## Abstract

The need to store large quantities of hydrogen in large diameter steel vessels under high pressures results in shell thicknesses that are too large to produce by most steel mills and not practical to fabricate. Accordingly, a research program was undertaken by Oak Ridge National Laboratory to develop a new concept of combining steel with concrete to construct such vessels economically and practically. The concept is to fabricate vessels where the steel shell thickness is approximately one half that required to resist the hoop forces due to internal pressure. As such, the steel shell is designed to carry the full amount of the longitudinal forces in the vessel but only one half of the hoop loads due to internal pressure. The other half of the hoop loads is carried by a prestressed and reinforced concrete shell. In large diameter vessels, the cost of the shell can further be reduced by using layered steel shell construction rather than solid-wall construction. Such shell construction has also the added advantage of easily venting the hydrogen that permeates through the steel shell directly to the atmosphere through vent holes. This mechanism prevents the hydrogen from damaging the steel shell. The theoretical formulation of the steel concrete shell design is presented in this paper. In addition, details of a full-scale mock up vessel designed, fabricated, and tested to prove the proposed methodology are given.

## 1 Introduction

The proliferation of hydrogen fueled automobiles and other transportation systems in the U.S., and especially in California, as well as worldwide necessitates the need to store large quantities of hydrogen at fueling stations and other central fueling terminals, Fig. 1. One economical way for storing large quantities of hydrogen under high pressure is in a large diameter pressure vessel consisting of a steel inner shell that carries 50% of the applied pressure coupled with a concrete outer shell that caries the remaining 50%. The advantage of such a system is the elimination of requiring very thick cylindrical shells that are hard, if not impossible, to produce at the steel mill and are very expensive to fabricate. Additional cost reduction can be achieved by building the inner steel shell out of layered rather than monoblock construction.

Fig. 1
Fig. 1
Close modal

The U.S. Department of Energy (DOE) in conjunction with Oak Ridge National Laboratory (ORNL) undertook a research program with the assistance of Global Engineering & Technology with the following objectives:

1. Obtain a conceptional design for dimensional proportions of steel–concrete vessels at high pressures with optimum cost.

2. Establish a design procedure for steel–concrete composite vessels.

3. Establish design details for venting the hydrogen to the atmosphere in order to prevent damaging the structural steel and concrete components.

4. Design and fabricate a mock up steel–concrete composite vessel with dimensions close to the smaller of the intended field-constructed vessels.

5. Hydrotest the mock-up vessel with water and then cycle the vessel with hydrogen to prove the integrity of the vessel during simulated operation.

## 2 Conceptional Design

A design pressure of 6250 psi (43.1 MPa) was selected to match existing technology for hydrogen dispensing equipment in the field. Various L/D ratios of the shell were investigated for cost comparison. Some of the parameters considered were

1. cost of monoblock versus layered steel shell materials;

2. cost of monoblock manufacturing versus layered shell manufacturing including welding;

3. cost of fabrication of concrete shell including reinforcement and prestressing;

4. ease of access to inside of vessel for installation of instruments;

5. cost of types of supports and lifting configurations;

6. cost of transportations of raw materials and completed vessel;

7. ease of installation of completed vessel in the field;

8. ease of monitoring hydrotesting and hydrogen cycling;

9. design details for venting the hydrogen to the atmosphere without damaging the carbon steel and concrete pressure components.

The cost analysis established the following parameters:

1. An L/D ratio of the shell between 2 and 4 results in an optimum cost.

2. A minimum diameter of 40 in. (1000 mm) is required for manufacturing purposes as well as instrumentation placement on the inside surface of the vessel.

3. A stainless steel liner is needed as a hydrogen barrier.

4. Vessel supports and lifting lugs are to be attached to the steel part of the vessel.

5. The inside steel shell and heads are to be constructed to the rules of the ASME Section VIII, Division 2, pressure vessel code “rules for construction of pressure vessels-alternative rules” as much as practicable. The outside prestressed and reinforced concrete shell is to be constructed to the rules of ACI 318 “building code requirements for structural concrete” and ACI 372R “design and construction of circular wire-and strand-wrapped prestressed concrete structures” as much as practicable.

## 3 Design of Steel–Concrete Composite Vessel

The design of the steel–concrete vessel consists of the following steps:

1. establish the thickness of the inner steel vessel;

2. adjust the thickness of the outer concrete shell as well as the prestress level at the outside of the concrete shell to maintain the stress levels in the steel and concrete within their allowable stress levels at the design and hydrotest conditions;

3. check discontinuity stresses between the heads and the composite steel–concrete shell;

4. perform a finite element analysis for the total composite construction to check various stress levels;

5. check other miscellaneous items such as thermal, lifting, and transportation stresses.

### 3.1 Inner Steel Vessel

#### 3.1.1 Thickness of Heads and Shell.

The thickness of the steel heads due to internal pressure is determined from VIII-2 as
$t=Ri (exp P/2S−1)$
(1)
The thickness of the steel shell needed to transfer the axial load in the vessel due to internal pressure is obtained from equating the end force due to pressure to the circumferential cross section of the shell multiplied by the allowable stress. The resultant equation is
$t=Ri[(1+P/S)0.5–1]$
(2)

The steel shell is constructed as a layered shell in accordance with paragraph 4.13 of VIII-2 “design rules for layered vessels.” The thickness of the shell obtained from Eq. (2) is about one-half that required to resist the hoop stress due to internal pressure. The needed additional thickness is furnished by the concrete shell.

