Structures Flashcards
What is a truss?
An assembly of long/ thin members
In trusses if a force is positive the structure is under what?
Tension
For a truss if the force is negative that means?
Compression occurs
What does the method of joints involve?
Writing two force equations, starting with a joint with a single unknown force- this can be a heavily lengthy process
What does the method of sections involve?
Considering the whole structure - it all must be in equilibrium. Take a cut through a section. Use of rotation moments
If there are more restraints than required what would we say about the structure?
It is statically indeterminate
What is if there are more members than necessary, if an external load is applied compared to the required number of members to prevent collapse?
The structure will deform slightly less
What is a pinned support?
The structure is free to rotate about the joint, but no translation movement occurs
At each joint how many force equations are there?
2 - horizontal and vertical forces
How many total force equations are there when considering a structure?
2j - two times the number of joints
If 2j>b+k what happens?
A mechanism forms- structural collapse
b+ k = 2j is necessary but not /// for stability
sufficient (as it depends on the arrangement of the members)
What is b in the equation 2j = b+k?
the number of members
What is k in the equation 2j = b+k?
the number of restraints (forces split horizontal and vertical from supports)
What is a simple truss?
A stable statically determinate structure with the right number of supports ( most often a pin and a roller - providing three unknowns)
What is a compound truss?
The joining of two simple trusses at a single joint - an extra member is added
What method has to be used to find forces in a compound truss?
Method of sections
What is a complex truss?
Where there are overlapping members - even though it is statically determinate you can’t use method of joints or method of structures - instead use of simultaneous equations - eg 12 force equations are needed for 6 joints
Why are some trusses statically indeterminate (eg have redundant members?)
Extra members are needed to mitigate against the loss of a member
What is strength?
Ability of structure to carry loads
What is stability?
Structures remain stable
What is stiffness?
Structures don’t deform excessively
How is the capacity of a tension member determined?
allowable stress (normal) x area
How is the capacity of a compression member determined?
Use of cross sectional area and length - long thin members are prone to buckling (sudden change in shape under load - we want to prevent this )
How do you calculate stiffness?
force/ displacement (elongation)
How do you calculate stress?
force/area
Thermal strain causes —- axial stress
no (since the bar is free to expand)
When a force is applied to a heated material to prevent thermal expansion, the strain due to thermal expansion is equal to what?
The strain due to the applied force
Under self weight deformation stress and strain become linear functions of what?
distance from the bar
What kind of function does elongation of a bar against distance from tension point become under self weight?
Quadratic
What is shear strain?
The angle between two line segments when sheer stress is applied (typically defined in radians )
What is positive sheer strain?
When the angle of the object decreases
Is bearing stress typically uniform?
No - bearing stress is not typically uniform
What is bearing stress?
Stress that occurs because of the contact between two surfaces
At the infinitesimal level there is only what two types of stain?
normal and shear
A shear stress of t(xy) describes what?
the surface is orthogonal to x and the stress acts in the y direction
What is engineering shear strain defined as when strain happens in multiple directions?
the sum of the angles of deformation
How is shear strain defined?
shear stress (t)/G
What is poissons effect?
strain in the x direction leads to a negative strain in the y direction
When applying poisons effect although strain occurs in both directions, stress only occurs in…?
one direction
How do you work out strain in the x direction in a 3D model?
(oxx -oyy - ozz) /E
What are typical values for v?
0 to 0.5
What is bulk stress?
a special case where all normal stresses are the same and there is no shear stress (eg a cube underwater)
How can you define volumetric strain?
v-v0/v
exx+eyy+ezz (sum of strains in x, y and z directions)
What is the key concept linking volumetric strain and bulk stress?
the stress in all directions is the same (ob) hence you can rewrite the matrix calculation including this
What is volumetric strain as a function of bulk stress?
(1-2v) 3ob/E
What is the material bulk modulus?
bulk stress/ volumetric strain
How can you calculate the material bulk modulus?
E/ 3(1-2v)
bulk stress/ volumetric strain
What does a bulk modulus of infinity mean?
the material is incompressible (no matter the stress there is no strain)
What are the steps in accomplishing a nice relationship between max stress, maximum bending moment, y max and moment of inertia?
- plane sections remain perpendicular to the beams’ axis
- hooke’s law - move to stresses
- use of force equilibrium
- moment equilibrium (and use of second moment of area)
What is the euler-bernolli beam theory?
for an elastic beam where H is much smaller than L, considering small deflections and zero shear force, the plane section remains plane and perpendicular to the beam’s axis
