Can be in a variety of forms -Time Domain or Frequency Domain (or Probability Domain) For example,

Force Displacement Acceleration Velocity Pressure Temperature

Loads can be applied to points , surfaces or bodies They can be constant, or time dependent

p

F

G

t

F

t

F

t

F

FEA Loads

In many industries, such as the aircraft industry, different levels of loading have to be accounted for. Limit Loads

Worst cases used for Limit loads for design. Greatest actual loads structure expected to be subjected to.

Ultimate Loads

Obtained by applying an factor to the Limit Loads. For example DEF STAN requirements quote an Factor of 1.5.

Proof Loads

Structure must withstand without detrimental distortion. Obtained by applying a Proof factor A typical factors for aircraft design would be 1.125 (depends on spec)

Loading Types in Design

End loads (compression or tension) Bending moments Shear forces Stresses Torques

Resultant Load Types in an FE Model or Test Component

Two sets of units are in general use: Imperial: Formerly the standard used in the UK , still used in the USA. SI: Based on the metric system, now in general use outside USA.

The main (SI) units needed to know are:- (Imperial equivalents) length metre (m) inch (in) 0.254 m

foot (ft) 0.3048 m mass kilogram (kg) slug (lb s2/ft) temperature kelvin (K) or Celsius (C) Fahrenheit (F) time seconds (s) Derived units are force newton (N) =kg m s-2 pound (lb) 4.448 N

kilonewton (kN) kilopound (kip) 4.448 kN stress pascal (Pa) = N/m2 psi = lb/ in2 6895 Pa moment/torque Nm lb in 0.1130 stress intensity (K) MPa√m ksi√in 1.099 MPa√m work, energy joule (J) = kg m2 s-2 =Nm in lb 0.1130 J power watt (W) = kg m2 s-3 =J s-1 frequency hertz (Hz) = cycle per second linear acc m/s2 rotational acc rad/s2

gravity (g) 9.81 m/s2 32.1740 ft/s2

Units

Common SI prefixes are

1012 tera 109 giga (G) 106 mega (M) 103 kilo (k)

10-3 milli (m) 10-6 micro (μ)

10-9 nano 10-12 pico

Important conversions Esteel = 30 x 106 lb wt/ in2 = 207 GN/m2

Typical yield stresses of common metallic materials 200 – 750 MN/m2

Units

Typicalload history showing random loading sequences in time and frequency domains

Loads

Typical PSD Loadings for a Missile Design

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1 10 100 1000 10000

Frequency (Hz)

PS

D (g

^2/H

z)

Vertical & Lateral Vertical non-Operational Lateral non-Operational

F16 POD Vibration Profile Duration Lateral non-operational 5 minutes Vertical non-operational 5 minutes Lateral performance profile 30 minutes Vertical performance profile 30 minutes

Typical PSD Loadings for a Component Attached to a Fighter Aircraft

t

Stress

Perturbation (exceedance)

Mean stress

A flight is divided into stages. Each one is characterized by a mean stress (steady cases) and several perturbations (ground

manoeuvres,rolling phases,dynamic landing, for example).

t

Stress

= (in exceedence diagram?)

Aircraft Flight Description

-3

-2

-1

0

1

2

3

4

5

6

7

8

10 100 1000 10000 100000 1000000 10000000

G le

vel

Exceedances per 1000hours

A Typical Aircraft ‘g’ Spectrum

Fatigue loading cycles on undercarriages and related structure must consider a number of effects (for example),

• The aircraft descent velocity • Spin up and spring back effects • Braking • Taxiing • Runway conditions • Engine run-up • Ground-Air Ground Cycle

*  Its character is the atmosphere itself and is independent of the aircraft.

*  It produces the most damaging fatigue loads on subsonic transport/civil aircraft.

* Turbulence loads are produced by the energy from the lateral component of the turbulence velocity (assumed to be simultaneous over the whole aircraft).

* ESDU 69023 provides methods of quantifying these effects.

