Air Force Research Laboratory
Space Vehicles Directorate
UN-SPEC-12311
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DRAFT
STRESS ANALYSIS GUIDELINES
UNIVERSITY NANOSAT-4 PROGRAM
University Nanosat Program Office
3550 Aberdeen Ave. SE
Building 472
Kirtland AFB, NM 87117-5776
The publication of this material does not constitute approval by the government of the findings or
conclusion herein. Wide distribution or announcement of this material shall not be made without the
specific approval of the sponsoring government activity.
Distribution limited to US Government agencies and their contractors.
University Nanosat-4 Program
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SIGNATURE PAGE
Prepared by:
Jeff Ganley, University Nanosat Structural Engineer
Date
AFRL/VSSV
Approval:
Scott Franke, University Nanosat Program Manager
Date
AFRL/VSSV
Approval:
George Hunyadi, University Nanosat Systems Engineer
Date
Jackson & Tull Chartered Engineers, AFRL/VSSV
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REVISIONS
Revision
Description
—
Initial Release
A
Nanosat-4 Cycle Revision
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Date
Approval
3/9/2003
MEK
11/14/05
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JMG
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TABLE OF CONTENTS
1.
PURPOSE ............................................................................................................................................................1
2.
SYSTEM DESCRIPTION .................................................................................................................................1
3.
LOADS ASSESSMENT .....................................................................................................................................1
3.1
3.2
3.3
3.4
ENVIRONMENTAL LOAD CASES .................................................................................................... 1
TEST LOAD CASES ........................................................................................................................ 2
SUMMARY OF LOAD CASES .......................................................................................................... 2
FACTORS OF SAFETY ..................................................................................................................... 3
4.
INITIAL HAND CALCULATIONS .................................................................................................................5
5.
FINITE ELEMENT MODELING ....................................................................................................................5
6.
STIFFNESS ANALYSIS ....................................................................................................................................5
7.
ANALYSIS OF CRITICAL DETAILS ............................................................................................................5
7.1
7.2
7.3
7.4
7.5
7.6
8.
STRESS CALCULATIONS ................................................................................................................ 6
ALLOWABLES ................................................................................................................................ 6
STABILITY ANALYSIS .................................................................................................................... 7
JOINTS ANALYSIS .......................................................................................................................... 7
MARGINS OF SAFETY .................................................................................................................... 7
OPERATING MARGINS ................................................................................................................... 7
CREATE A MARGIN OF SAFETY SUMMARY...........................................................................................8
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LIST OF TABLES
Table 3-1:
Table 3-2:
Table 3-3:
Table 7-1:
Nanosat Structure Design Limit Load Factors ........................................................................... 1
Individual Load Cases ................................................................................................................ 3
Factors of Safety (valid for test-verified hardware and configurations only)............................. 4
Example Margin of Safety Summary ......................................................................................... 8
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Purpose
The purpose of this document is to establish guidelines for the preparation of stress analysis
reports in support of the University Nanosat Program. This document provides a general outline for
stress analysis reports (Sections 2-8), including guidelines/instructions on the contents of each
Section. This document should be used as a guide, as appropriate - University program specific
deviations based on unique requirements are expected. Further questions should be directed to the
University Nanosat Program Office.
2.
System Description
The system description should including the following information:
3.

Description of overall system, from a structural standpoint, including labeling of all
subsystems. Clear use of diagrams and unambiguous naming convention is critical.

Relevant geometry/dimensioning, including alternate geometries (e.g. deployed antennas).

Component and system level mass properties and CG locations (supporting analysis is
required as a separate deliverable).

Description of sign conventions and coordinate systems. Universities should use the
coordinate system origin as defined in Figure 6-1 of UN4-0001, “Nanosat-4 User’s Guide”.
Loads Assessment
Identify loads that are being used to calculate margins (i.e. summary of load cases). Reference UN4-0001,
“Nanosat-4 User’s Guide”, Section 6.3.
3.1
Environmental Load Cases
There are three types of environmental loads that must be considered in the structural analysis:

Limit: Table 6-3 from document UN4-0001, “Nanosat-4 User’s Guide”, (replicated as Table
3-1 below) provides generalized design limit load factors for NS-4. These loads take into
account the worst case launch load environment, which is a combination of steady state, low
frequency, transient loads and high frequency vibration loads. The load factors are in g's and
should be applied on each spacecraft major axis, independently. All accelerations should be
applied through the center of mass of the analyzed component using the NS -4 coordinate
system origin defined in Figure 6-1 of document UN4-0001, “Nanosat-4 User’s Guide”.
Table 3-1: Nanosat Structure Design Limit Load Factors
Load Factor (g)
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NX
NY
NZ
20.0
20.0
20.0
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
Pressure: For pressurized or vented containers, stresses resulting from internal/external
pressure loads must be superimposed on stresses resulting from limit and thermal loads.
According to NSTS 14046, in circumstances where pressure stresses have a relieving or
stabilizing effect on structural capability, the minimum guaranteed value of the relieving
pressure shall be used to determine the stress relief. To be conservative, it is recommended
that pressure stresses only be combined with mechanical and thermal stresses when additive.

