Dynamics and Stability Section 1- 4 Flashcards
Why is the study of earthquakes critical in civil engineering?
To design structures that can withstand seismic forces, minimizing the risk of catastrophic failure during an earthquake
What are the problem faced by civil engineers in structures?
- Dynamics
- Time-dependent behaviour
- Instability
What are some of the core components?
- Water waves
- Fluid flow, fluid quality
- Soil behaviour
- Foundations
- Tall and exposed structures subject to wind
- Structures susceptible to repetitive loading
- Structures subject to hazardous dynamic loading
What can induce repetitive loading?
Traffic
How are the forces distributed in cable stayed bridges?
- The deck is acting like a compression member and cable is connected to the deck
- Deck doing more work
What is the main static load?
Gravity main static load → dead and live load
What are two types of dynamic loading?
Wind and seismic
How did the Tacoma Narrows bridge collapse?
Moderate wind loading induced violent oscillations
What is the Tacoma Narrows Bridge an example of?
Fluid-Structure Interaction
What risks do earthquakes impose?
Fire from destruction of:
- power lines
- gas mains
How does fatigue in a material occur?
- Crack initiation
- Crack propagation
- Fatigue fracture
What is buckling?
Mode of failure under compression of a structural component that is thin (see shell structure) or much longer than wide
When is a material in compression in its linear elastic phase?
Pre buckling
When is a material in compression weakly stable?
Global buckling
When a material in compression unstable?
Interactive buckling
What is critical bifurcation?
- Occur when the load reaches a critical value, leading to large deformations or to collapse of the structure
- Changes behaviour
What is Newton’s first law of motion?
A body remains at rest or continues to move at a uniform velocity if there is no external force acting on it
What is Newton’s third law of motion?
If body A exerts a force on body B then body B exerts
a force equal in magnitude and opposite in direction on body
A
What is Newton’s second law of motion?
The rate of change of momentum of a body is directly
proportional to the external force acting on a body and takes
place in the direction of the force
What is the elastic potential energy also known as?
Strain energy
Where is the elastic potential energy stored?
Stored in a linearly elastic rotational spring of stiffness c and rotated θ
How can you work out strain energy?
U=1/2cθ^2
What are degrees of freedom?
The number of independent parameters that define its configuration or state
In a 2D system how man independent displacement components are there?
3
What are the components of a 3D system?
- 3 translation components
- 3 rotational components
In a 3D system how many DOFs are there?
6
How can the number of DOFs decrease?
Adding more constraints
What are the types of motion?
- Rectilinear
- Plane curvilinear
- General curvilinear
What is the coordinate system in rectilinear motion?
Cartesian
What is the coordinate system in plane curvilinear motion?
Plane-polar
What is the coordinate system in general curvilinear motion?
- Cylindrical polar
- Spherical polar
Whats the difference between cylindrical and spherical polar?
C - radius, distance upwards and angle
S - one radius and two angles
How do vectors in a cartesian system behave?
- Fixed
- Unit vectors do not vary with time
How does accleration behave in projectiles?
Constant
How do the components in curvilinear motion behave?
In plane polar coordinates, the radius of motion r is fixed
and only the angle θ varies
How can the position vector r be calculated?
radius*e_r
What is Gruebler’s equation for planar mechanisms?
3(n-1) - 2j
