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Mechanic > Statics > Flashcards

Statics Flashcards

1
Q

What is a scalar? examples

A

a quantity characterised by a positive or negative number

eg. mass, volume and length

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2
Q

What is a vector? examples

A

a quantity that has magnitude and direction

eg. position, force and moment

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3
Q

What is a force?

A

a push or pull between two objects

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4
Q

What are the conditions for the equilibrium of a particle?

A

a particle is at equilibrium if:
it is at rest
it is moving at constant velocity

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5
Q

What is Newton’s first law of motion?

A

the vector sum of all force acting on a particle at equilibrium is zero
ƩF = 0

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6
Q

How does Newton’s second law of motion relate with the equilibrium of a particle?

A

ƩF = ma, when the forces fulfill Newton’s first law of motion; ma = 0, a = 0, therefore the particle is moving in constant velocity or is at rest.

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7
Q

What is a moment of a force?

A

The moment of a force about a point or axis is a measure of the tendency of the force to cause a body to rotate about the point or axis
• Sometimes referred to as torque

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8
Q

Why is the moment of a force not unique? 93)

A

The axis about which a moment is taken is an arbitrary choice.
• The choice of axis is usually made to fit the context of the situation being studied. In the previous diagram of the spanner (wrench), the obvious purpose was to rotate the nut and so the moment was calculated as the turning effect on the nut about its axis.
• We must ALWAYS state the axis about which the moment is calculated.

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9
Q

What is a resultant moment?

A

Resultant moment where all the forces are co- planar and are about a common axis.

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10
Q

What is Varignon’s theorem?

A

Moment of a force about an axis is equal to the sum of the moments of the forces’ components about the point

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11
Q

What is a moment of a couple? (2)

A
  • Resultant force = 0

* Tendency to rotate in specified direction

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12
Q

What are the 3 types of couples in a moment of a couple?

A

• Couple
– two parallel forces
– same magnitude but opposite direction
– separated by perpendicular distance d

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13
Q

What is the result when you calculate the total moment due to the two forces about any axis in a moment of a couple?

A

If we calculate the total moment due to the two forces about ANY axis (perpendicular to page), the result will be the same and equal to Fd.

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14
Q

What does it mean that couples are free vectors?

A

Couples are free vectors.
They can be thought of (and do) have an identical effect on an object regardless of where
the forces are applied.
Since ΣF=0, a couple is a pure turning action.

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15
Q

What are equivalent couples?

A
  • Two couples are equivalent if they produce the same moment

* The forces of equal couples lie on the same plane or planes parallel to one another

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16
Q

What happens when a couple vector is moved?

A

The couple is a free vector.

It may act anywhere.

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17
Q

What is a concurrent force system?

A

A concurrent force system is where lines of action of all the forces intersect at a common point O. There is no moment about O. Vector summation of forces.

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18
Q

What are coplanar force system? (4)

A
  • Lines of action of all the forces lie in the same plane
  • Resultant force of this system also lies in this plane
  • All couple vectors are perpendicular to the page and can be added. They are free vectors.
  • Can move FR to a line where (MR)O = 0.
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19
Q

What are parallel force system? (4)

A

• Consists of forces that are all parallel to the z axis
• Resultant force at point O must also be parallel to this axis
• All moment vectors are in the plane of the plate and can be
summed vectorially.
• Can move FR to a line where (MR)O =0

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20
Q

What is the magnitude of the resultant force equal to?

A

• Magnitude of the resultant force is equal to the total area A under the loading diagram.

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21
Q

What is the principle of transmissibility?

A

For the purpose of determining a moment, the point of application
of the force on the object may be anywhere along its line of action.

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22
Q

Why are couple moments a floating vector?

A

The total moment of the two
forces about any point is the same. Therefore, a couple is a
‘floating’ vector that can be applied anywhere to the object.

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23
Q

What are internal forces in a rigid body equilibrium?

A

Internal forces that act between particles within the boundary of the free body diagram exist in
equal and opposite pairs. They cancel internally and are not shown on the FBD.

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24
Q

What is the distributed weight of a rigid body equilibrium?

A

The distributed weight of a body may be replaced with a single equivalent force, W = mg , acting through the centre of gravity.

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25
Q

What is the support of a rigid body equilibrium?

