royal albert bridge at saltash 1859 balance of forces in

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Microsoft PowerPoint - ES226_Class_22_Frames_Slides.ppt [Compatibility Mode]Royal Albert Bridge at Saltash 1859 Isambard Kingdom Brunel, Engineer
Saltash Brunel
Balance of Forces in Equilibrium PULLEYS, FRAMES, AND MACHINES
Compute the forces in pulleys, ropes, beam, and frame members that require multiple free-body diagrams.
Compute the reactions for compound beams, frames, or similar devices.
Show why it is advantageous to: Separate elements at pins and draw multiple FBDs & identify 2-force members
Statics:Hibbeler 2
W
T
FBD Top
Fb
FBD
W
Fbar T
Pulleys – Method of Joints Approach Pulleys – Method of Joints Approach
Pulleys – Method of Joints Approach Ay
P
Cy
RR
R
R P
Given: A frame and loads as shown.
Find: The reactions that the pins exert on the frame at A, B, and C.
Plan:
a) Draw a FBD of members AB and BC.
b) Apply the equations of equilibrium to each FBD to solve for the six unknowns.
QUICK PROBLEM SOLVING (continued)
BY
BY = 0 and BX = 500 N
Summing moments about A and C on each member, we get:
0.2m 0.4m
BY
For FBD of BC:
For FBD AB: CY
WORKING EXAMPLE
Given: The wall crane supports an external load of 700 lb.
Find: The force in the cable at the winch motor W and the horizontal and vertical components of the pin reactions at A, B, C, and D.
Plan:
a) Draw FBDs of the frame’s members and pulleys.
b) Apply the equations of equilibrium and solve for the unknowns.
Statics:Hibbeler 5
T T
T = 350 lb
+Fx = Cx – 350 = 0 Cx = 350 lbFBD of pulley C
C
350 lb
+↑ Fy = Cy – 350 = 0 Cy = 350 lb +FX = – Bx + 350 – 350 sin 30° = 0
Bx = 175 lb
By = 303.1 lb FBD of pulley B
BY
BX30°
FBD of member ABC
4 ft 4 ft
+MA = TBD sin 45° (4 ft) – 303.1 (4 ft) – 700 (8 ft) = 0
TBD = 2409 lb
AY = – 700 lb
AX = 1880 lb
45
+ DX = –2409 cos 45° = –1700 lb
+ DY = 2409 sin 45° = 1700 lb
45 °
B
Why are trusses like donuts?
Donuts are not good in compression either After the 5th one you feel kinda sick
Both = fun! You can’t drive to school without them
If they fall to the ground they are not any good anymore
Analysis of Machines
Pliers, Cutters, and Grips Find vertical clamping force at E
APPLICATIONS
How is a frame different than a t ?truss?
How can you determine the forces at the joints and supports of a frame?
Find all reaction forces and forces at pinned connections in press
Statics:Hibbeler 7
(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
Time (sec)
A cc
BACK
bridge cood. (ft)