Structural Methods and Materials - UMD

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

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

Structural Methods and Materials• Excel Solver Routine to Minimize Margins• Load Paths• Octave Rule • Aerospace Structural Materials

– Strength Design– Stiffness Design– Buckling Design

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International Space Station

2



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

4



Loads Sources

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

• Crash Landing• On-Orbit

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Structural Parameters

6

Derived Geometric Features:

Material Inputs:

Applied Loads:

Assuming surface gravity :𝑔𝑔 = 32.2 𝑓𝑓𝑓𝑓

𝑠𝑠2= 385.4 𝑖𝑖𝑖𝑖

𝑠𝑠2

Cannister radius 𝑅𝑅 = 25 𝑖𝑖𝑖𝑖

Cannister length 𝐿𝐿 = 100 𝑖𝑖𝑖𝑖

Shell thickness 𝑡𝑡 = 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 × 10−6𝑖𝑖𝑖𝑖

𝑖𝑖𝑖𝑖 � °𝐹𝐹

Aluminum tensile yield strength 𝜎𝜎𝑇𝑇𝑇𝑇 = 37 × 103 𝑝𝑝𝑝𝑝𝑖𝑖

Aluminum tensile ultimate strength 𝜎𝜎𝑇𝑇𝑇𝑇 = 42 × 103 𝑝𝑝𝑝𝑝𝑖𝑖

Cannister cross sectional area

𝐴𝐴 = 2𝜋𝜋𝑅𝑅𝑡𝑡= 15.71 𝑖𝑖𝑖𝑖2

Cannister area moment of inertia

𝐼𝐼 =𝜋𝜋4𝑅𝑅04 − 𝑅𝑅𝑖𝑖4 ≈ 𝜋𝜋𝑅𝑅3𝑡𝑡

= 4909 𝑖𝑖𝑖𝑖4

Concentrated tip load 𝑊𝑊𝑓𝑓𝑖𝑖𝑡𝑡 = 200 𝑙𝑙𝑙𝑙

Canister structural weight 𝑊𝑊𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑠𝑠𝑓𝑓𝑐𝑐𝑐𝑐 = 2𝜋𝜋𝜌𝜌𝑡𝑡𝑅𝑅𝑙𝑙 = 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 = 𝜎𝜎𝑏𝑏𝑐𝑐𝑖𝑖𝑏𝑏𝑖𝑖𝑖𝑖𝑏𝑏 + 𝜎𝜎𝑖𝑖𝑛𝑛𝑐𝑐𝑛𝑛𝑐𝑐𝑛𝑛 =𝑀𝑀𝑅𝑅𝐼𝐼

+𝑊𝑊𝑓𝑓𝑖𝑖𝑡𝑡

𝐴𝐴𝑔𝑔𝑥𝑥

Bending Moment : 𝑀𝑀 = 𝑔𝑔𝑓𝑓𝑐𝑐𝑐𝑐𝑖𝑖𝑠𝑠(𝑊𝑊𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑠𝑠𝑓𝑓𝑐𝑐𝑐𝑐ℎ𝐶𝐶𝐶𝐶 + 𝑊𝑊𝑓𝑓𝑖𝑖𝑡𝑡ℎ𝑓𝑓𝑖𝑖𝑡𝑡)

𝑔𝑔𝑓𝑓𝑐𝑐𝑐𝑐𝑖𝑖𝑠𝑠 = 5.82 + 8.52 = 10.3 𝑔𝑔

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

𝜎𝜎𝐿𝐿𝐿𝐿 =(286900)(25)

4909+

20015.71

4.85 = 1459 + 61.75 = 1521 𝑝𝑝𝑝𝑝𝑖𝑖



Pressurization Loads

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NASA STD 5000 – Pressurized Structure𝐹𝐹𝐹𝐹𝐹𝐹 = 2.0

Hoop Stress : 𝜎𝜎𝐻𝐻𝑛𝑛𝑛𝑛𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑓𝑓

= 14.7 𝑡𝑡𝑠𝑠𝑖𝑖 25 𝑖𝑖𝑖𝑖0.1 𝑖𝑖𝑖𝑖

= 3675 𝑝𝑝𝑝𝑝𝑖𝑖

Longitudinal Stress : 𝜎𝜎𝐿𝐿𝑛𝑛𝑖𝑖𝑏𝑏 = 𝑃𝑃𝑃𝑃2𝑓𝑓

= 1838 𝑝𝑝𝑝𝑝𝑖𝑖



Launch Vehicle Vibration EnvironmentFrequency (Hz)

Power Spectral Density(g2/Hz)

Design for a known case or for worst case

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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

𝐸𝐸𝐼𝐼𝑔𝑔𝑊𝑊𝑓𝑓𝑖𝑖𝑡𝑡𝑙𝑙3 + 0.236𝑊𝑊𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑠𝑠𝑓𝑓𝑐𝑐𝑐𝑐𝑙𝑙3

= 78 𝐻𝐻𝐻𝐻

𝑓𝑓𝑖𝑖 𝜉𝜉<150 Hz 0.045

150-300 Hz 0.020>300 Hz 0.005

𝑅𝑅𝐿𝐿𝐹𝐹𝑖𝑖 =𝜋𝜋𝑓𝑓𝑖𝑖𝑃𝑃𝐹𝐹𝑃𝑃4𝜉𝜉

𝑅𝑅𝐿𝐿𝐹𝐹𝑖𝑖 =𝜋𝜋(77)(0.1)

