Statics sem 1 and 2??

Question 1

What is a force?

Answer 1

An interaction that when unbalanced will change the acceleration of an object

Question 2

What is a vector?

Answer 2

Something with magnitude and direction

Question 3

What equations do we write for force equilibrium in 2D

Answer 3

ΣFx = 0
ΣFy = 0

Question 4

How do you calculate moment?

Answer 4

Force x Perpendicular Distance

Question 5

How is friction calculated?

Answer 5

F ≤ μR
μ is coefficient of friction and R is reaction force

Question 6

What is the strategy for resolving forces in 2D?

Answer 6

• draw FBD of entire system and each individual body
• for each FBD: -> Resolve forces twice in perpendicular directions
  -> Take moments once

Question 7

For a fixed grounding point, how many degrees of freedom is there and how many reaction components?

Answer 7

1 degree of freedom
2 reaction components

Question 8

For a roller grounding point, how many degrees of freedom is there and how many reaction components?

Answer 8

2 degrees of freedom
- 1 reaction component

Question 9

Is tension positive or negative in pin jointed structures and which way do the arrows face?

Answer 9

Positive, arrows point towards each other

Question 10

What is the strategy of solving pin Jointed Structures?

Answer 10

1. Draw FBD of the entire frame
   -> Resolve twice and take moments to find Reaction Force
2. Draw the FBD of each node of interest
   -> Start with least number of unknowns and choose orientation carefully

Question 11

What are the 3 zero force members?

Answer 11

See image of whole deck.
If 0 going into a joint, 0 out
If a straight line with joint in middle, 0 on both sides
T beam: 0

Question 12

What is the strategy for method of sections questions?

Answer 12

• Solve for external reactions using conventional pin jointed structures approach
• Cut max of 3 beams (exceptions in K trusses0 and redraw FBD with beam forces
• Resolve and take moments to find these values

Question 13

Walk through the process of finding the statical determinacy of a structure?

Answer 13

n = nodes m = members, r = reaction forces
Count them each and then work out 2n and m+r
- 2n = m+r Statically determinate (can be solved)
- 2n < m+r Statically indeterminate
-2n > m+r Mechanism
BE CAREFULL< CAN BE A MIX

Question 14

State Hooke’s law.

Answer 14

F=kx
k = spring stiffness, x = extension

Question 15

How do you calculate stress?

Answer 15

σ = F/A
Stress = Force / Area. Often measured in MPa

Question 16

How do you calculate strain?

Answer 16

ε = e / L
strain = extension / length
No unit

Question 17

How do you calculate Youngs Modulus?

Answer 17

E =σ/ε = FL/eA

Question 18

What is proof stress?

Answer 18

A line made to estimate the yield point.
A line with gradient E drawn from 0.2% strain

Question 19

What actually is Poisson’s ratio a measure of?

Answer 19

The ratio of direct to perpendicular strain

Question 20

WRITE POISSON RATIO EQUATIONS ON FORMULA SHEET!!!!

Question 21

For materials in parallel (like a sandwich) what happens to the force and strain in each material?

Answer 21

Total force is sum of forces in each material
Constant strain throughout whole object

Question 22

For materials in series (like 2 rods) what happens to the force and strain in each material?

Answer 22

Constant force / stress throughout whole thing
Separate strains

Question 23

Describe variation in length as a function of distance

Answer 23

e(L) = 0->L∫ F / EA(x) .dx

Question 24

How is shear stress calculated?

Answer 24

τ = F/A (MPa)

Question 24

How do you calculate thermal strain?

Answer 24

ε = α ΔT where α is the coefficient of thermal expansion. This is added to otherwise normal strains

Question 25

How is shear stress calculated?

Answer 25

γ = Δl / L (imagine a parallelogram, L is height, delta l is the bit from bottom left to top left)

Question 26

How is the shear modulus calculated

Answer 26

G =τ / γ. Typically in GPa

Question 27

What is G equal to for isotropic materials

Answer 27

G = E / 2(1+ν)

Question 28

Definition of isotropic?

Answer 28

A property which is the same no matter the direction or orientation

Question 29

What arises when applying a shear stress

Answer 29

Complementary shear stresses, opposite and equal forces in the other direction

Question 30

write 2D STRESSES FORMULA ON SHEET

Question 31

How do you set up Mohr's Circle?

Answer 31

Y AXIS IS FLIPPED REMEMBER Drawn on x axis σy is on the left of the circle σx is the right of the circle So 1/2 (σy+σx) is centre point Draw a line of 2θ, starting at σx. Corresponding y value is shear stress(tau, remember axis flipped) x value is direct stress (sigma)

Question 32

What is the principle torsion equation, name all the parts

Answer 32

T / J = τ / r = Gθ/L T = torque J = second moment of area τ = shear stress r = radius G = shear modulus θ = angle of interest (rad) L = length of shaft

Question 33

WRITE 2ND MOM OF AREA OF SHAPES ON FORMULA SHEET

Question 34

What is 2nd mom of area of a circle?

Answer 34

π/2 r⁴ =J

Question 35

What is 2nd moment of area of a rectangle ( width b and height h)

Answer 35

J = 1/12 ( bh³ + hb³)

Question 36

What is 2nd moment of area of a triangle (width b and height h)

Answer 36

J = 1/36 ( bh³ + hb³)

Question 37

How are power and torque related?

Answer 37

Power = torque x angular frequency

Question 38

How do we solve Beam Questions asking for shear force and bending moment diagrams?

Answer 38

1. Draw FBD and determine support reactions using equilibrium 2. Cut the beam at the final cut and draw FBD of the cut section 3. Evaluate equations for v and M 4. All length terms in the bending moment equation and shear force must be written using Macaulay notation 5. Always indicate the powers even if 0 or 1

Question 39

What is the principle bending equation, state all the terms

Answer 39

M / I = E / R = σ / y M = bending moment I = 2nd Moment of Area E = Young's Modulus R = Radius of curvature σ = Bending Stress y = Distance from Neutral Axis

Question 40

How do you find the position of the Neutral Axis?

Answer 40

Sum of the products between the distance of the centroid of each portion of the cross section and their areas //// Total Area of Cross section s₁A₁ +s₂A₂ / (A₁+A₂)

Question 41

What is the parallel axis theorem?

Answer 41

Ixx = īxx + Ay²

Question 42

What is the complete method of finding the second moment of area?

Answer 42

1. Draw out a diagram and label dimensions 2. Determine location of area using y bar = s1A1+s2A2 / A1+A2 3. Calculate Ixx about centroid of each section 4. Apply parallel axis theorem to determine I of the whole shape

Question 43

What is the complete method of finding the maximum of a beam

Answer 43

1. Find support reactions from FBD ΣFx = 0 ΣFy =0 ΣM =0 2. Find equation of shear force using Macaulay notation 3. M = ∫v.dx Integrate the shear force to find bending moment. Apply boundary conditions to find C₁ 4. Determine equation for slope (θ) and deflection (υ) θ = 1/ EI ∫M.dx υ = ∫θ .dx 5. Determine C₂ and C₃ from the boundary conditions