CHAP6.

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CHAP6.
Structural Analysis
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6.1 Simple Trusses
1. Definition of Truss
A structure composed of slender members jointed
together at their end points by bolting, welding
or pinning.
2. Planar Trusses
planar trusses lie in a single and one often need
to support roofs and bridges.
Bridge truss
Roof truss
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3. Assumption for Truss
(1) all loading are applied at the joints a.
members weights are neglected (W ltlt external
force) b. members weights are included
(2) members are jointed together by smooth pin
(No friction forces)
Because of the two assumptions, the truss member
is a two-force member
T
Note Compression member must be made thicken
than tension member because of the buckling or
column effect in compression member.
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4. Simple Truss
A simple truss is constructed by starting with a
basic triangular element and connecting two
members to form an additional element.
Simple form of rigid or stable truss
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6.2 the Method of Joints
1. Objective Evaluate the force acting on
each member of a truss structure to analyze or
design a truss 2. Concept A truss is in
equilibrium, so each of its joint also is in
equilibrium Force system acting at pin or
joint is coplanar and concurrent

• Therefore, we have
• member equilibrium is automatically satisfied at
  each joint
• Only force equilibrium SFx0 and SFy0 is
  necessary

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3. Analysis Procedure
Support A is pin constraint. Support C is roller
constraint.


(1) Draw the free-body diagram of a joint having
at least one known force and at most two unknown
forces. For the given truss, only joint B is
satisfied.
F.B.D of joint B
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(2) Establish the sense of the unknown forces
(a) assume the unknown member forces to be in
tension.
(b) Determine correct sense of unknown member
forces by inspection
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(3) Apply the force equilibrium equations
SFx0 500FBC sin450
SFy0 -FAB-FBCcos450

(4) Solve the unknown forces and check their
correct sense
FBC- 500/sin45-500v2N (in compression) FAB-FBC
cos45500N (in tension)
(5) Continue to analyze then joints by repeating
steps (1) to (4)
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choose joint C first, then joint A
F.B.D of joint C
equilibrium equation at joint C
SFx0 500v2 cos45-FAC0
SFy0 Cy-500v2 sin450
FAC500N (in tension) Cy500N
F.B.D joint A
AxAy500N
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6-3 zero-force members
1. zero-force member A member supports no
loading, which is used to increase the stability
of the truss and to provide support if the
applied loading is changed.
2. Rules for determining zero-force members
(1) If only two members form a truss joint and no
external load or support reaction is applied to
the joint.
Ex.
Joint A and joint D are formed by two members AF
AB, EDCD respectively and no loading is
applied. Hence, members AF, A, ED and CD are
zero-force members.
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F.B.D of joint A
Equations of equilibrium
FAF

• SFx0 , so FAB0
• SFy0 , so FAF0

FAB
A
Equations of equilibrium
F.BD of joint D

• SFx0, FEDFDC cos?0
• SFy0, FDC sin?0
• So, FDC0,FED0

D
FED
x
FDC
y
The equivalent system is given as shown.
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(2) If three members form a truss joint for which
two of the members are collinear , the third
member is zero-force members provided no external
force or support reaction is applied to the joint.
EX
Joint D 3 members AD, ED and CD (ED DC
collinear) Joint C 3 members AD, DC and CB (DC
CB collinear) No external force or support
reaction is applied to the joint D C. ?AD and
AC zero-force members
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6-4 The method of section

• 1. Purpose
• Determine the loadings acting within a body
  .
• 2. Principle
• If a body is equilibrium , then any part
  of the body is also in equilibrium.

T
Imaginary section
Apply the equations of equilibrium to the
sectioned part to determine the loading at the
section.
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3. Analysis procedure
(1) Determined the external reactions at the
constraints F.B.D of entire truss.

F.B.D. of entire truss
Equations of equilibrium
500-Ax0

Cy-Ax0

500x2-Cyx20

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(2) Cut or section the truss through not more
than three members in which the forces are
unknown. (Because three independent equilibrium
equations for three unknowns.)
three possible ways of section for given truss
(3) Draw the free-body diagram of the part of
sectioned truss which has the least number of
forces acting on it.
Section(1)
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(4) Establish the sense of the unknown member
force
500N
y
45
x
F
FBC
AB
(5) Apply the equations of equilibrium and check
the correct sense of solve forces.

1. Moments should be summed about a point lying at
   the intersection of the lines of actions of two
   unknown forces. The third unknown is determined
   directly from the moment equation.
2. Forces may be summed perpendicular to the
   direction of the two unknown forces which are
   parallel.

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(6) Continue to analyze other new sections by
repeating steps(1)to(5).
Section (2)
F.B.D. of right part of section (2)
Equations of equilibrium
So, FAC500N
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6.6 Frames and Machines
1. Definition (1)Frames A stationary
structure composed of pin-connected
multiforce members is used to support loads.
Ex
bicycle frame
hoist
E
???
Engine jig.
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(2) Machine A structure composed of
pin-connected multiforce members with moving
parts is designed to transmit and alter the
effect of forces.
Excrusher
2. Assumptions (1) The structure is properly
supported. (2) The structure contains no
more supports or members than necessary to
prevent its collapse. (3) The joint
reactions of the structure can be determined
from the equilibrium equations.
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3. Analysis procedure
(1) Draw the free body Diagram of entire
structure, a part of structure, or each
of its members. (a) Isolate each part by
drawing its outline shape. Show all
forces and/or couple moments act on
the part. (b) Identify all the two-force
member in the structure. (c)
Forces common to any two contacting
members act with equal magnitudes but
opposite sense on respective members.
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Free body diagrams of members AB BC.
By inspection, member AB is a two-force member.
(2) Apply the equations of equilibrium (a)
Count the total number of unknowns to make
sure that an equivalent number of equilibrium
equations can be written for solutions.
, Cx , Cy (3)
Unkoown
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(b) Moments should be summed about a point that
lies at the intersection of the lines of
action of as many unknown forces as
possible.
Equations of equilibrium for member BC.
(2) Check the correct sense of the unknown forces.
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