structural design practices

Structural Design PracticesENAE 483/788D - Principles of Space Systems Design

U N I V E R S I T Y O FMARYLAND

Structural Design and Analysis Example• What employers look for when hiring• Common design issues• Considerations when beginning the design• Material properties / applications• Example of “complete” spacecraft component

structural design and analysis

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What Employers Want

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• “Hands on structural/mechanical design, analysis and test.”• “Fabrication of hardware – even better.”• “All the theory makes more sense when you have practical application

to hardware.”• “Work in a team environment on a project and show an enjoyment for

the process.” • “The real world - at least in the projects [Orbital] works on - has a

lot of that, and it helps to have experienced that.”• “Has had some good FEA/FEM experience.”

– NX or Creo is what Orbital uses, SpaceX uses Unigraphics/NX• Understanding of analysis/FEM, and ability to identify sources of error.



Common Issues in Structural Design

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• Static analysis is straightforward; dynamics is tricky.– Frequency-dependent interactions between subsystems are

complex.– As much as possible, try to decouple, i.e. isolate, structures or

components from each other.

• Structural design is very dependent on the design requirements of other subsystems such as thermal, propulsion, communications, and power.

• Accordingly, aerospace vehicles inherently have very little structural margin.



Commonly designed for launch loads

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• Spacecraft protected from atmospheric heating and loads by fairing (acoustic)• Fairing jettisoned when atmospheric effects become negligible (shock)• Spacecraft attached to rocket by adapter, transfers loads between the two

(acceleration, random vibe)• Spacecraft usually

separated from rocket after completion of thrusting (acceleration, shock)

• Clamps/Spring bands used for attachment and separation (shock)

V.L. Pisacane, Fundamentals of Space Systems, 2nd ed., Oxford University Press, 2005



Acoustics/Launch Transients(@launch/landing)

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• Acoustic vibration loads will be greatest immediately before/after launch (or landing if using retrorockets), as the ground serves as a huge reflecting surface, directing all of the sound pressure energy produced by the rocket engines back up at the payload. The fairing enclosure can provide only modest acoustic isolation, and sound pressure levels inside can reach 145 dB (about the level of a jet engine w/ afterburner, well above the threshold for creating physical pain in humans.


𝐹𝐹𝑚𝑚𝑚𝑚𝑚𝑚,𝑙𝑙𝑚𝑚𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑡𝑡𝑡𝑡𝑚𝑚𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝑙𝑙𝑡𝑡 < 2(𝐹𝐹𝑡𝑡𝑙𝑡𝑡𝑙𝑙𝑡𝑡𝑡𝑡)

• Launch/landing transients occur as the engines are activated, going from 0 thrust loading to some nonzero value. This is analogous to a step input applied to the launch vehicle, and the relevant dynamic analysis applies.



Atmospheric flight, staging (mid launch/landing)

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• Max winds are usually the high altitude winds (> 100 mph), combined with launch accelerations/random vibration are often the critical loading case.

• Transonic buffeting occurs when shock waves are impacting the fairing/heat shield, and can reduce the clearance between internal components and the shielding structure.

𝑎𝑎 =𝑇𝑇�𝑊𝑊 𝑔𝑔

• Maximum sustained acceleration is achieved prior to stage separation

• Separation transient will add on to this




Late launch/landing events

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• Fairing separation / heat shield separation use pyro mechanisms and impart high frequency content, but are generally only a concern for electronics and components mounted in the immediate proximity

• Spin stabilization may use small solid rockets or gas thrusters to spin up to 200 rpm, yielding tangential and centripetal accelerations.

• Spacecraft separation again may produce high frequency shock, more of a concern for electronics.