Thermal: thermal stresses shall only be combined with mechanical and pressure stresses
when additive. Thermal stresses shall not be used for stress relief.
Test Load Cases
In addition to the environmental loads given in Section 3.1 above, the satellite system must also
be analyzed for the sine burst test loading given in Section 8.1.3 of document UN4-0001, “Nanosat4 User’s Guide”. The sine burst test (conducted at AFRL) will verify the structural integrity of the
integrated Nanosat-4 System (University nanosatellite, plus Lightband Nanosat-4 Separation System
(NSS), via a sine burst test at a level 1.2 times limit loads (x, y, and z axes). During this test, no
detrimental permanent deformation or ultimate failures shall occur. Note that because the sine burst
test may constitute a critical load case, test loads, in addition to the environmental loads described in Section
3.1, must be considered in the sizing and analysis of structural members.
3.3
Summary of Load Cases
The stress analysis should address Load Cases 1 - 6 as applicable below. Depending on the
specifics of each university satellite design, additional load cases may be required.
Load Case 1 – Limit Loading: Load Case 1 includes all permutations of positive and negative
20G loading, and ensures that maximum tensile and compressive stresses are accounted for in the
analysis.
Load Case 2 – Test Loading: Load Case 2 ensures that the applied test loads do not result in
permanent deformation or structural failure. This should not be the case if Load Case 1 is properly
designed for. However, it is prudent to complete a separate load case summary for the test loads, as
higher margins of safety are appropriate for the test loading (a known loading that the satellite will
experience).
Load Case 3 – Pressure Loading: For pressurized or sealed compartments, maximum design
pressures should be used to calculate stresses for superposition on other load cases. If pressure
loads result in stress relief, then minimum guaranteed pressure may be used to calculate relief
stresses per NSTS 14046 (not recommended). For vented compartments, transient pressure loads
shall be included if such loads are significant. Proper design of vents, however, should limit
pressure loading to less than 0.5 psi.
Load Case 4 – Thermal Loading: Thermal stresses shall be calculated based on the maximum
and minimum temperatures (plus margin) to which the payload is subjected. Maximum and
minimum temperatures values should be based on a nanosatellite thermal analysis and should be
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coordinated (i.e. verified) through AFRL.
Load Cases 1-4 are summarized in Table 3-2 below.
Table 3-2: Individual Load Cases
Load Case
Ref
1A
1B
1C
1D
1E
1F
2A
2B
2C
2D
2E
2F
3A
3B
4A
4B
Inertial Loads
X
Y
Z
+20.0G
-20.0G
+20.0G
-20.0G
+20.0G
-20.0G
+24.0G
-24.0G
+24.0G
-24.0G
+24.0G
-24.0G
-
Pressure
Maximum Design
Minimum Guaranteed
-
Thermal
Max Temp.
Min Temp.
Note
1
1
1
1
1
1
2
3
4
4
Notes for Table 3-2:
1. See Section 3.4 for applicable factors of safety for yield and ultimate
2.
Applicable in cases where the pressure related stresses add to overall stress state
3.
Can be used in cases where pressure related stresses result in overall stress relief
4.
Applicable in cases where thermal stresses add to the overall stress state.
Load Case 5 – Combined Loading: Combines inertial, pressure, and thermal loads as
appropriate to account for cases in which such loads result in additive (i.e. worst case) stresses.
3.4
Factors of Safety
Factors of safety to be used in structural design and analysis are: 2.0 for yield and 2.6 for
ultimate. The University is required to perform stress analysis in sufficient detail to sho w that
design Factors of Safety (FS) are met or exceeded and that a Margin of Safety (MS) of zero or
greater exists for both yield and ultimate stress conditions, i.e.,
MS 
AllowableS tress
 1  0 where FS = Factor of Safety
( FS )  ( ActualStress )
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(Eqn. 1)
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All stress analysis shall incorporate methods and assumptions consistent with standard
aerospace practices. Allowable mechanical properties of structural materials shall be obtained from
MIL-HDBK-5H, Metallic Materials and Elements for Aerospace Vehicle Structures. Buckling,
crippling, and shear failures shall be considered ultimate failures.
Factors of safety (FS) shall be applied to the load cases given in Table 3-2. A summary of
required factors is provided in Table 3-3 below.
Table 3-3: Factors of Safety (valid for test-verified hardware and configurations only)
Load Type
Inertial (analysis)
Inertial
(Sine Burst Test)
Pressure
Pressure
Pressure
Pressure
Thermal
Component Applicability
All
All
Pressure vessels
Pressure lines
Pressure fittings
Sealed containers
All
FS (yield)
K1, YIELD = 2.0
K1, YIELD = 1.67
FS (ult.)
K1, ULT = 2.6
K1, ULT = 2.17
Note
K2, YIELD = 2.0
K2, YIELD = 2.0
K2, YIELD = 2.0
K2, YIELD = 2.0
+10C (over max T)
-10C (below min T)
K2, ULT = 5.0
K2, ULT = 5.0
K2, ULT = 5.0
K2, ULT = 5.0
+10C (over max T)
-10C (below min T)
1
1
2
Notes for Table 3-3:
1. Definitions for pressurized versus sealed containers are according to NASA-STD-5003, Para. 3.0
2.
K3, YIELD and K3, ULT as determined by increase in thermal stresses at 10C above TMAX and 10C below TMIN.
Factors of safety shall be applied to individual stress components and combined according to NSTS
14046, Para. 5.1.1.1. This will result in a factored, combined stress that can be used in safety margin
calculations (see Equation 2).
KC S  K1SI  K 2SP  K3ST
(Eqn. 2)
Where,
 S = combined stress in a given direction