A

Supports provide reaction forces and reaction moments that prevent an object moving. Many different types of support exist and may constrain movement in one or more directions and rotations. The reactions forces provided by supports grow, shrink and change direction as
needed, to maintain static equilibrium.

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26
Q

What is a two force member of a rigid body equilibrium?

A

A Two Force Member is subject to two forces (only). To be in static equilibrium, the two forces
must be equal, opposite and collinear (otherwise an unbalanced moment exists)

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27
Q

What is a three force member of a rigid body equilibrium?

A

A Three Force Member is subject to three forces (only). To be in static equilibrium, the forces
must be concurrent or parallel (otherwise an unbalanced moment exists).

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28
Q

When determining the moment of a force about a specific axis, the axis must be along……

A

the y axis

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29
Q

The triple scalar product u x (r x F) results in….

A

a vector quantity

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30
Q

If three couples act on a body, the overall result is that….

A

The net force equals 0 but the net moment is not necessarily equal to 0.

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31
Q

A general system of forces and couple moments acting on a rigid body can be reduced to a…..

A

single force and a single moment

32
Q

The original force and couple system and an equivalent force-couple system have the same _____ effect on a body.

A

external

33
Q

The forces on a pole can be reduced to a single force and a single moment at what point….

A

At any point

34
Q

Consider two couples acting on a body. The simplest possible equivalent system at any arbitrary point on the body will have….

A

one couple moment

35
Q

Consider three couples acting on a body. Equivalent systems will be _____ at different points on the body.

A

the same even when located

36
Q

The resultant force (FR) due to a distributed load is equivalent to the ____ under the distributed loading curve, w = w(x)

A

Area under the distributed loading curve

37
Q

The line of action of the distributed load’s equivalent force passes through the ____ of the distributed load.

A

Centroid

38
Q

What the three rules that apply to dimensional homogeneity?

A

In every analytically derived equation, both sides of the equation must have identical dimensions. All numbers appearing in the equation must be dimensionless constants.

If either or both sides of a theoretically derived equation have/has more than one member joined by addition or subtraction, then all of these members must have identical dimensions.

Exponents and arguments of transcendental functions in a theoretically derived formula must be dimensionless.

39
Q

What is archimedes principle?

A

Archimedes’ Principle states that the upward directed vertical force on a submersed body is
equal to the weight of the fluid displaced by the body.

40
Q

What are conditions for a rigid body equilibrium?

A

A rigid body in equilibrium must have both the resultant force and the resultant moment equal to zero

41
Q

What are support reactions?

A

If a support prevents the translation of a body in a given direction, the a force is developed on the body in that direction.

42
Q

What happens is a rotation is prevented?

A

If a rotation is prevented, a couple moment is exerted on the body

43
Q

What are the three cases for zero force members?

A

Case 1: Only two members joined at a pin without an external load. Both
members are zero-force members.

Case 2: Three members join at a pin without an external load, two of which are collinear. The third member will be a zero-force member and the collinear members will support the equal loads. The same
situation exists when one of the collinear members is replaced with an external force.

Case 3: This case is not zero-force, but when configured as in the diagram,
the opposite member-member and force-member pairs have equal forces.

44
Q

What is the first case of zero force members?

A

Case 1: Only two members joined at a pin without an external load. Both
members are zero-force members.

45
Q

What is the second case of zero force members?

A

Case 2: Three members join at a pin without an external load, two of which are collinear. The third member will be a zero-force member and the collinear members will support the equal loads. The same
situation exists when one of the collinear members is replaced with an external force.

46
Q

What is the third case of zero force members?

A

Case 3: This case is not zero-force, but when configured as in the diagram,
the opposite member-member and force-member pairs have equal forces.

47
Q

When the cross sectional area A is larger, ∆l will be….

A

When the crosssectional area A is larger, ∆l will be smaller.

48
Q

What is the elastic modulus?

A

If the material is linear (limited to some maximum stress), then the loadextension, or stress-strain relationship may be measured and plotted as a straight line

49
Q

What is poisson’s ratio?

A

The diameter of the loaded bar will alter in proportion with the axial strain.
The transverse strain is opposite to the axial strain (a stretched bar will reduce its diameter).
The ratio of transverse to axial strain is called Poisson’s Ratio

50
Q

What happens to a material when it is stretched in one direction according to poisson’s ratio?