𝑎𝑎𝑡𝑡 = 𝑟𝑟𝛼𝛼𝑎𝑎𝑙𝑙 = 𝑟𝑟𝜔𝜔2



S/C system limit loads for ELVs (in gs)

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Stress Analysis

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• Hooke’s Law : σ = Stress (P/A), ε = Strain (∆L/L), E = Elastic/Young’s Modulus

• Yield/ultimate strengths forcommon aerospace materials arecompiled in the aerospace industrystandard MMPDS, formerly theMIL-HDBK-5• Poisson’s Ratio, 0.1≤ ν ≤ 0.35

𝜎𝜎 = 𝐸𝐸𝐸𝐸

ν =𝐸𝐸𝑙𝑙𝑚𝑚𝑡𝑡𝑡𝑡𝑡𝑡𝑚𝑚𝑙𝑙𝐸𝐸𝑚𝑚𝑚𝑚𝑡𝑡𝑚𝑚𝑙𝑙




Normal Stress Conditions

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• Effective stiffness:

• Examples: Static weight (on pad), axial thrust load

𝑃𝑃 =𝐴𝐴𝐸𝐸𝐿𝐿∆𝐿𝐿 → 𝐾𝐾𝑡𝑡𝑒𝑒 =

𝐴𝐴𝐸𝐸𝐿𝐿




Bending Stress Conditions

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• Bending (transverse) stress is a maximum furthest from neutral axis:

• Worst-case example: axial + transverse

• Examples: Thrust vectoring, wind gusts, axial + transverse launch accelerations• See Roark and Young’s Formulas for Stress and Strain for I, A

𝜎𝜎 =𝑀𝑀𝑀𝑀𝐼𝐼

→ 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 =𝑀𝑀(ℎ2)𝐼𝐼

𝜎𝜎 = ±𝑃𝑃𝐴𝐴

±𝑀𝑀(ℎ2)𝐼𝐼




Shear Stress Conditions (Bending and Twisting)

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• Bending shear stress is a maximum at the neutral axis:

• α depends on shape of cross-section

• Examples: Accompanies bending, especially important for bonded materials (sandwich structures, lap joints)

• Twisting due to torque• Shear modulus, G, and twist angle, ϕ• Again, see Roark for J, 𝛼𝛼

𝜏𝜏 =𝑉𝑉𝑉𝑉(𝑀𝑀)𝐼𝐼𝐼𝐼

→ 𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 = 𝛼𝛼𝑉𝑉𝐴𝐴

= 𝛼𝛼𝜏𝜏𝑚𝑚𝑎𝑎𝑎𝑎


𝜏𝜏 =𝐺𝐺𝑀𝑀

𝐺𝐺 =𝐸𝐸

2(1 + ν)

ϕ =𝑇𝑇𝐿𝐿𝐽𝐽𝐺𝐺



Buckling in Compression (Linear Elastic Instability)

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• Buckling in long* beams depends on end boundary conditions:

• L = column length, ρ = ⁄𝐼𝐼 𝐴𝐴 “Radius of Gyration”, C depends on end B.C.s

• Applies to columns with:1. Slenderness ratio (L’/ρ) ≥ 110

2. Stress doesn’t exceed elastic limit of the material

3. A “stable” cross-section (closed section with relatively thick walls)

• Again, see Roark

𝜎𝜎𝑙𝑙𝑡𝑡 =𝐶𝐶𝜋𝜋2𝐸𝐸( �𝐿𝐿 𝜌𝜌)

→ 𝜎𝜎𝑙𝑙𝑡𝑡𝐴𝐴 = 𝑃𝑃𝑙𝑙𝑡𝑡




Knock Down Factors (Euler Theory is Overly Optimistic)

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International Space Station

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Close-up of Z1 Truss

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Structural Example

• Storage canister for ISS solar array deployment system

• 200 lb tip mass• Cantilever launch

configuration• Thin-wall aluminum shell

structure

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Loads Sources

• Launch– Accelerations– Pressurization– Acoustics– Random Vibration– Thermal

• Crash Landing• On-Orbit

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Structural Parameters

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Derived Geometric Features:

Material Inputs:

Applied Loads:

Assuming surface gravity :𝑔𝑔 = 32.2 𝑓𝑓𝑡𝑡

𝑡𝑡2= 385.4 𝑡𝑡𝑙𝑙

𝑡𝑡2

Cannister radius 𝑅𝑅 = 25 𝑖𝑖𝑖𝑖

Cannister length 𝐿𝐿 = 100 𝑖𝑖𝑖𝑖

Shell thickness 𝐼𝐼 = 0.10 𝑖𝑖𝑖𝑖

Geometric Inputs:

