Elastic Deformation

Question 1

Definition of a force.

Answer 1

Influence in a body that causes it to accelerate.

Question 2

What are the conditions for a body to be at equilibrium?

Answer 2

The vector sum of the forces acting on it must be zero.
The body must have a constant momentum.
The sum of the components of the forces must also be zero in any given direction.

Question 3

What is the extra condition of static equilibrium?

Answer 3

There must be no torque caused by the lines of actions of the forces.

Question 4

Definition of a torque/moment.

Answer 4

The product of a force and its perpendicular distance to the point of turning.

Question 5

What does a free body diagram show?

Answer 5

The isolated body and all the forces acting upon it.

Question 6

What to look out for on free body diagrams?

Answer 6

The lines of actions of each force, if it’s not through the CoM then a torque could be caused.

Question 7

Conditions for equilibrium.

Answer 7

Vector sum of forces is zero

Vector sum of moments at any point is zero.

Question 8

Sketch shear force and bending moment diagram for 3 point bend applied force P.

Answer 8

Check

Question 9

Sketch shear force and bending moment diagram for 4 point bend for two applied forces P.

Answer 9

Check

Question 10

For stress, what are the letters of the double suffix.

Answer 10

First letter is direction of applied force

Second letter in the direction of the normal to the surface.

Question 11

Derive the equations for normal and shear stresses for a rotated set of axes within a square of material.

Answer 11

Check derivation

Question 12

Derive the Mohr’s circle stress equations.

Answer 12

Check derivation.

Question 13

What are the axes in Mohr’s circle?

Answer 13

Normal on horizontal

Shear on vertical

Question 14

How are rotations by an angle θ in real space represented on Mohr’s circle?

Answer 14

Real θ equates to 2θ on the circle.

Question 15

What is the principle shear stress on Mohr’s circle?

Answer 15

The maximum value of normal stress.

Question 16

What do the letters on a displacement gradient tensor show, double suffix?

Answer 16

The first is the direction of displacement

The second is the direction of the original length.

Question 17

Define engineering strains.

Answer 17

Check

Question 18

Define tensor strains.

Answer 18

Check

Question 19

When are engineering strains used?

Answer 19

For relationships with elastic constants such as YM and SM.

Question 20

When are tensor shear strains used?

Answer 20

Useful when considering transformations of reference axes.

Mohr’s circle

Question 21

What directions are positive and negative on Mohr’s circle?

Answer 21

If a clockwise rotation is caused it is positive, if an anticlockwise rotation is caused then negative.

Question 22

Equations for Poisson’s ratio

Answer 22

Check

Question 23

State the equations that form the basis of Hooke’s law

Answer 23

Check Leonard-Jones and VdW

Question 24

Hooke’s Law equations incorperating Poisson’s ratio for isotropic materials.

Answer 24

Check

Question 25

State both shear modulus equations

Answer 25

Check

Question 26

Derive the link between shear modulus and YM

Answer 26

Check derivation

Question 27

Equations for spring and dashpot.

Answer 27

Check

Question 28

Derive Maxwell model of viscoelasticity

Answer 28

Check derivation

Question 29

Derive the Voigt or Kelvin model of viscelasticity

Answer 29

Check derivation

Question 30

Derive the standard linear model for viscoelasticity (Zener model)

Answer 30

Check derivation

Question 31

Derive the stresses in a thin spherical pressure vessel.

Answer 31

Check

Question 32

Derive the stresses in a thin cylindrical pressure vessel

Answer 32

Check

Question 33

Equations for torsion of a thin walled cylinder

Answer 33

Check

Question 34

Derive the equation for torsion of a solid rod.

Answer 34

Check

Question 35

Derive the equations for stress and strain in a beam under bending

Answer 35

Check

Question 36

Equation for total bending moment in bent beam.

Answer 36

Check

Question 37

Derive the equation relating normal stress to moment of inertia and YM

Answer 37

Check