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Statics:Hibbeler 1
FINDING ZERO-FORCE MEMBERS
Given: P1 = 240 lb and
P2 = 100 lb
Plan:
Check if there are any zero-force members.
Solution:
Members AB and AC are zero-force members.
M h dMethod of Sections
METHOD OF SECTIONS - EXAMPLE
Given: Loads as shown on the roof truss.
Find: The force in members DE, DL, and ML.
Plan:
a) Take a cut through the members DE, DL, and ML.
b) Work with the left part of the cut section.
c) Determine the support reactions at A.
d) Apply the E of E to find the forces in DE, DL, and ML.
METHOD OF SECTIONS - EXAMPLE
Given: Loads as shown on the roof truss.
Find: The force in members DE, DL, and ML.
Plan:
a) Take a cut through the members DE, DL, and ML.
b) Work with the left part of the cut section.
c) Determine the support reactions at A.
d) Apply the E of E to find the forces in DE, DL, and ML.
METHOD OF SECTIONS - EXAMPLE
Given: Loads as shown on the roof truss.
Find: The force in members DE, DL, and ML.
Plan:
a) Take a cut through the members DE, DL, and ML.
b) Work with the left part of the cut section.
c) Determine the support reactions at A.
d) Apply the E of E to find the forces in DE, DL, and ML.
METHOD OF SECTIONS – CHANGE UP
Given: Loads as shown on the roof truss.
Find: The force in members CD, DM, and ML.
Plan:
a) Take a cut through the members CD, DM, and ML.
b) Work with the left part of the cut section. Why?
c) Determine the support reactions at A.
d) Apply the E of E to find the forces in CD, DM, and ML.
Statics:Hibbeler 2
METHOD OF SECTIONS – CHANGE UP
Given: Loads as shown on the roof truss.
Find: The force in members CD, DM, and ML.
Plan:
a) Take a cut through the members CD, DM, and ML.
b) Work with the left part of the cut section. Why?
c) Determine the support reactions at A.
d) Apply the E of E to find the forces in CD, DM, and ML.
QUESTION
As shown, a cut is made through members GH, BG and BC to determine the forces in them. Which section will you choose for analysis?
QUESTION
When determining the force in member HG, which one equation of equilibrium is best to use?
GROUP PROBLEM SOLVING
Given: Loading on the truss as shown.
Find: The force in members BC, BE, and EF.
PlPlan:
a) Take a cut through the members BC, BE, and EF.
b) Analyze the top section (no support reactions!).
c) Draw the FBD of the top section.
d) Apply the equations of equilibrium such that every equation yields answer to one unknown.
SOLUTION
+ FX = 5 + 10 – FBE cos 45º = 0 FBE = 21.2 kN (T)
+ ME = – 5(4) + FCB (4) = 0 FCB = 5 kN (T)
+ MB = – 5 (8) – 10 (4) – 5 (4) – FEF (4) = 0 FEF = – 25 kN or 25 kN (C)
Method of Sections – Useful?
Statics:Hibbeler 3
Cut to Find Force in OE and LE and LK Cut to Find Force in OE and LE and LK
Cut to Find Force in OE and LE and LKTEDA Stadium Tianjin, China
Smithfield Bridge, Pittsburgh 1882
Smithfield
Lindenthal Projects
Statics:Hibbeler 4
oya be t de atSaltash 1859 Isambard Kingdom Brunel, Engineer
SaltashBrunel
Balance of Forces in Equilibrium
Balance of Forces in EquilibriumElevation View of Cairo Bridge
(Source: S. Nam, University of Illinois)
2D Schematic of Cairo Bridge
(Source: S. Nam, University of Illinois)
View of Finite Element Model
-1
-0.5
0
0.5
1
0 10 20 30 40
Time (sec)
Acc
. (g)
Statics:Hibbeler 5
Animation of Bridge Deflection
(Source: S. Nam, University of Illinois)
BACK
Graph of Maximum Deflection
Vertical Displacement
0
2
4
6
8
10
0 500 1000 1500 2000 2500 3000 3500 4000
bridge cood. (ft)
Example 3Find all Zero-Force MembersFind forces in members JE and GF
Method of Joints
Statics:Hibbeler 6
Zero-Force Members Zero Force Members (not Two-Force!)
Zero Force Members (not Two-Force!)Zero-Force Members
Bridge over Falls River Structural Models
Statics:Hibbeler 7
Zero-Force Members Zero-Force Members
Zero-Force Members