Aluminum modulus 𝐸𝐸 = 1 × 107𝑝𝑝𝑝𝑝𝑖𝑖

Aluminum mass density 𝜌𝜌 = 0.10 𝑙𝑙𝑙𝑙/𝑖𝑖𝑖𝑖3

Aluminum coefficient of thermal expansion 𝛼𝛼 = 13 × 10−6 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∙ °𝐹𝐹

Aluminum tensile yield strength 𝜎𝜎𝑇𝑇𝑀𝑀 = 37 × 103 𝑝𝑝𝑝𝑝𝑖𝑖

Aluminum tensile ultimate strength 𝜎𝜎𝑇𝑇𝑇𝑇 = 42 × 103 𝑝𝑝𝑝𝑝𝑖𝑖

Cannister cross sectional area

𝐴𝐴 = 2𝜋𝜋𝑅𝑅𝐼𝐼= 15.71 𝑖𝑖𝑖𝑖2

Cannister area moment of inertia

𝐼𝐼 =𝜋𝜋4𝑅𝑅0

4 − 𝑅𝑅𝑖𝑖4 ≈ 𝜋𝜋𝑅𝑅3𝐼𝐼= 4800 𝑖𝑖𝑖𝑖4

Concentrated tip load 𝑊𝑊𝐼𝐼𝑖𝑖𝑝𝑝 = 200 𝑙𝑙𝑙𝑙

Canister structural weight 𝑊𝑊𝑐𝑐𝑎𝑎𝑖𝑖𝑖𝑖𝑝𝑝𝐼𝐼𝑐𝑐𝑟𝑟 = 2𝜋𝜋𝜌𝜌𝐼𝐼𝑅𝑅𝑙𝑙 = 157 𝑙𝑙𝑙𝑙



Launch Accelerations±4.85 g

±5.8 g

±8.5 g

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NASA STD 5000 – General Structure𝐹𝐹𝐹𝐹𝐹𝐹 = 1.4

Launch Acceleration Stress :

𝜎𝜎𝐿𝐿𝐿𝐿 = 𝜎𝜎𝑏𝑏𝑡𝑡𝑙𝑙𝑏𝑏𝑡𝑡𝑙𝑙𝑎𝑎 + 𝜎𝜎𝑙𝑙𝑛𝑛𝑡𝑡𝑚𝑚𝑚𝑚𝑙𝑙 =𝑀𝑀𝑅𝑅𝐼𝐼

+𝑊𝑊𝑡𝑡𝑡𝑡𝑡𝑡

𝐴𝐴𝑔𝑔𝑚𝑚

Bending Moment : 𝑀𝑀 = 𝑔𝑔𝑡𝑡𝑡𝑡𝑚𝑚𝑙𝑙𝑡𝑡(𝑊𝑊𝑙𝑙𝑚𝑚𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡ℎ𝐶𝐶𝐶𝐶 + 𝑊𝑊𝑡𝑡𝑡𝑡𝑡𝑡ℎ𝑡𝑡𝑡𝑡𝑡𝑡)

𝑔𝑔𝑡𝑡𝑡𝑡𝑚𝑚𝑙𝑙𝑡𝑡 = 5.82 + 8.52 = 10.3 𝑔𝑔

𝑀𝑀 = 10.3 157 50 + (200)(100) = 286,900 𝑖𝑖𝑖𝑖 � 𝑙𝑙𝑙𝑙

𝜎𝜎𝐿𝐿𝐿𝐿 =(286900)(25)

4800+

20015.71

4.85 = 1494 + 61.75 = 1556 𝑝𝑝𝑝𝑝𝑖𝑖



Pressurization Loads

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NASA STD 5000 – Pressurized Structure𝐹𝐹𝐹𝐹𝐹𝐹 = 2.0

