Mechanics And Fluids Flashcards
Newton’s first law
A body at rest or in constant motion remains in that state until acted upon by an external unopposed force
Mechanics
The study of objects at rest or in motion and the effects of forces on a body
Newton’s second law
An unopposed forces causes a mass to accelerate
ΣF= ma
Newton’s third law
Every force has an equal and opposite reaction
Two divisions of mechanics
Statics
Dynamics
In statics, ΣF….
ΣF= 0
Because a=0
Statics is the study of…
Of forces acting on a non-accelerating body
Dynamics is the study of…
Motion of a body, both in translation and rotation
So ΣF cant be 0
Types of loading
- Tension: pull apart
- Compression: push together
- Moment: rotation
- Shear: distort shape
Scalar
Only has magnitude
Vector
Has magnitude and direction
Can be broken into x and y components
Adding vectors
Cx= Ax+Bx Cy= Ay+By C= sqrt(Cx^2 + Cy^2)
Multiplying vectors
Can only be multiplied by a scalar
Changes the vector’s magnitude
Does NOT change the vector’s diction
No negative numbers for the test
Unit vectors
i has magnitude of 1 in x direction
j has magnitude of 1 in y direction
When a vector component is multiplied by i or j
Magnitude of vector component is unchanged
The direction of the vector com pone is defined as parallel to the x or y axis
ΣF= Fxi + Fyj
When drawing FBDs
- Forces are detached from ground and other bodies
- All external forces are indicated (weight is applied at center of gravity)
- Indicate magnitude and direction of known external forces
- Include dimensions
Reaction forces in rollers/rockers
Perpendicular to the roller/rocker
Reaction forces in pins
Have x and y components
Truss
A simple skeletal structure (made of triangles
In theory, the individual members of a simple true are only subject to…
Tension (pulling) and compression (pushing)
No bending forces
Why structures are built with triangles
- Pinned triangles are naturally rigid
- Joint strength becomes less critical
- High stiffness can be achieved for small amount of material used
- Ease of construction
Members in tension
Tension forces tend to pull the member apart
Member tends to “stretch”
More economical
Can be made lighter/thinner
Members in compression
Compressive forces tend to “squeeze” the member
Long slender members tend to buckle easily and can only carry smaller loads
Shorter members can carry higher compressive loads
Assumptions for static analysis of truss bridges
- ΣF at each joint (node) must equal zero
- Each element is a “two force” member.
Tension: ⬅️➖➡️
Compression: ➡️➖⬅️ - Joints are pinned and frictionless (pins will not support a moment)
- Forces can only be applied at joints (no bending)
- No deformation occurs to change dimensions
- External reactions are statically determinant, and supports are frictionless