500333315003333

+=−=+=−=−=+=

Now, let’s draw a separate FBD for each member and recount equations and unknowns.

14


Observation

•Sometimes the only way to find all the loads on a frame is to draw a separate FBD for each member.

15


Ax

Ay

1000 lb

6’ 4’

BD

BDBD

x

y

ij

k^

^^

+

ABC is now statically determinate, because it has only three unknowns.

Now, let’s use the fact that BD is a 2-force member.

16


Observation

•Using what we know about two-force and three-force members reduces the work.

17


Why is this a frame, and not a truss?ADC and BGC are 3-force members.

Any 2-force members?DH and GH

Statically determinate?No.

18


x

y

ij

k^

^^

+

0 cos cos 0HD HGxF F Fθ θ+→ =⇒− + =∑0 sin sin 800 0HD HGyF F F Nθ θ+↑ =⇒+ + − =∑

800 N

FHDFHG

€

θ

€

θ

€

∴FHD = FHG =800 N

2sin θ( )

19


Suppose that one pair of lines form an angle, and a second pair of lines form an angle. If each line in the second pair is perpendicular to a line in the first pair, then the two angles are equal.

Nixon(?) Theorem

€

∴FHD = FHG =800 N

2sin θ( )=

800 N

2 15( )

= 894 N

20


Ax

Ay

Bx

By

Cx

Cy

Cy

Cx

894 N 894 N

Statically determinate:6 equations6 unknowns

x

y

ij

k^

^^

+

3004003004005000

xyxyxy

A NA NB NB NC NC

=−=+=+=+=+=

21


Given: The 150 N squeezeapplied to the pliers shownat right.

Required: Find forceapplied to the round rodand the magnitude of theforce at pin A.

Why is this a frame, and not a truss?3-force membersAny 2-force members?No.Statically determinate?Yes. (So, what?)

22


00 =⇒=→+∑ xx AF01500 =−−⇒=↑+∑ NFAF yy

0)160(150)30(0 =−+⇒=+∑ mmNmmFMA

( ) NNmmmmNFNAA yx 800333.515030

160150,950,0 ==⎟⎟⎠⎞⎜⎜⎝

⎛===

23


Given: The 150 N squeezeapplied to the wire cuttersshown at right.

Required: Find forceapplied to the round wireand the magnitude of theforce at pin A.

Why is this a frame, and not a truss?3-force membersAny 2-force members?Yes.Statically determinate?Yes. (So, what?)

24


150 N

150 N

F

F

Ay

Ay

Ax

Ax

Cy

Cx

Cy

Cx

Dy

Dy

Statically determinate?

Yes.

10 equations 7 unknowns

25


0 0x xxF AC+→=⇒−−=∑0 150 0y yyF ACF N+↑=⇒−−−− =∑( )0 (30)150(160)50 0Ay

M Fmm NmmCmm+ =⇒− +− =∑0 0xxF A+→=⇒=∑0 0y yyF ADF+↑=⇒−+=∑ ( )0 (30) 80 0yAM FmmDmm+ =⇒ + =∑0 0y yyF DB+↑=⇒−=∑0 0xxF C+→=⇒=∑0 150 0y yyF CB N+↑=⇒++ =∑ ( )0 150(110) 30 0yCM NmmBmm+ =⇒− − =∑

150 N

150 N

F

F

Ay

Ay

Ax

Ax

Cy

Cx

Cy

Cx

Dy

Dy

26


F = 150 N (9.8) = 1470 N

F = 150N (5.33) = 800 N

ef 202, module 3, lecture 3 frames ef 202 - week 11

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