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111 > Bending > Flashcards

Bending Flashcards

1
Q

Define Beams

A

Members that have loads applied perpendicular to the longitudinal axis

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2
Q

What are Internal forces

A

reaction forces that oppose the motion of the beam as a result of a load

ie. if you stretch the beam, the internal force will provide unequal but opposite force

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3
Q

What is a sagging beam

A

Beam with positive bending moment

looks like a smile

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4
Q

What is a hogging beam

A

Beam with negative bending moment

looks like a frown

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5
Q

Define Positive shear force

A

Clockwise Shear Force

(Left side has a force Upwards, internal side has a force Downwards)

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6
Q

Define Negative shear force

A

clockwise Shear Force

(Right side has a force Upwards, Left side has a force Downwards)

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7
Q

Will the Following Beam produce a Positive Shear Force at Point A , or a negative Shear force?
Explain Why?

A

Positive Shear Force
Point Force is trying to push beam down
Hence a Shear force is going to be in a direction to oppose this motion.
hence positive shear force

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8
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
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9
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
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10
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
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11
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
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12
Q

Which of the Following Shear Force Diagrams is correct?

A

E
Beam is Hogging, internal forces want to pull the beam clockwise , hence positive shear force
Point Load , the shear force of every cross-section will equal the point load, not dependant on distance

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13
Q

Which of the Following Shear Force Diagrams is correct?

A

C
Beam is Hogging, internal forces want to pull the beam clockwise , hence positive shear force
Distributed load, the total shear force of the cross sections is directly proportional to the distance
Maximum Shear Force at support of beam , Q = W(L-x)

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14
Q

Which of the Following Bending Moment Diagrams is correct?

A

D
Beam is Hogging, Hence Negative Bending Moment
Point Load , Bending moment as you go towards the point load will decrease, as there is less distance between the cross-section and the point load.

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15
Q

Which of the Following Bending Moment Diagrams is correct?

A

A
Beam is Hogging, Hence Negative Bending Moment
Distributed load,Maximum Shear Force at support of beam , Q = W(L-x) , hence Maximum bending moment is at the same point

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16
Q

What is Bending moment?

A

How much an object bending / moving at that specific point.
Higher the magnitude, higher the chance of breaking there

17
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
18
Q

Draw the Bending Moment and Shear Force diagram for the Following Beam

A
19
Q

using superposition find the Shear Force Diagram

A
20
Q

using super position find the bending moment diagram

A
21
Q

What is the bending moment at a Pin/Roller Support

A

0 unless there is an externally applied moment at the support

Has to be 0 , as the support doesn’t move

22
Q

Explain the Concept of a Neutral Surface

A

When a Beam is Bent, some of the atoms are compressed and some are stretched

A Beam is composed of an infibate amount surfaces (cross sections)
Some of these Surfaces are Compressed and some are Stretched

Compressed surfaces have -ve strain , Tensile surfaces have +ve Strain

So observing these surfaces, as you go from negative strain to positive, there must be a surface that experiences 0 strain and zero stress. - called a neutral surface

23
Q

What is a Neutral Axis

A

The Intersection of the Neutral Surface and the cross-section of the beam

24
Q

What are the 4 Assumptions in calculating the Deformation of a Beam

A
  • Cross Section of a Straight Beam Remains plane when a beam deforms due to bending
    ( take two points on opposite sides of the beam, before bending they are reflections of one-another in the neutral axis , after bending this still must be the case)
  • The Neutral Surface and Neutral Axis is subjected to zero Normal Stress
  • Longitudinal Strain Varies lineraly from Zero at the Neutral Axis to the maximum at the outer fibres of the beam
  • Material is Homogenous and Elastic for the whole duration of bending
    Hence we assume
    Stress = Elastic Constant * Strain
25
Q

Derive how do you calculate the stress of at a point of a beam subject to bending deformation

A
26
Q

Derive the formula to calculate the internal force of a point of distance y from the neutral axis

A
27
Q

Derive the formula to calculate the internal moment of a point of distance y from the neutral axis

A
28
Q

Derive the formula to calculate the position of the neutral axis

A
29
Q

Derive how

A
30
Q

Calculate the Position of the Neutral Axis of the Following Shape.

A
31
Q

Calculate the Position of the Neutral Axis of the Following Shape.

A
32
Q

Using a rectangle derive the formula for the parallel axis theorem.

A
33
Q

Using the Parallel Axis Theorem work out the second moment of area of the following shape .

A
34
Q

What is the maximum stress acting on the beam made of the following cross section , if it is bent with a bending moment of 2000 kNM

A
35
Q

what does the second moment of area tell us about a shape

A

It’s a measure of a shape’s ability to resist bending or flexure when subjected to a load. The greater the second moment of area, the more resistance the shape has to bending.

36
Q

Using the Parallel Axis Theorem work out the second moment of area of the following shape .

A
37
Q

A Beam with the following cross section is subject to a bending moment of 12kNM
Calculate the direct stress along the top surface of the hollow area and the bottom surface along the hollow area.
The maximum Direct Stresses
And Plot a Direct STress Distribution

A
38
Q

the following I-Beam carries a bending moment of 2000 kNM calculate the maximum stress at the top and bottom of the Flange/ Web Joints

A

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