Hoop Stress : 𝜎𝜎𝐻𝐻𝑛𝑛𝑛𝑛𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑡𝑡

= 14.7 𝑡𝑡𝑡𝑡𝑡𝑡 25 𝑡𝑡𝑙𝑙0.1 𝑡𝑡𝑙𝑙

= 3675 𝑝𝑝𝑝𝑝𝑖𝑖

Longitudinal Stress : 𝜎𝜎𝐿𝐿𝑛𝑛𝑙𝑙𝑎𝑎 = 𝑃𝑃𝑃𝑃2𝑡𝑡

= 1838 𝑝𝑝𝑝𝑝𝑖𝑖



Launch Vehicle Vibration EnvironmentFrequency (Hz)

Power Spectral Density(g2/Hz)

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Random Vibration Loads

(repeat for each axis)

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Miles’ Equation

http://www.vibrationdata.com/tutorials_alt/RLF.pdf

FOS = 3.0 - 3 standard deviations is recommended for >99% confidence

Fundamental bending frequency for a cantilevered beam w/ tip mass (Roark’s Formulas for Stress and Strain:

𝑓𝑓1 =1.7322𝜋𝜋

𝐸𝐸𝐼𝐼𝑔𝑔𝑊𝑊𝑡𝑡𝑡𝑡𝑡𝑡𝑙𝑙3 + 0.236𝑊𝑊𝑙𝑙𝑚𝑚𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑙𝑙3

= 77 𝐻𝐻𝐻𝐻

𝑓𝑓𝑖𝑖 𝜉𝜉<150 Hz 0.045

150-300 Hz 0.020>300 Hz 0.005

𝑅𝑅𝐿𝐿𝐹𝐹𝑙𝑙 =𝜋𝜋𝑓𝑓𝑙𝑙𝑃𝑃𝐹𝐹𝑃𝑃4𝜉𝜉

𝑅𝑅𝐿𝐿𝐹𝐹𝑙𝑙 =𝜋𝜋(77)(0.1)

4(0.045)= 3.42 g

𝑀𝑀 = 𝑅𝑅𝐿𝐿𝐹𝐹𝑙𝑙 𝑊𝑊𝑙𝑙𝑚𝑚𝑙𝑙𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡ℎ𝐶𝐶𝐶𝐶 + 𝑊𝑊𝑡𝑡𝑡𝑡𝑡𝑡ℎ𝑡𝑡𝑡𝑡𝑡𝑡𝑀𝑀 = 3.42 157 50 + 200 100 = 95,247 𝑖𝑖𝑖𝑖 � 𝑙𝑙𝑙𝑙

𝜎𝜎𝑃𝑃𝑅𝑅 =𝑀𝑀𝑅𝑅𝐼𝐼

=95247 50

4800= 992 𝑝𝑝𝑝𝑝𝑖𝑖



Thermal Loads

Assume support structure shrinks only halfas much as canister

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𝐹𝐹𝐹𝐹𝐹𝐹 = 1.4 General Structure, Metal

𝜎𝜎𝑇𝑇𝑙𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑙𝑙 = 𝐸𝐸𝐸𝐸𝑡𝑡𝑙𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑙𝑙 = 𝐸𝐸𝛥𝛥𝐿𝐿𝐿𝐿

= 𝐸𝐸𝛼𝛼Δ𝑇𝑇

Assuming -100°𝐹𝐹 temperature change𝛥𝛥𝐿𝐿 = 𝛼𝛼Δ𝑇𝑇 = 13 × 10−6 −100 = 0.13 𝑖𝑖𝑖𝑖

𝜎𝜎𝑇𝑇𝑙𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑙𝑙 = 𝐸𝐸𝐸𝐸𝑡𝑡𝑙𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑙𝑙 = 𝐸𝐸𝛥𝛥𝐿𝐿𝐿𝐿

= 1070.5 0.13

100= 6500 𝑝𝑝𝑝𝑝𝑖𝑖



Launch Loads Summary

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Load Source Limit Stresses FOS Design Stresses

