solid mechanics. reactions and internal force diagrams. step by step example. part 1
TRANSCRIPT
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Bloque A. Sistemas isostáticos reticulados planos.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Solid Mechanics
Block A. Internal forces. Diagrams.
Degree in Architecture.
San Pablo CEU University – Institute of Technology.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
Note that the 50 kN load that
rests on the hinge can be
located on any of the three
systems that converge at the
hinge.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
As the hinge bonds both horizontal and vertical
movement of the three solids that meet on it, two
unknowns appear at point “C” on each of the three
subsystems.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
As the hinge bonds both horizontal and vertical
movement of the three solids that meet on it, two
unknowns appear at point “C” on each of the three
subsystems.
Vertical movement is the only one linked by the roller at
E, so just one reaction will appear on each of the solids
that meet at that point.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
As the hinge bonds both horizontal and vertical
movement of the three solids that meet on it, two
unknowns appear at point “C” on each of the three
subsystems.
Hint:
If unknowns are
positive you’ll always
obtain the correct sign
in the result.
Vertical movement is the only one linked by the roller at
E, so just one reaction will appear on each of the solids
that meet at that point.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
If any of the subsystems is a 3-unknown one, this
will mean that it’s a statically determiate one and
it’s reactions don’t depend on the behaviour of the
rest of the solids.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
If any of the subsystems is a 3-unknown one, this
will mean that it’s a statically determiate one and
it’s reactions don’t depend on the behaviour of the
rest of the solids.
System CDE meets this condition, so we’ll solve it
in first place.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
1 – General layout.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
3 3
3
3 3
3 1000
3
0
100 3100
3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
3 3
3
3 3
3 1000
3
0
100 3100
3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
3 3
3
3 3
3 1000
3
0
100 3100
3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
3 3
3
3 3
3 1000
3
0
100 3100
3
3 4 3 40
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
50 0 50
100100 3 50 2 0 100
3
100 1000
3 3
3 3
3
3 3
3 1000
3
0
100 3100
3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Subsistema 4
50 0 50
100100 3 50 2 0 100
3
100 1000
3 3
3 3
3
3 3
3 1000
3
0
100 3100
3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
1 1
2 2
4 3 60 3
53 4 100 0
2
3 2500
2 3
1 2 1 2
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
2 2
2 2
2
2
4 3 340
4 3 0
59073 750 8
9015
250 6
1 1
2 2
4 3 60 3
53 4 100 0
2
3 2500
2 3
1 2 1 2
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
2 2
2 2
2
2
4 3 340
4 3 0
59073 750 8
9015
250 6
1 1
2 2
4 3 60 3
53 4 100 0
2
3 2500
2 3
1 2 1 2
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
8 60 6 80 60 3
58 100 0
2
3 3 2500
2 2 3
3 25060 3
2 3
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
8 60 6 80 60 3
58 100 0
2
3 3 250 500 6 25
2 2 3 8
3 250 59060 3 73 75
2 3 8
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Exercise 1 - Reactions on each subsystem
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Bloque A. Sistemas isostáticos reticulados planos.
If you want to learn how to draw internal force diagrams for this example go for it on Part 2.
Solid Mechanics – Academic Year 2014/2015 Prof: Maribel Castilla Heredia @maribelcastilla v.1.0 October 2014
Solid Mechanics
Block A. Internal forces. Diagrams.
Degree in Architecture.
San Pablo CEU University – Institute of Technology.