with your host…

Dr. Hyland

426, Lecture 8 - Questions Addressed What phenomena drive structural design requirements?What are some simple types of structures and how do they respond

to forces?What geometric and material properties are most important to the performance of structures? What structural types are especially relevant to the design challenge?

Suggested reading:L&W, Chapter 11

Likely structural design requirements:

o Steady-state Thruster accelerations

o Launch loads

o Propulsion system engine vibrations

o Transient loads during pointing maneuvers, attitude control burns or docking events

o Pyrotechnic shock from separation events, deployments

o Thermal environments

Main challenges:

maintaining structural integrity during launch and boost burns

Pressure and centrifugal loads

The Simplest Structure of All:

The Ideal Axial Member or Strut

PP

LL

Area A

Resists only axial forces – either tension or compression

= Stress = P/A

= strain = L/L

Hook’s Law: = E

E = Modulus of elasticityMaterials are also characterized by:

Ftu = Allowable tensile ultimate stress

Fcy = Allowable compressive yield stress

= Coefficient of thermal expansion

Representative Stress-Strain Curves

Strain,

Str

ess,

0.002

A

BCA, CA

B

C

Ductile (aluminum alloy, Kevlar)

Perfectly brittle (glass)

Relatively brittle (cast iron, Graphite-Epoxy)

A = Proportional Limit

B = Yield Stress

C = Ultimate Stress

Numerous types of truss structures can be built from axial members alone:

Good design practice for precision space structures recommends the use of Statically Determinate designs.

For 3-D structures, no more than three, non-coplanar struts meet at a joint

For a 2-D structure, no more than two struts meet at a joint

Under these conditions, the forces in all members can be determined solely from static force equilibrium at each joint. Analysis is more accurate since the force distributions are independent of material properties.

Example: A cantilevered frame attached to an accelerating support

M

#1

#2

L

M

F=M

–F–F1

–F2

F1

F1

F2F2

x

x

y

Equilibrium along x: F1sin + F2 = 0

Equilibrium along y: – F1cos + M = 0

F1 = M/cos ,

F2 = –M tan

2 21 2

1 22 21 2

cos , tan

ratio of elastic modulus to

supported mass per str. vol. kk

L LL L

V V

EV

M AL

Simple model for sizing the structural framework for piggy-back vehicle

x

3 Estimate spacecraft mass density, . Total mass 2 L

Size the structure to withstand the takeoff burn event causing the largest acceleration

One basic requirement is that payload component

relative positions should not shift by

more than some max allowable. This translates into a maximum tolerable deflection

of the tip of the frame.

A second requirement is, of course, that the supporting frame should not break

or buckle

LC

arr

ier

Vehic

le

and p

rim

ary

paylo

ad

More complex structures: Beams

Beams resist both axial loads and lateral forces and torques

M

S

W(s)x

M(s) M(s+s)

s

S

Moment Equilibrium:

0

S x M x x M x

dM xS x

dx

2

2

Constitutive relation:

w

M x EIx

Beam x-section

S

2t

3I tb2b

More complex structures: Beams

m

E, L4I b

m

E, L4I b

22

2

Total mass,

Volume of beam

b

b effeff

bnat

L LbV

EV

VbL L

Lateral accelerations:

2

2b

bnat

L

VV

L

Axial accelerations:

Everything is scaled by L, b and the speed, Vb!

Internal Loads Constrain the Main Structural Form

• For economy in structural mass large shells holding gas at some pressure must act as membranes in pure tension.

• There is a direct relationship between the internal loading and the shape of the surface curve of such a membrane configuration.

• When the major internal loads are pressure and artificial gravity the possible membrane shapes must be doubly symmetric, closed shells of revolution

• Possibilities:• Sphere: rotate 1 about r or z• Cylinder: rotate 2 about z• “Pancake”: rotate 2 about r• Torus: Rotate 3 about r• Dumbell: Rotate 3 about z

A Cassini oval is the set of points in the plane such that the product of the distances to two fixed points is constant.

Rm

meridian

m

Rhh

Doubly-Curved Shells as Pressure vessels

2

hm

pR

t

2

2h h

hm

pR R

t R

2Internal pressure, N/ m

Shell thickness

Meridonial radius of curvature

Hoop radius of curvature

m

h

p

t

R

R

Toroidal Shell Under Internal Pressure

2

Stress resultants:

2 cos,

2 1 cos0

2Internal pressure, N/ m

s

s

pr rN

rN

prN

p

x

y

z

R (= 1/ )

s r

Property

Material

Tensile Modulus

(109 N/m2)

Breaking Tenacity

(109 N/m2)

Density

(103 kg/m3)

Modulus speed

(km/s)

Tenacious speed

(km/s)

Kevlar 29 (w/resin) 83 3.6 1.44 7.59 1.58

Kevlar 49 (w/resin) 124 3.6 1.44 9.28 1.58

S-Glass 85.5 4.59 2.49 5.86 1.37

E-Glass 72.4 3.45 2.55 5.33 1.16

Steel Wire 200 1.97 7.75 5.08 0.504

Polyester 13.8 1.16 1.38 3.16 0.915

HS Polyethylene 117 2.59 0.97 11.0 1.63

High Tenacity Carbon 221 3.10 1.8 11.1 1.31

Carbon nanotubes 13,000 130 1.3 100 10

Material Properties

o L&W list properties only for metals – Here’s some non-metalic materials

o Most precision space structures are made of carbon or graphite composites with titanium joints and end fittings

o We should be looking for materials with high strength-to-weight

Hope you enjoyed the show!

And may your shields never fail….