4(0.045)= 11.67 g

𝑀𝑀 = 𝑅𝑅𝐿𝐿𝐹𝐹𝑖𝑖 𝑊𝑊𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑠𝑠𝑓𝑓𝑐𝑐𝑐𝑐ℎ𝐶𝐶𝐶𝐶 + 𝑊𝑊𝑓𝑓𝑖𝑖𝑡𝑡ℎ𝑓𝑓𝑖𝑖𝑡𝑡𝑀𝑀 = (11.67) 157 50 + 200 100 = 149,950 𝑖𝑖𝑖𝑖 � 𝑙𝑙𝑙𝑙

𝜎𝜎𝑃𝑃𝑅𝑅 =𝑀𝑀𝑅𝑅𝐼𝐼

=(149950) 50

4909= 763.7 𝑝𝑝𝑝𝑝𝑖𝑖



Thermal Loads

Assume support structure shrinks only halfas much as canister

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𝐹𝐹𝐹𝐹𝐹𝐹 = 1.4 General Structure, Metal

𝜎𝜎𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑛𝑛𝑐𝑐𝑛𝑛 = 𝐸𝐸𝜀𝜀𝑓𝑓𝑇𝑐𝑐𝑐𝑐𝑛𝑛𝑐𝑐𝑛𝑛 = 𝐸𝐸𝛥𝛥𝐿𝐿𝐿𝐿

= 𝐸𝐸𝛼𝛼Δ𝑇𝑇

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

𝜎𝜎𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑛𝑛𝑐𝑐𝑛𝑛 = 𝐸𝐸𝜀𝜀𝑓𝑓𝑇𝑐𝑐𝑐𝑐𝑛𝑛𝑐𝑐𝑛𝑛 = 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 2043

Pressurization 3675 2.0 7350

Random Vibration 763 3.0 2291

Thermal 6500 1.4 9100

Total 24546

𝑀𝑀𝐹𝐹 =𝐴𝐴𝑙𝑙𝑙𝑙𝐴𝐴𝐴𝐴𝐴𝐴𝑙𝑙𝑙𝑙𝐴𝐴 𝐿𝐿𝐴𝐴𝐴𝐴𝐿𝐿𝑃𝑃𝐴𝐴𝑝𝑝𝑖𝑖𝑔𝑔𝑖𝑖 𝐿𝐿𝐴𝐴𝐴𝐴𝐿𝐿

− 1 =𝜎𝜎𝑇𝑇𝑇𝑇

𝜎𝜎𝐷𝐷𝑐𝑐𝑠𝑠𝑖𝑖𝑏𝑏𝑖𝑖− 1 =

3700024546

− 1 = 0.507

𝑀𝑀𝐹𝐹 = 50.7%

The structure is over-designed by 51%… it’s 51% 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

• 51% margin indicates that canister is substantially overbuilt - if launch loads turn out to be critical load case, redesign to lighten structure and reduce mass.

• Did we consider all the cases? What about buckling?

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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

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



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, 𝑇𝑇 = 𝑓𝑓 𝜔𝜔

𝜔𝜔𝑛𝑛

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

𝑇𝑇 =𝑥𝑥𝑛𝑛𝑇𝑇𝑓𝑓𝑥𝑥𝑖𝑖𝑖𝑖

= 1 −𝜔𝜔𝜔𝜔𝑖𝑖

2

+ 2𝜁𝜁𝜔𝜔𝜔𝜔𝑖𝑖

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 𝜔𝜔𝑖𝑖 reduces transmissibility by 66%... Enough to assume input won’t be amplified

𝜔𝜔𝑖𝑖 =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


𝜔𝜔𝑐𝑐𝑛𝑛𝑛𝑛𝑡𝑡𝑛𝑛𝑖𝑖𝑐𝑐𝑖𝑖𝑓𝑓 ≥ 2𝜔𝜔𝑖𝑖,𝑠𝑠𝑇𝑇𝑡𝑡𝑡𝑡𝑛𝑛𝑐𝑐𝑓𝑓 𝑠𝑠𝑓𝑓𝑐𝑐𝑇𝑇𝑐𝑐𝑓𝑓𝑇𝑇𝑐𝑐𝑐𝑐



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 (7075-T6, 2024)– 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 (Ti-6Al-4V)– 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 design𝜎𝜎𝑇𝑇𝑛𝑛𝑓𝑓/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

𝑃𝑃𝑐𝑐𝑐𝑐 ∝𝑀𝑀3

𝑙𝑙4𝐿𝐿3𝐸𝐸𝜌𝜌3

𝜔𝜔 ∝ℎ𝐿𝐿2

𝐸𝐸𝜌𝜌

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𝑃𝑃𝑛𝑛𝑐𝑐𝑥𝑥 =𝑀𝑀𝐿𝐿𝜎𝜎𝑇𝑇𝑛𝑛𝑓𝑓𝜌𝜌



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.

GlassFRP BasaltFRP AramidFRP CarbonFRPCreep-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 Methods and Materials - UMD

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