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Mechanics of Materials > Beams > Flashcards

Beams Flashcards

1
Q

What is shear?

A

The internal shear at a section is the sum of all shearing forces acting on an object up to that section.

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2
Q

Is shear and shear stress the same?

A

Shear is not the same as shear stress, since the area of the object is not considered.

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3
Q

What is a typical application of shear?

A

At a section on a horizontal beam defined as the sume of all vertical forces between the section and of the ends.

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4
Q

Does it matter what end is chosen when finding the shear?

A

No the direction in which the summation proceeds is not important.

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5
Q

Why doesn’t the direction matter when summing up shear?

A

The values of shear will differ only in sign for summation to the left and right ends.

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6
Q

Is there a advantage that one end would have to another when summing up shear?

A

Yes the direction that results in the fewest calculations should be selected to save time and will be less difficult to calculate.

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7
Q

What is the sign convention of shear in a beam?

A

Shear is positive when having a clockwise rotation and negative when having a counter clockwise rotation. This is with respect to the section.

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8
Q

What is the moment on a beam?

A

The sum of all the moments and couples located between the section and one of the ends.

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9
Q

What is the sign convention of moments on beams?

A

Moments in a beam are positive when the upper surface of the beam is in compression and the lower surface is in tension and negative when the lower surface is in compression and the upper surface is in tension.

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10
Q

What is the change in shear magnitude in a beam using an equation?

A

The change is magnitude of the shear between two points is equal to the integral of the load function.

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11
Q

What is the change in shear magnitude in a beam graphically?

A

The area under the load diagram between those points.

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12
Q

What is the change in moment magnitude in a beam using an equation?

A

The change is magnitude of the moment between two points is equal to the integral of the shear function.

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13
Q

What is the change in shear magnitude in a beam graphically?

A

The area under the shear diagram between those points.

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14
Q

What are shear and moment diagrams?

A

Graphs of shear and moment as functions of position along the beam.

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15
Q

What is the shear at any section equal to in a shear diagram using the loads?

A

The sum of the loads and reactions from the section to the left end.

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16
Q

What is the magnitude of the shear at any section equal to in a shear diagram using the moment?

A

The shear at any section is equal to the slope of the moment function at that section.

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17
Q

What is the shear sign convention in shear diagrams?

A

Loads and reactions acting upward are positive.

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18
Q

When is the shear diagram straight and sloping?

A

For uniformly distributed loads.

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19
Q

When is the shear diagram straight and horizontal?

A

Between concentrated loads.

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20
Q

Where is the shear diagram undefined?

A

At points of concentrated loads.

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21
Q

On what side of the beam is the moment diagram drawn from?

A

On the compression side of the beam.

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22
Q

What is the moment at any section equal to in a moment diagram using the moments?

A

The sum of the moments and couples from the section to the left end.

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23
Q

What is the change in magnitude of the moment at any section equal to in a moment diagram using an equation?

A

The integral of the shear diagram.

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24
Q

What is the change in magnitude of the moment at any section equal to in a moment diagram graphically?

A

The area under the shear diagram.

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25
Q

What does a concentrated moment produce in a moment diagram?

A

It will produce a jump or discontinuity in the moment diagram.

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26
Q

Where does the maximum or minimum moment occurs?

A

Where the shear is either zero or passes through zero.

27
Q

When is the moment diagram parabolic and is curved downward?

A

For downward uniformly distributed loads.

28
Q

How is normal stress distributed in a bending beam?

A

It is distributed triangularly.

29
Q

What is bending stress or flexural stress?

A

It is normal stress, and is used to indicate the source of the stress.

30
Q

What is the neutral axis?

A

The centroid of the cross section

31
Q

What is the extreme fiber?

A

The top or bottom surface of the beam.

32
Q

How does bending stress vary in a beam?

A

It varies with depth within the beam.

33
Q

When does the bending stress increase in a beam?

A

It increases linearly

34
Q

Where is the bending stress distribution zero for beams in stress?

A

It is zero at the neutral axis.

35
Q

Where is the maximum bending stress?

A

It is at the extreme fibers as the maximum bending stress by compression and on the opposite side the maximum bending stress by tension.

36
Q

Can Hooke’s Law be used to find the stresses in beams?

A

Yes.

37
Q

When is Hooke’s Law valid?

A

It is valid from any point within a beam and any distance from the neutral axis.

38
Q

When will a beam have an instantaneous radius of curvature and instantaneous strain in the x direction.?

A

A loaded beam that is oriented with its longitudinal axis parallel to the x direction

39
Q

What moment of inertia does the bending stress equation use?

A

The centroidal moment of inertia.

40
Q

In what direction is the moment of inertia the strongest for a given direction?

A

With its longitudinal direction parallel to the given direction.

41
Q

What are the shear stresses in a vertical section of a beam consist of?

A

They consist of both horizontal and transverse shear stresses.

42
Q

What is the shear stress dependent on within a beam?

A

It is dependent on the location within the depth of the beam.

43
Q

Where is the shear stress zero within a beam?

A

It is zero at the extreme fibers.

44
Q

Where is the shear stress at its maximum within a beam?

A

At its neutral axis.

45
Q

What is the moment of the area equal to for a rectangular beam?

A

It is equal to the product of the area and the distance from the centroidal axis to the centroid of the area.

46
Q

What is the shear flow?

A

The shear per unit length.

47
Q

What is the vertical shear a function of?

A

Location along the x axis of the beam.

48
Q

What is this shear resisted by?

A

The entire cross section,

49
Q

What are the deflection, slope, moment, shear, and load of a loaded beam related to?

A

The slope is the derivative of the deflection, the moment is the derivative of the slope, the shear a derivative of the moment and the load is the derivative of the shear.

50
Q

What can you find if you know the moment function for a section of a beam?

A

The deflection at any point on that section can be found.

51
Q

How are the constants of integration determined for deflection on a beam?

A

They are determined from the beam boundary conditions.

52
Q

Do all the loads contribute to deflection on a beam?

A

Yes when multiple loads act simultaneously on a beam.

53
Q

What is super position?

A

Permits the deflection at a point to be calculated as the sum of the deflections from each individual load acting singly.

54
Q

What can superposition also calculate with beams that have loads?

A

It can also calculate the shear and moment at a point and to draw the shear and moment diagrams.

55
Q

What are the conditions for superposition to be able to calculate the deflection, shear and moment at a point?

A

As long as the normal stress and strain are related by the modulus of elasticity.

56
Q

What is a composite structure?

A

One in which two or more materials are used.

57
Q

How is the load distributed in composite structure?

A

Each material carries part of the applied load.

58
Q

What is the method of consistent deformations or the transformation method?

A

Assume that the strains are the same in both materials at the interface between them.

59
Q

Are the stresses the same in the transformation method?

A

No the stresses are not the same since the modulus of elasticity is different for each material.

60
Q

What are the steps in the transformation method?

A

It starts by determining the modulus of elasticity for each of the materials in the composite beam and then calculating the modular ratio.

61
Q

What is the modular ratio equal to?

A

The ratio of the larger modulus of elasticity to the smaller modulus of elasticity.

62
Q

By what factor is the area of the stronger material increased by?

A

A factor of the modular ratio.

63
Q

What is the transformed area used for in the transformation method?

A

It is used to calculate the transformed composite area or transformed moment of inertia.

Mechanics of Materials (4 decks)

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