Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O...
Transcript of Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O...
![Page 1: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/1.jpg)
Today:
Trusses
Book: Chapter 6.1-6.3
![Page 2: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/2.jpg)
A B
C
O
OA<OB
A particle is subjected to its own weight and
is kept in equilibrium by two cables AC and
BC. The tension in the cables are denoted TAC
and TBC respectively. Which of the following
statements is true?
A) TAC < TBC
B) TAC > TBC
C) TAC = TBC
![Page 3: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/3.jpg)
A B
O A
Consider the following experimental set-up
in the International Space Station (no
gravity!!!). Particle O is connected to 3 bars
(links). Bar OC is subjected to a force F.
Which of the following statements is true?
A) OA is loaded in compression
B) TOA = TOB
C) TOB = 0
D) TOC > TOA
C
![Page 4: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/4.jpg)
A particle is subjected to its own weight and is
kept in equilibrium by three forces with
magnitude FA, FB and FC. Points A and B are on
the y-axis and C is on the x-axis. Which of the
following is true?
A) FC>mg
B) FC>FA and FC>FB
C) FA+FB=0
D) FC=0
O A C
B
OA = OB
OC < OA
OC < OB
![Page 5: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/5.jpg)
Model of a truss structure
- All members are connected by pin joints (even when in
reality, the members are connected by welding or riveting).
- All external forces are applied at the pin connections.
- All members are assumed to be straight.
![Page 6: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/6.jpg)
![Page 7: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/7.jpg)
Design exercise
Design an efficient (=low weight) structure to attach the road sign to the wall. Take into account that the sign has a considerable mass and is subject to wind loads.
Schiphol airport P
Long term parking P3 ?
![Page 8: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/8.jpg)
Design exercise
Design a structure to
attach the road sign to
the wall.
Schiphol airport P
Long term parking P3
![Page 9: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/9.jpg)
Design exercise
Design a structure to
attach the road sign to
the wall.
Schiphol airport P
Long term parking P3
![Page 10: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/10.jpg)
Design exercise
Design a structure to
attach the sign to the
wall.
Schiphol airport P
Long term parking P3
![Page 11: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/11.jpg)
Design exercise
Design a structure to
attach the sign to the
wall.
Schiphol airport P
Long term parking P3
![Page 12: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/12.jpg)
Truss structure
A framework composed of members joined
at their ends to form a rigid structure
![Page 13: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/13.jpg)
![Page 14: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/14.jpg)
![Page 15: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/15.jpg)
Model of a truss structure
- All members are connected by pin joints (even when in
reality, the members are connected by welding or riveting).
- All external forces are applied at the pin connections.
- All members are assumed to be straight.
![Page 16: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/16.jpg)
![Page 17: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/17.jpg)
![Page 18: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/18.jpg)
A
C
D
Calculate the
forces in all the
members.
B
L
L
![Page 19: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/19.jpg)
Source: R.C. Hibbeler,
"Engineering Mechanics – Statics"
![Page 20: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/20.jpg)
A
B C D
E F
G
H K
L
M
Determine the zero-force
members of this structure
under the given load.
![Page 21: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/21.jpg)
A B C D
E
F
G
How many zero-force members does
this structure have for the given
external load?
A) 0
B) 1
C) 4
D) 5
![Page 22: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/22.jpg)
A
B
C
D E
G
How many zero-force members does
this structure have for the given
load?
A) 0
B) 3
C) 5
D) 7
H
F
![Page 23: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/23.jpg)
What are zero-force members good for?
- In case the structure is loaded in a different way
- To prevent buckling
![Page 24: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/24.jpg)
Method of joints
Determine the force in the members by
calculating the equilibrium of the joints
1. Draw Free Body Diagram
2. Determine the reaction forces at the supports of the whole structure
3. Calculate the forces in a joint with max. 2 unknowns
4. Proceed to the next joint with max. 2 unknowns until all joints are analyzed
![Page 25: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/25.jpg)
Determine the force in member DE.
Source: R.C. Hibbeler,
"Engineering Mechanics – Statics"
![Page 26: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/26.jpg)
1) Determine the force in
member DE.
2) Determine the force in
member DL.
![Page 27: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/27.jpg)
Method of sections
Determine the force in a members by dividing
the structure in two sections by cutting the members and
calculating the equilibrium of one of the sections.
1) Determine the section by cutting just three members (in general)
2) Use the moment equilibrium equation in a clever way.
![Page 28: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/28.jpg)
A
B
C
D
E G
Calculate the forces in members
CE, DE, DF
H
F
K
L
M
N
R
Q
![Page 29: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/29.jpg)
A
B
C
D
E G
Calculate the forces in member
HG
H
F
K
L
M
N
R
Q
![Page 30: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/30.jpg)
A
C
D
F
G K
Calculate the forces in member
EH
M H
L
R
B E
N
Q
![Page 31: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/31.jpg)
Rigid truss Flexible truss (mechanism)
3 members, 3 joints 4 members, 4 joints
![Page 32: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/32.jpg)
3 members, 3 joints 5 members, 4 joints 7 members, 5 joints
![Page 33: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/33.jpg)
Rigid truss consisting of triangular elements
Where
s = number of members
k = number of joints
![Page 34: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/34.jpg)
Non-rigid truss
Rigid truss
This is a necessary condition, but not sufficient!!
![Page 35: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/35.jpg)
Rigid or non-rigid?
![Page 36: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/36.jpg)
Rigid or non-rigid?
![Page 37: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/37.jpg)
Rigid or non-rigid?
![Page 38: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/38.jpg)
Rigid or non-rigid?
![Page 39: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/39.jpg)
Rigid or non-rigid?
![Page 40: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/40.jpg)
Constraints
![Page 41: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/41.jpg)
Constraints
![Page 42: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/42.jpg)
Constraint truss structure
Where
n = difference between number of unknowns and equations
r = number of constraints
s = number of members
k = number of joints
![Page 43: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/43.jpg)
Constraint truss structure
n < 0 kinematically indeterminate (mechanism)
n >= 0 kinematically determinate (necessary, not sufficient)
n = 0 statically determinate
n > 0 statically indeterminate
![Page 44: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/44.jpg)
Statically determinate?
![Page 45: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/45.jpg)
Exercises
Problems: 9.13, 9.83, 9.84, 9.85, 9.25,9.2, 9.3, 9.78
Test: Problem 2 , Statics exam, Jan 9 2003.
Chapter: 9
![Page 46: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/46.jpg)
![Page 47: Today: Trusses Book: Chapter 6.1-6 - TU Delft OCW · Today: Trusses Book: Chapter 6.1-6.3 . A B C O ... 3 joints 5 members, 4 joints 7 members, ... n > 0 statically indeterminate](https://reader034.fdocuments.us/reader034/viewer/2022042708/5aff907d7f8b9a0c028b6e60/html5/thumbnails/47.jpg)
Calculate the reaction forces
in hinge A when the normal
reaction force on the nose
wheel from the previous
example is 24 kN.
Source: R.C. Hibbeler,
"Engineering Mechanics – Statics"