Launch Accelerations

1556 1.4 2178

Pressurization 3675 3.0 11025

Random Vibration 992 3.0 2976

Thermal 6500 1.4 9100

Total 25280

𝑀𝑀𝐹𝐹 =𝐴𝐴𝑙𝑙𝑙𝑙𝐴𝐴𝐴𝐴𝑎𝑎𝑙𝑙𝑙𝑙𝑐𝑐 𝐿𝐿𝐴𝐴𝑎𝑎𝐿𝐿𝑃𝑃𝑐𝑐𝑝𝑝𝑖𝑖𝑔𝑔𝑖𝑖 𝐿𝐿𝐴𝐴𝑎𝑎𝐿𝐿

− 1 =𝜎𝜎𝑇𝑇𝑙𝑙

𝜎𝜎𝐷𝐷𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑙𝑙− 1 =

3700025280

− 1 = 0.464

𝑀𝑀𝐹𝐹 = 46.4%

The structure is over-designed by 46%… it’s 46% heavier than necessary



Observations about Launch Loads• Individual loads could be applied to same position

on canister at same times - conservative approach is to use superposition to define worst case

• 46% margin indicates that canister is substantially overbuilt - if launch loads turn out to be critical load case, redesign to lighten structure and reduce mass.

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Load Path

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• The stiffer structural member carries the greater part of the loading1. Honeycomb penthouse deck

attached to outer structure via flat plate, supporting instrument electronics

2. Flat plat offers little resistance to bending

3. Thrust load path is predominantly through the center structure (vertical plate)

• Control load paths by controlling stiffness




Dynamic Interactions

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• Every structure has a fundamental resonant frequency

• Use this to control load paths by controlling stiffness

R. Stengel, Space System Design, Princeton University



Transmissibility

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R. Stengel, Space System Design, Princeton University

Transmissibility or “Q Factor” is the response to sinusoidal oscillation at different frequencies, \

Assuming component frequency 𝜔𝜔 = 𝜔𝜔𝑙𝑙, and structural damping 𝜁𝜁 = 0.05

𝑇𝑇 =𝑥𝑥𝑛𝑛𝑙𝑙𝑡𝑡𝑥𝑥𝑡𝑡𝑙𝑙

= 1 −𝜔𝜔𝜔𝜔𝑙𝑙

2

+ 2𝜁𝜁𝜔𝜔𝜔𝜔𝑙𝑙

2

→12𝜁𝜁

= 10

At twice the natural frequency, 𝜔𝜔𝜔𝜔𝑛𝑛

= 2 , T=0.33

Keeping the component frequency an octave ( 𝜔𝜔𝜔𝜔𝑛𝑛

= 2)above the mounting structure’s 𝜔𝜔𝑙𝑙 reduces transmissibility by 66%... Enough to assume input won’t be amplified

𝜔𝜔𝑙𝑙 =𝑘𝑘𝑚𝑚



The Octave Rule

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• “Rule” applied to ensure the interaction between spacecraft components and their mounting structure is minimized.

• General loads estimate applicable to components and secondary structures


𝜔𝜔𝑙𝑙,𝑙𝑙𝑛𝑛𝑚𝑚𝑡𝑡𝑛𝑛𝑙𝑙𝑡𝑡𝑙𝑙𝑡𝑡 ≥ 2𝜔𝜔𝑙𝑙,𝑡𝑡𝑙𝑙𝑡𝑡𝑡𝑡𝑛𝑛𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡𝑡𝑡𝑙𝑙𝑙𝑙𝑡𝑡𝑙𝑙𝑡𝑡𝑡𝑡



What changed between the Falcon 9 v1.0 and v1.1?

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The Falcon 9 v1.1 uses the vehicle’s skin to resolve the vertical thrust loads, avoiding the need for specialized thrust structures (like in the tic-tac-toe of v1.0).



