Oxidizer Tank Strength Checks Presented here are some simple design checks that were performed on the oxidizer tank, including hoop and axial stress, snap ring failure, snap ring groove failure, and snap ring contac area failure on the bulkheads. Note that a more detailed FEA has been performed on the bulkheads and is a separate document.

Oxidizer Tank Hoop and Axial Stress Failure Analysis and Factor of Safety Analyzes the hoop stress at the thinest section of oxidizer tank, which will be where the bulkhead seals against the tank casing.

Material Yield Strength Sy  276MPa

Tank Working Pressure P  1000psi

Inner Tank Radius r  4.53in Tank Thickness t  .22in Hoop Stress P r  σh     t 

σh  141.969 MPa

σ1  σh

Axial Stress 2

σa 

P r

( r  t) 2  r2

σa  69.302 MPa

σ2  σa

Von Mises Stress σ3  0

1 2 2   

  σ  σ  2   σ  σ  2   σ  σ   1 2 2 3 1 3  σ'     2   σ'  122.961 MPa

Factor of Safety Nsf 

Sy σ'

Nsf  2.245

 122.961 MPa

ORIGIN  1

Snap Ring Groove Analysis on Oxidizer Tank (Failure Due to Over Compression of Snap Ring Seat)

Groove OD

Groove ID

Max Working Pressure

ODG  9.222in

IDG  9.06in

P  1000psi

Material Yield Strength Sy  276MPa Inner Tank Radius r  4.53in

Groove Seat Area

 OD  2  ID  2 G G 2 AG        π  2.326 in 2 2      P  r2  π σx.G    191.089 MPa A

Smalley WH-900

G

σx  σx.G

τxy  0MPa

σy  0MPa

τxz  0MPa

σz  0MPa

τyz  0MPa

 σx τxy τxz   191.089 0 0      s   τxy σy τyz    0 0 0   MPa    0 0 0   τxz τyz σz   σp  reverse ( sort ( eigenvals ( s) ) )

 191.089  σp   0   MPa  0      σ  σ  2   σ  σ  2   σ  σ    p1 p2  p2 p3  p1 p3 σ'G   2  NsfG 

Sy σ'G

 1.444

1 2 2   

   

 191.089 MPa

Direct Ring Failure on Oxidizer Tank

Max Ring Rated Load

Max Pressure in Chamber

Chamber ID

PMR  102130lbf

P  1000psi

ID  9in

Ring Load 2

4  ID  PR  P    π  6.362  10  lbf 2

Safety Factor Nsf 

PMR PR

Smalley WH-900  1.605

Snap Ring Groove Failure at Oxidizer Tank Ends (Failure Due to Shear between groove OD and chamber OD and Seat Compression)

Combustion Chamber OD

Snap Ring Groove Diameter

Oxidizer Chamber ID

OD  9.5in

DGroove  9.222in

ID  9in

Length from Groove to Chamber End

Max Pressure in Chamber

L  .325in

P  1000psi

Cross Sectional Area

Force on Cross Section

2  2 D OD  Groove   2  ACS  π     4.088 in   2  2    



2 ID   4    P  6.362  10  lbf 2    

F  π 

Shear Plane Area ASP  π DGroove L  6.075  10

3 2

m

Normal Stress

Shear Stress

F σn   107.302 MPa ACS σx  σn τxy  τ

τ 

σy  0MPa

τxz  0MPa

σz  0MPa

τyz  0MPa

F ASP

 46.584 MPa

 σx τxy τxz   107.302 46.584 0      s   τxy σy τyz    46.584 0 0   MPa    0 0 0   τxz τyz σz   σp  reverse ( sort ( eigenvals ( s) ) )

 124.704  σp   0   MPa  17.402      σ  σ  2   σ  σ  2   σ  σ    p1 p2  p2 p3  p1 p3 σ'    2  Nsf 

Sy σ'

σy  0  2.056

1 2 2   

   

 134.253 MPa

Bulkhead Snap Ring Area Failure

Oxidizer Chamber ID

Snap Ring ID

Max Pressure in Chamber

IDChamber  9.05in

IDRing  8.472in

P  1000psi

Force On Cross Section

Length Between Bulkhead Top and O-Ring Gland

2   ID Chamber   4 F  π     P  6.433  10  lbf 2    

L  .24in

Cross Sectional Area 2 2  ID  IDRing   Chamber  2 ACS  π       7.954 in 2 2     

Shear Plane Area 2

ASP  π IDRing L  6.388 in Normal Stress

Shear Stress

F σn   55.758 MPa ACS σx  σn

τ 

σy  0MPa

τxz  0MPa

σz  0MPa

τyz  0MPa

F  69.432 MPa ASP τxy  τ

 σx τxy τxz   55.758 69.432 0      s   τxy σy τyz    69.432 0 0   MPa    0 0 0   τxz τyz σz   σp  reverse ( sort ( eigenvals ( s) ) )

 102.699  σp   0   MPa  46.941      σ  σ  2   σ  σ  2   σ  σ    p1 p2  p2 p3  p1 p3 σ'   2 

1 2 2   

   

 132.557 MPa Nsf 

Sy σ'

 2.082

O-Ring Gland Design O-Ring Stretch less than 5% O-Ring Compression 10%-30% O-Ring Gland Fill 65%-85% O-Ring ID

Gland Diamter

Gland Width

ID  8.75in

DGland  8.75in

WGland  .21in

O-Ring Width

Housing Diameter

CS  .1875in

DHousing  9.07in

O-Ring Stretch

  DGland  ID    100  0 ID   O-Ring Compression

  DHousing  DGland    CS   2    100  14.667  CS   O-Ring Gland Fill 2   CS    π    2     100  82.178  DHousing  DGland      WGland 2  