A

When a material is stretched in one direction, it
contracts in directions at right angles to the tension.
(if free to do so)

51
Q

What happens to a material when it is squashed in one direction according to poisson’s ratio?

A

When a material is squashed in one direction, it
expands in directions at right angles to the
compression. (if free to do so)

52
Q

What is a beam? (2)

A

A beam is a structure that supports transverse loads at locations which do not coincide with its supports.

Loads are therefore transferred along the length of the beam, by a combination of internal forces, to the support(s).

53
Q

What are the three externally applied forces internal forces replaced with?

A 
Normal (N), shear (V) forces and
couple moments (M).
54
Q

What happens to the forces and movement in the cut section?

A

Opposite faces of a ‘cut’ section will have equal but opposite sense forces and moments.

55
Q

What does the slope of the bending moment diagram equal to??

A

In words, the slope of the bending moment diagram equals the magnitude of the shear force at that location.

56
Q

What is the slope of the shear force diagram negative to?

A

The slope of the shear force diagram is the negative of the magnitude of the distributed load at that location.

57
Q

What is the area under the shear force diagram (in the absence of an externally applied couple)?

A

(In the absence of an externally applied couple) The area under the shear force diagram between two locations equals the change in bending moment magnitude.

58
Q

What is the area under the shear force diagram (In the absence of an externally applied force)?

A

(In the absence of an externally applied force) The area under the distributed load diagram between two locations equals the change in shear force magnitude.

59
Q

What happens at the location of an externally applied concentrated force?

A

At the location of an externally applied concentrated force, there is a step change in the magnitude of the shear force, equal in magnitude to the applied force. Since the slope of the bending moment diagram equals V, there is also a step change in the slope of the bending moment diagram at that location.

60
Q

What happens at the location of an externally applied couple?

A

At the location of an externally applied couple, there is a step change in the magnitude of the bending moment diagram at that location, equal in magnitude to the applied couple. A couple has no effect on the shear force diagram.

61
Q

What is the neutral plane/neutral axis? (3)

A

Between the upper and lower surfaces of a beam in pure bending there exists an unstrained surface called the neutral plane or neutral axis.

It coincides with the centroid of area of the cross-section.

The strain in the material in the axial direction is proportional to the distance, y, above or below the neutral plane.

62
Q

Where does the maximum axial stress occur at?

A

The maximum axial stress occurs at the fibre of the cross-section at greatest distance from the neutral surface, ymax.

63
Q

What is tension positive?

A

Force component N, acting normal to the beam’s cut

section tension positive

64
Q

What is shear force?

A

V, acting tangent to the cut section is the shear force

65
Q

What is sagging positive?

A

Couple moment M is referred as the bending moment sagging positive


66
Q

What is the effect of a concentrated force on the shear force and bending moment diagram? (2)

A

At location of F there is a step change in the internal shear force V equal to the magnitude of F.

At location of F there is a step change in the slope of the bending moment diagram.

67
Q

What is the effect of a concentrated couple moment on the shear force and bending moment diagram?

A

At location of M0 there is no effect on the shear force diagram.

At location of M0 there is a step change in the bending moment diagram equal in magnitude to M0.

68
Q

What is the second moment of area?

A

Second Moment of Area is an area property and is unrelated in any practical way with anything to do with mass and inertia.

69
Q

What is the centre of gravity?

A

Locates the resultant weight of a system of particles

70
Q

What is the centre of mass? (2)

A

When g is everywhere constant, the location of the
centre of gravity coincides with that of centre of mass

Particles have weight only when under the influence of
gravitational attraction, whereas centre of mass is
independent of gravity

71
Q

What is a composite area?

A

A “composite area” consists of a number of connected
“simpler” shaped areas, which may be, for example,
rectangular, triangular or semicircular.

72
Q

What is a second moment of area of the composite area?

A

Second moment of area of the composite area =
algebraic sum of the second moments of area of
all its constituent parts.

73
Q

What is the summation?

A 
Second moment of area
of the entire area about
the reference axis is
determined by summing
the contributions of its
constituent parts.
74
Q

Is the second moment of area always positive?

A

yes

75
Q

What is the magnitude of the resultant weight vector the total of?

A

The magnitude of the resultant weight vector is the total weight of the object.

76
Q

What is the parallel axis theorem?

A

The relationship between magnitude of the second moment of area for centroidal and non-centroidal parallel axes

Mechanic (3 decks)

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