En2225531 Final Closed

Front 1

Principle of Impulse and Momentum

Back 1

Impulse = Int( F dot dt)= mv2-mv1
The integration of Newton's 2nd Law over a certain time interval.
Relates outside force applied to it's velocity wrt time. It is a vector solution with no conservative forces.

Front 2

Conservative Force

Back 2

Scalar (such as that of gravity or a spring) for which path doesn't matter.
Force where the PE and KE before= the PE and KE after
1/2 mv1^2 + v1= 1/2mv2^2 + v2

Front 3

Planar Motion

Back 3

a 2D representation of 3D motion that does not rotate

Front 4

Instantaneous Center

Back 4

a point of a rigid body whose velocity at a particular instant of time is zero

Front 5

Coefficient of Restitution

Back 5

e=change momentum after/change in momentum before
a value that relates masses and velocities when dealing with linear momentum
measure of how elastic or inelastic a collision is between two bodies

Front 6

Relationship between Force and Potential Energy

Back 6

PE is force through a distance and has units N*m, while Force is only N.
U12=mg(y2-y1) PE is equal to the work (force over a distance) done on an object as it moves from one position to another.
U=∫ r1,r2 Fdr = mv2^2 - mv1^2 Force is needed over some distance to produce a potential energy

Front 7

Principle of Work and Energy

Back 7

Int s1,s2(F ds)= 1/2 mv2^2 - 1/2 mv1^2
Relates a change in the position of an object to the change in the change in its velocity.
The potential and kinetic energy of the system involved is assumed to be equal. This can be a flaw since energy is tranformed when work takes place (into sound, heat, etc) and those other transformations are not taken into account.
Work and Energy is a scalar equation.
Conservative Forces can be used for W&E.

Front 8

Modulus of Resilience

Back 8

area under the linear elastic portion of the stress-strain curve

Front 9

inertial reference frame

Back 9

a system that is not accelerating or rotating, that can be used as a frame of reference

Front 10

Relationship between Newton's 2nd Law and the Principle of Angular Impulse or Momentum? What is H0?

Back 10

∫ t1,t2 (r x ∑F)dt= (H0)2 - (H0)1 (angular momentum)=mv2-mv1
H0 is angular momentum.
The Principle of Angular Impulse or Momentum is the change of the angular momentum over time. Angular Momentum is the integration of Newton's 2nd Law crossed with r, over a span of time.
vt=movement tangent to the curve
vn=movement pointed toward the center of curvature

Front 11

Equivalent Static Load

Back 11

static load which will produce the same deflection as the max deflection under a dynamic load
Found by finding the maximum deflection and the maximum moment of the body. By equating the strain energy to the potential energy, one can then solve for the load.
The assumption is that there are only small deflections and no permanent deformation.

Front 12

Modulus of Toughness

Back 12

total area under the stress-strain curve

Front 13

Column Design Steps

Back 13

1. Choose material, find Cc
2. Choose the orientation of the column- determine effective length (x and y), calculate kxL, kyL
The weak direction with shortest Le and strong direction with largest

Front 14

Effective Length

Back 14

manipulates the value of the length of the beam so that it is appropriate for Euler's Eqn based on the ends (free, fixed,etc)
L_e = k*L

Front 15

Columns

Back 15

Long slender members subjected to an axial compressive force.
Buckling is the lateral deflection that occurs

Front 16

slenderness ratio

Back 16

L/r
r is the smallest radius of gyration of the column: r=sqrt(I/A)
Buckling of a column occurs where the ratio gives the greatest value

Front 17

Equation for Biforcation point

Back 17

d^2 v/ dx^2 + Pv(x) =0

Front 18

Real Column Assumptions

Back 18

1. Initially straight and constant section area
2. Homogeneous and remains elastic (small deflections)
3. Load is applied along central axis of column
4. Pinned end conditions- no moment on end

Front 19

Ultimate Load of a Column depends on

Back 19

1. Material Properties
2. Geometry (I, A, Depth)
3. End Conditions
4. Initial Column Eccentricity
5. Load Eccentricity

Front 20

Euler's Equation

Back 20

σ_crit=(π^2*E)/(L/r)^2<BR>The flaw of Euler's Eqn is that the curve goes to infinity, implying that the column does not fail and that the modulus of elasticity is constant. AISC E2-1/2 avoid this flaw. The data is below that of Euler's Eqn in order to design steel structures that are guaranteed not to fail (well below σyield). <BR>The eqns E2-1/2 are 2 standard deviations that ensure structural stability. Cc is the critical slenderness ratio found using 50% σyield (so that the safety of the structure is ensured). <BR>If value of slenderness ratio<Cc -> use E2-1<BR>> Cc -> use E2-2

Front 21

Section Modulus

Back 21

Determines how the weight ofthe beam affects the load-carrying capacity
I/y

Front 22

Second Moment of Inertia

Back 22

Measure of the scatter of the area.
I=∫y^2 dA

Front 23

Impulsive Force

Back 23

Force applied over a short period of time
∫ F dt

Front 24

Damping factor

Back 24

the ratio of the amount of damping present to the amount of damping needed for the system to be critically damped
η=b/(2*sqrt(a*c))

Front 25

Tuning factor

Back 25

a ratio of the wave encounter frequency to the natural frequency
Λ = w_e/w_n

Front 26

Natural Frequency

Back 26

w_n = sqrt(c/a)

Front 27

Dynamic Magnification Factor

Back 27

sqrt( (1-Λ^2)^2 + (2*η*Λ)^2)

Front 28

Synchronous Roll

Back 28

occurs when the ship's movement matches that of the natural frequency of the waves' movement

Front 29

Static Response

Back 29

amplitude of the wave Fo/c

Front 30

beam

Back 30

structural member which undergoes a load causing bending

Front 31

shear area

Back 31

the area upon which most of the shear load acts

Front 32

Elastic Flexture formula and its assumptions

Back 32

Formula which relates the beam bending moment due to loading to the stress experience by the beam fibers.
σ=(M*y)/I
1. pure bending, no vertical or horizontal shear forces
2.initially straight, constant cross-section shape
3. homogeneous, obeys Hooke's Law, material is loaded in the linear elastic range, small deflections
4. Modulus of Elasticity is the same in tension and compression

Front 33

radius of gyration

Back 33

calculated using the geometry of the column and is used to find slenderness ratio (kL/r). this ratio determines if a column's length is too long and lowers its load-carry capacity