S/C stiffness requirements for ELVs (minimum spacecraft fundamental frequency to avoid resonance w/ launch vehicle)

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https://spacex.com/sites/spacex/files/falcon_9_users_guide_rev_2.0.pdf



Aerospace Structural Materials

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Aerospace Structural Materials

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• Aluminum– High stiffness/density ratio, excellent workability, non-magnetic, moderate cost,

high corrosion-resistance• Al-Li alloys can reduce LV weight by nearly 30%• Al-Li sheet laminates with fiber/epoxy sandwiches for fatigue resistance

• Titanium– Non-magnetic, stronger than aluminum, difficult to machine, suitable for

cryogenic applications, not suitable for high-temperature applications

• Steel alloys– High strength (absolute magnitude), high temperature applications, magnetic

(can interact negatively with magnetosphere)



Common Composite Structural Materials

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Material Properties UsesS-Glass Moderate σ, Low $,

Fatigue InsensitiveSolid rocket engine

casing, Pressure vessels, thermal

decouplingAramid (Kevlar) High σ, Low $,

Impact resistant, RF transparent

SRE casing, Press.Vess.,

Shrouds/FairingsHigh Tensile Carbon Fiber

Reinforced Polymer

High σ, Low $ Interstages

High Modulus-CFRP

High E, reasonable $

Optimized structures, solar arrays, antenna

reflectorsUltra HM-CFRP High E, low Coef.

Therm. Exp., very high $ (10X HT)

Thermo-elasticallystable structures, telescopes, wave

guides



Common Composite Structural Materials

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ReinforcingMaterial

Yield Strengthksi (MPa)

Tensile Strengthksi (MPa)

Elastic Modulusksi (GPa)

Strain at Breakpercent

Steel 40-75(276-517) N/A 29,000

(200) N/A

Glass FRP N/A 70-230(480-1,600)

5,100-7,400(35-51) 1.2-3.1

Basalt FRP N/A 150-240(1,035-1,650)

6,500-8,500(45-59) 1.6-3.0

Aramid FRP N/A 250-368(1,720-2,540)

6,000-18,000(41-125) 1.9-4.4

Carbon FRP N/A 250-585(1,720-3,690)

15,900-84,000(120-580) 0.5-1.9



Structural Materials Selection

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Material Ultimate Strength(MPa)

Elastic Modulus(GPa)

Density(kg/m3)

Steel 4100 210 7700Aluminum 620 73 2700 Titanium 1900 115 4700

E-Glass Fiber 3400 72 2550S-Glass Fiber 4800 86 2500Carbon Fiber 1700 190 1410Boron Fiber 3400 400 2570

Graphite Fiber 1700 250 1410

When/why do you choose to use a certain material?



Structural Materials Selection

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Performance Index

Strength design𝜎𝜎𝑙𝑙𝑙𝑙𝑡𝑡/𝜌𝜌

Stiffness Design𝐸𝐸/𝜌𝜌

Buckling Design𝐸𝐸/𝜌𝜌3

Steel 530 5.2 0.46Aluminum 230 5.2 3.7Titanium 405 4.9 1.1

E-Glass Fiber 1300 5.5 4.3S-Glass Fiber 1920 5.9 5.5Carbon Fiber 1200 11.6 68Boron Fiber 1320 12.5 23

Graphite Fiber 1200 13.3 89



Creep in Composite Structures

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An important factor when choosing the type of reinforced composite for a structural application is understanding the limits of a fiber to resist long term loading.

Continuous and cyclic loading on a fiber reinforced polymer in excess of its ability to resist those loads may induce long-term deflection, fatigue failure, or creep-rupture in the structural component.

To eliminate the deflections caused by creep, the stresses in FRP reinforcement in structural members must be less than the creep-rupture stress limit.

GFRP BFRP AFRP CFRPCreep-RuptureStress Limit, Ff,s

0.20 0.20 0.30 0.55

Carbon FRPs have a much greater useable strength after the application of the reduction factor, equating to less material and less mass.

•American Concrete Institute (ACI) Committee 440, 440.6-08 "Specification for Carbon and Glass Fiber-Reinforced Polymer Bar Materials for Concrete Reinforcement," 2008•Prince Engineering, PLC, "Characteristics and Behaviors of Fiber Reinforced Polymers (FRPs) Used for Reinforcement and Strengthening of Structures," 2011


U N I V E R S I T Y O FMARYLANDR. Stengel, Space System Design, Princeton University

structural design practices

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