SI = stress component due to inertial loading

SP = stress component due to pressure loading

ST = stress component due to thermal loading

KC = combined FS

K1 = FS for SE

K2 = FS for SP

K3 = FS for ST
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Initial Hand Calculations
With the environmental loading and required factors of safety defined in Section 3, an initial
structural design should be developed utilizing hand calculations (and possibly rudimentary FEA), with
conservative design assumptions. While this step will likely not be included in the final stress analysis
report because of significant design changes through the design process, it is nonetheless an important and
required step in the design process. This analysis should be used as a baseline in the development of a
detailed finite element model in section 5.
5.
Finite Element Modeling
Per document UN4-0001, “Nanosat-4 User’s Guide”, Universities are required to provide a
Nanosatellite structural finite element analysis (FEA) as part of the flight competition.
For detailed finite element models (FEM) it may be possible to determine stresses directly from
the FEA. For finite element analysis, always include specific details of the model, including:


Loads inputs (location, type of load, load vector)
Element properties

Boundary conditions
In addition, verify the output using simple checks:
 Check that applied loads are equal to reaction loads

Check F.E. output with hand calculations
Use engineering judgment to focus on areas you believe to be critical and verify the FE results
with hand calculations where possible. To the maximum extent possible, finite element analysis
should be verified through independent checks – this should be an integral part of the process of
building the satellite finite element model.
6.
Stiffness Analysis
Per document UN4-0001, “Nanosat-4 User’s Guide”, the Nanosat shall have a fundamental
frequency above 100 Hz given a fixed-base condition at the SIP. The universities are responsible
for demonstrating by analysis and test that the Nanosat meets the stiff ness requirement. The finite
element model developed in Section 5 will be used to verify the above analysis requirement.
Further model verification is then accomplished through University stiffness testing (the testing
requirement). Acceptable tests for verifying natural frequencies include modal survey and sine
sweep vibration. Sine sweeps shall be conducted from 20 to 2000 Hz at 0.25g.
Following integration of the Nanosat with the Lightband, AFRL will conduct a system level sine
sweep test to determine the natural frequency of the integrated Nanosat -4 System. The integrated
sine sweep will be conducted from 20 to 2000 Hz.
7.
Analysis of Critical Details
The stress analyst should identify critical structural details. Some examples of where critical
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details may exist within a given structure are as follows:

All structural members that are part of a structural load path.

Critical fasteners and joints (including those loaded in tension and shear)

Structural or mechanical supports for heavier items

Pressurized components (along with potential interactions with other structural loads)

