Dynamics and Stability Section 1- 4

Question 1

Why is the study of earthquakes critical in civil engineering?

Answer 1

To design structures that can withstand seismic forces, minimizing the risk of catastrophic failure during an earthquake

Question 2

What are the problem faced by civil engineers in structures?

Answer 2

• Dynamics
• Time-dependent behaviour
• Instability

Question 3

What are some of the core components?

Answer 3

• 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

Question 4

What can induce repetitive loading?

Answer 4

Traffic

Question 5

How are the forces distributed in cable stayed bridges?

Answer 5

• The deck is acting like a compression member and cable is connected to the deck
• Deck doing more work

Question 6

What is the main static load?

Answer 6

Gravity main static load → dead and live load

Question 7

What are two types of dynamic loading?

Answer 7

Wind and seismic

Question 8

How did the Tacoma Narrows bridge collapse?

Answer 8

Moderate wind loading induced violent oscillations

Question 9

What is the Tacoma Narrows Bridge an example of?

Answer 9

Fluid-Structure Interaction

Question 10

What risks do earthquakes impose?

Answer 10

Fire from destruction of:
- power lines
- gas mains

Question 11

How does fatigue in a material occur?

Answer 11

1. Crack initiation
2. Crack propagation
3. Fatigue fracture

Question 12

What is buckling?

Answer 12

Mode of failure under compression of a structural component that is thin (see shell structure) or much longer than wide

Question 13

When is a material in compression in its linear elastic phase?

Answer 13

Pre buckling

Question 14

When is a material in compression weakly stable?

Answer 14

Global buckling

Question 15

When a material in compression unstable?

Answer 15

Interactive buckling

Question 16

What is critical bifurcation?

Answer 16

• Occur when the load reaches a critical value, leading to large deformations or to collapse of the structure
• Changes behaviour

Question 17

What is Newton’s first law of motion?

Answer 17

A body remains at rest or continues to move at a uniform velocity if there is no external force acting on it

Question 18

What is Newton’s third law of motion?

Answer 18

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

Question 19

What is Newton’s second law of motion?

Answer 19

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

Question 20

What is the elastic potential energy also known as?

Answer 20

Strain energy

Question 21

Where is the elastic potential energy stored?

Answer 21

Stored in a linearly elastic rotational spring of stiffness c and rotated θ

Question 21

How can you work out strain energy?

Answer 21

U=1/2cθ^2

Question 22

What are degrees of freedom?

Answer 22

The number of independent parameters that define its configuration or state

Question 23

In a 2D system how man independent displacement components are there?

Answer 23

3

Question 24

What are the components of a 3D system?

Answer 24

• 3 translation components
• 3 rotational components

Question 25

In a 3D system how many DOFs are there?

Answer 25

6

Question 26

How can the number of DOFs decrease?

Answer 26

Adding more constraints

Question 27

What are the types of motion?

Answer 27

• Rectilinear
• Plane curvilinear
• General curvilinear

Question 28

What is the coordinate system in rectilinear motion?

Answer 28

Cartesian

Question 29

What is the coordinate system in plane curvilinear motion?

Answer 29

Plane-polar

Question 30

What is the coordinate system in general curvilinear motion?

Answer 30

• Cylindrical polar
• Spherical polar

Question 31

Whats the difference between cylindrical and spherical polar?

Answer 31

C - radius, distance upwards and angle
S - one radius and two angles

Question 32

How do vectors in a cartesian system behave?

Answer 32

• Fixed
• Unit vectors do not vary with time

Question 33

How does accleration behave in projectiles?

Answer 33

Constant

Question 34

How do the components in curvilinear motion behave?

Answer 34

In plane polar coordinates, the radius of motion r is fixed
and only the angle θ varies

Question 35

How can the position vector r be calculated?

Answer 35

radius*e_r

Question 36

What is Gruebler’s equation for planar mechanisms?

Answer 36

3(n-1) - 2j