ES196 Engineering Structures Flashcards
Reaction forces
Develop when an external force is applied to a body
If two forces have intersecting lines of action
They combine as vectors and act at the point of intersection
Principle of transmissibility
If a force is translated along its line of action - size of moment of force doesn’t change
Convenience of line of action
In practice, force acts at a point, but line of action allows force to be translated without affecting moment
Moment of a couple
Force x distance between points of application of force
(independent of reference point)
(r2-r1)xP
What causes an internal force
An external force haha!
Types of loads on a beam
Concentrated load (at a point)
Distributed load N/m
Reaction forces (forces holding beam up)
The moment of a force
describes the tendency of a rigid
body to rotate and is characterised by a force, a centre of
rotation and the perpendicular distance between centre of
rotation and point of application of the force
Static and Kinetic friction
Static friction is the friction present between two or more objects that are not moving with respect to each other. Kinetic friction is the friction present between two or more objects that are in motion with respect to each other.
Fs ≤ μsN
Fd = μkN
Usually μk is less than μs
https://www.youtube.com/watch?v=RIBeeW1DSZg last q
Fluid definition
A fluid is any continuous
substance which, when at
rest, exerts only normal
forces on its boundary
surfaces
Fluids may be either
liquids (hydrostatic
pressure) or gases (aerostatic pressure)
Types of loads
Dead - self weight
Live - people, cars, moveable furniture (assumed by designer)
Environmental - Loads that act due to weather/natural stuff
Types of support
Roller support - 1 unknown, orthogonal to surface its on (allows movement parallel to surface + rotation)
Pin joint - 2 unknowns, x and y components
(allow for rotation, no translation)
Fixed support - x,y and reaction moment
(no translations/rotations)
If a certain degree of freedom is restrained at a support
There will be a corresponding reaction force/moment
Why trusses are more efficient than beams (qualitative)
All material is being used close to failure stress, however beams act in bending and a lot of material is not under stress
Compression vs tension members
Compressive members break easier esp when long
Conditions for a truss system to not collapse
All connections between members must be “pins”, that is connections that allow members to
rotate relative to each other. If this is not the case, bending may occur in members
* All loads on a truss must be applied at the “nodes” where members meet. Again, if this is not
the case members will be in bending and inefficiently used.
* Trusses must consist of a number of triangles
In triangles, you cannot change the angle between pins (deflection) without changing the length of a side.
Deriving performance index
- Don’t want objective to depend on design properties (free variables), only materials
Relationship between sf and bm diagrams
dv/dx = -w where w is distributed load
So change in v = area under loading diagram
DM/dx = V
Change in M = area under sf diagram
Warren truss
Symmetrical
Bending moment at a pin joint
Zero bending moment - as rotation isn’t restricted, so there will be no moment reaction
Zero force members
3 members connected at a joint, with two aligned. Only one member has component in vertical direction, so vertical must carry no force.
Other when two members at a joint, and aren’t aligned, both must be zero force
True when no external load on members
Can remove zero force members from example
Used to prevent buckling of longer members, and unexpected loads won’t cause structures to fail
Condition for principle of superposition of forces for beams
Linear system (in linear elastic range)
WITHIN ELASTIC LIMIT
Lever rule
a1F1 = a2F2
Where a is respective distance to force on beam