Components (typically interfaces) subject to thermal stresses
It may also be possible to use FEA results to identify highly stressed hardware. But you should
always corroborate FEA results with engineering judgment and hand calculations where possible.
7.1
Stress Calculations
Using the load cases identified in Section 3, determine the stresses to which all critical details
are subjected.
Hand Calculations
Often, the simplest and fastest method of analysis is hand analysis. In cases where the load path
is well-understood (i.e., single load path), hand analysis may be used to determine loads and
stresses. In cases where redundant load paths exist, overlapping assumptions may be used to
determine a reasonable estimate of internal loads and stresses. For example, if two [approximately
equal] load paths exist, then one might assume that 60% of the load is taken in eac h of the load
paths for 120% of load (note: a good FE analysis may obviate the need for overlapping
assumptions). Always include a free-body diagram showing applied loads and reaction loads. The
free-body diagram serves to document your load path assumptions.
In many cases, seemingly complicated structures can be simplified to a beam or plate for the
purpose of analysis. Engineering judgment would be required in establishing the end constraints for
beams, effective section, and type of loading. For hand calculations of such models, show the
appropriate formula used to determine stresses. Formulas for beams and plates with various end
constraints may be found in Young, Roark’s Formulas for Stress & Strain, or Bruhn, Analysis &
Design of Flight Vehicle Structures.
7.2
Allowables
Allowables for metals
Allowable mechanical properties of structural metals shall be obtained from MIL-HDBK-5H,
“Metallic Materials and Elements for Aerospace Vehicle Structures”. Allowables for metallic
materials are dependent on the type of material, temper, grade, and orientation. Be sure to include
the correct parameters in your determination of allowables. In addition, only the materials with
high resistance to stress corrosion cracking listed in the latest version of MSFC-STD-3029,
“Metallic Materials for Stress Corrosion Cracking Resistance in a Sodium Chloride Environments ”
shall be used.
Allowables for non-metallic materials used in structural applications
It is the responsibility of the university to provide strength data to support the analysis of nonmetallic components. Data may be obtained from material suppliers, independen t tests, or other
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references.

Regarding supplier-furnished strength data, it will be necessary to ensure that the material
provided is the material for which strength data is applicable. This is generally accomplished
with a certificate of compliance.

For test-derived allowables, adequate testing must be conducted to ensure validity of results.
In addition, test conditions must take into account actual environmental conditions expected during
flight. As an alternative, data may be provided that demonstrates the material’s behavior when subjected
to anticipated environmental conditions.

All allowables must take into account all appropriate “knockdown” factors for temperature,
pressure, radiation, etc.
7.3
Stability Analysis
Structural elements should be analyzed for compressive failure modes, such as column or plate
buckling. Susceptibility to this type of failure mode depends on the following:

Type of loading, including the eccentricity of the applied compressive force (i.e., distance
from the centroid of the section)


Material
Boundary conditions such as beam end fixity or plate edge fixity

Beam slenderness ratio, or thickness of plate
Some of the methods used for analyzing this type of failure mode may be found in Bruhn,
Analysis & Design of Flight Vehicle Structures. Margins of safety for this failure mode should be
included in the margin of safety summary.
7.4
Joints Analysis
Identify all critical fasteners, and calculate margins of safety for these fasteners based on the
applied load and the material capability of the fastener.
Hole bearing - in cases where fasteners are used in shear, it will be necessary to show that
bearing stresses caused by the fasteners against the hole do not exceed the capability of the joined
material.
7.5
Margins of Safety
For each critical detail, a margin of safety (MS) should be calculated for the critical load case
(i.e., the load case resulting in the highest combined stress). The margin of safet y is calculated
using Equation 3, which is obtained by combining equations 1&2:
MS 
Allowable Stress
1  0
KC S
(Eqn. 3)
Where K C S is the combined, factored stress as calculated in Equation 2.
7.6
Operating Margins
Mechanisms are required to maintain specified operating and holding torque/force margins (see
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Equations 4 and 5).
Operating Torque Margin 
Holding Torque Margin 
Available Driving Torque
 1  1.0
Resisting Torque
(Eqn. 4)
Available Holding Torque
 1  1.0
Torque applied by limit load
(Eqn. 5)
Note: For linear devices, “Force” replaces “Torque” in the above equations
Calculations of the required holding force/torque margins should be included in the analysis.
8.
Create a Margin of Safety Summary
Once the university has completed the stress analysis, the results should be summarized in a
margin of safety (MS) summary. This summary provides key information on each structural detail,
including the load case in question, failure mode, and margin of safety. When AFRL reviews the
stress analysis, they will review this table first. For the lowest margins, AFRL will review the
approach in detail to ensure that the analysis is acceptable. An example of a margin of safety
summary is provided in Table 7-1.
For each University satellite design, there will be numerous entries in this table (>25) - enough
to completely summarize key areas of concern. It is not acceptable for a margin of safety to be less
than zero. The margin of safety summary provides a means of verifying that the structural design is
sufficient to withstand the predicted launch and on-orbit environment.
Table 7-1: Example Margin of Safety Summary
Structural Detail
Fastener X1, Stack
Separation System
Upper plate
Fastener X4, battery
box to MSDS
...
...
...
Load Case
+20.0G x-direction
(Load Case 1A)
-24.0G z-direction
(2F)
-20.0G z-direction
(1F)
Failure Mode
Margin of Safety
Ref. Page
Fastener Yield,
tension
Yield in tension
1.5
X2
2.5
X3
Fastener Yield,
tension
6.2
X5
-END-
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