Aircraft Loading: Landing & Ground Loads

Aircraft Loading: Atmospheric Turbulence

F18 Buffet Environment

Exceedance Data

10 102 103 104 105 1 2 3 4 5 6 7 8

0 -1 -2

G le

vel

Exceedances (Counts per 1000hrs)

Fatigue Data Processing

G le

vel

Exceedances (Counts per 1000hrs)

1 2 3 4 5 6 7 8

10 102 103 104 105

n0 n1 n2 n3

Fatigue Data Processing, cont.

1 2 3 4 5 6 7 8

0 -1 -2

10 102 103 104 105

G le

vel

Exceedances (Counts per 1000hrs)

7.5g load level paired with -1.0g

Load Level Cumulative Counts

Discrete Counts

8.0g n0n0

7.5g n1-n0n1

7.0g n2-n1n2

6.5g n3-n2n3

.

Fatigue Data Processing, cont.

GLevel

-3 0-2 592-1 11720 337352 217813 120964 138505 59946 34247 10438 17

OCCUR.

Load Level Cumulative Counts

Discrete Counts

8.0g n0n0

7.5g n1-n0n1

7.0g n2-n1n2

6.5g n3-n2n3

.

A fatigue spectrum has the following occurrences.

What are the exceedances?

(note previous explanation)

Worked Example: Occurrences to Exceedances

If the load levels are now at each ‘g’:

Load Level Cumulative Counts

Discrete Counts

8.0g 1717

7.0g 10431060

6.0g 34244484

5.0g 5994n3

.

Occur Exceed

Exceedances at 7.5g

Solution G

Level-2.5 0-1.5 592-0.5 17640.5 35499

1.5 582062.5 364243.5 243284.5 104785.5 44846.5 10607.5 17

Exceed

Note increment is mid way in interval

Worked Example: Occurrences to Exceedances, cont.

Consider the accumulation of occurrences as follows and plot the curve.

G CummLevel Occur

2 582062 364243 364243 243284 243284 104785 104785 44846 44846 10607 10607 178 17 1

2

3

4

5

6

7

8

1 10 100 1000 10000 100000 Exceedances per 1000hrs

Airc

raft

'g' l

evel

Cummulative Occurrences Correct Exceedance Data Wrong Exceedance Data

Cumulative occurrences Correct exceedence data Wrong exceedence data

Worked Example: Occurrences to Exceedances, cont.

2 no 25Kg masses

.

X

Y

Z

Y Z

X

A Typical Automotive Application – PASCAR Type Analysis (Modified to Induce Dynamic Behaviour)

Fixed

Load Case

Damage (per second)

Passes

Passes in measured history

Damage Increment

Steering Lock to Lock 1.49E-07

768

3

0.00

Figure of Eight

1.30E-06

256

3

0.00

Cobblestone Slalom 4.40E-03

768

10

0.34

Chatter Bumps 0.00E+00

512

3

0.00

Resonance Part One 8.00E-05

384

3

0.01

18" Chuckholes 7.00E-03

640

3

1.49

Railroad Crossing 6.22E-05

768

3

0.01

Road 11 to Road 12 Intersection 5.80E-05

448

3

0.01

Body Twist 2.60E-05

512

3

0.01

Accel over 5 Bumps

3.00E-04

512

3

0.05

30" Chuckholes 1.80E-03

512

3

0.31

Pt B, Road 11 to Postel Rd Intersection

4.10E-05

64

3

0.00

Postel Road Braking 0.7g 4.86E-02

64

10

0.31

Road 10, wot to 90 kph, Point B

9.23E-05

64

3

0.00

Kerb Island Road 6

0.90E-05

80

3

0.00

Resonance Part 2

3.00E-04

384

3

0.04

Jounce / Rebound Holes

5.30E-04

512

3

0.09

Body Twist Slalom

0.00E+00

896

3

0.00

PASCAR Type Analysis

Mode 1

Mode 5

Mode 3 Mode 2

Mode 4

11.2 Hz 17.6 Hz 8.8 Hz

26.9 Hz 121.4 Hz

PASCAR Type Analysis