#### 3.1.2 Stress in Layered Steel Shell Due to Fabrication.

Welding of the longitudinal seams of any individual layer in a layered shell causes shrinkage of the welds. This shrinkage results in locked-in residual tensile stress in the individual layer being welded and compressive stress in the layers underneath it. These secondary stresses are normally ignored in commercially fabricated layered vessels since they do not contribute to the stress calculations for determining the required thickness of the layered shell. However, they are important in the steel–concrete composite vessel since they must be combined with the stresses obtained from the prestressing wires on the outside surface of the concrete as well as the stress due to internal pressure in order to obtain the full stress pattern needed for design.

The compressive stress in the inner layer due to weld shrinkage of the longitudinal welds of the outer layers is obtained from strain gage rosettes attached to the inside surface of the inner layer. The pertinent equations for calculating the stress from measured strain are
$σθ=[Es/(1−μs2)](εθ+μsεL)$
(3)
$σL=[Es/(1−μs2)](εL+μsεθ)$
(4)

The stress distribution in the steel layered shell due to weld shrinkage of the longitudinal welds of the layers can be formulated from deflection compatibility equations and the stress results obtained from Eqs. (3) and (4) for the inner layer. The stress pattern through the wall of a layered cylinder due to shrink fitting the layers (autofrettaging) is based on the details shown in Fig. 2 as well as the derivations and experimental verifications given by Jawad [1].

Fig. 2
Fig. 2
Close modal

Define to as the thickness of the outer layer being shrunk and ti as the thickness of all layers underneath it. Also, define Ro and Rf as the outside and inside radii of the layer being shrunk and Rf and Ri as the outside and inside radii of all layers underneath it as shown in Fig. 2. Define w as the width of the weld seam in the outer layer and n as the number of weld seams in the outer layer. Define pf as the interface pressure between the outer layer and all layers underneath it.

The deflection of the inside surface of a cylinder due to internal and external pressure is given by [2]
$δi=[Ri Pi(Ro2+Ri2)+μsRi Pi (Ro2−Ri2)−2PoRiRo2] /Es(Ro2−Ri2)$
(5)
Similarly, the deflection of the outside surface of a cylinder due to internal and external pressure is given by [2]
$δo=[2Pi Ri2Ro−RoPo(Ro2+Ri2)+μsRo Po (Ro2−Ri2)] /Es(Ro2−Ri2)$
(6)
The shrinkage due to welding of seam w in the outer layer is given by
$δw=(K)(w)$
(7)

The value of the weld shrink factor K in Eq. (7) depends on many variables such as weld width and thickness, weld process, and number of weld passes. The value of K is obtained by trial and error as explained below.

The inward radial deflection of the outer layer due to weld shrinkage of seam “w” is expressed as
$ΔW= (δW n)/(2π)$
(8)
The compatibility equation between layer to and layer ti is given by
$Δw−Δo=Δi$
(9)
From Eq. (5), the deflection of the inside surface of outer layer due to to interface pressure Pf is
$Δi=(Pf Rf) [Ro2 (1+μs)+Rf2 (1−μs)]/Es(Ro2−Rf2)$
(10)
Similarly, from Eq. (6), the deflection of the outside surface of inner layer ti due to interface pressure pf is
$Δo=(Pf Rf)[Rf2 (−1+μs)–Ri2 (1+μs)]/Es(Rf2−Ri2)$
(11)
Substituting Eqs. (7), (8), (10), and (11) into Eq. (9) and solving for the unknown interface pressure pf gives
$Pf=K3/[Rf(K1−K2)]$
(12)
where
$K1=Ro2(1+μs)+Rf2(1−μs)/[Ro2−Rf2]$
$K2=Rf2(−1+μs)−Ri2(1+μs)/[Rf2−Ri2]$
$K3=(Es)(K)(w)(n)/(2π)$

The above derivations are based on the following assumptions:

1. The width w of the weld seams is the same in all layers.

2. Weld parameters such as voltage, amperes, and speed are constant from weld to weld such that the shrinkage constant K does not vary from weld to weld or layer to layer.

3. The number of welds n in each layer is constant throughout the layers.

4. The modulus of elasticity, Es, is the same for all layers.

The actual interface pressure pf in Eq. (12) is based on a selected value of constant K. Once the pressure pf is known, then the circumferential stresses in the outer and inner cylinders are obtained from the following equations:

Due to external pressure Po
$σθ=[−PoRo2−Po (Ri2Ro2/R2)] /(Ro2−Ri2)$
(13)
Due to internal pressure Pi
$σθ=[PiRi2+Pi (Ri2Ro2/R2)] /(Ro2−Ri2)$
(14)

The value of K in Eq. (12) is determined as follows:

1. The values of circumferential compressive stress in the inner layer due to wrapping each of the outer layers as obtained from the strain gage readings and Eqs. (3) and (4) are plotted as shown in Fig. 3.
Fig. 3

Stress from strain gage measurements versus stress from assumed value of K

Fig. 3

Stress from strain gage measurements versus stress from assumed value of K

Close modal
2. A value of K between 0.05 and 0.50 is assumed.

3. Equations (12) through (14) are solved for each welded outer layer and the resultant curve based on an assumed value of K is plotted as shown in Fig. 3.

4. If the curve from the equations does not match the actual data, then a new value of K is assumed and the procedure is continued until a satisfactory curve is obtained.

5. Once the value of K is established, then the stress distribution in the various layers due to the wrapping process is determined from Eqs. (12) through (14). Figure 4 shows a typical stress distribution in the layered shell due to wrapping stress.
Fig. 4

Wrapping stress distribution through thickness

Fig. 4

Wrapping stress distribution through thickness

Close modal

The wrapping stress in the various layers is added to the stress in these layers due to prestressing the concrete outer shell and stress due to internal pressure to obtain the overall stress pattern in the shell.

### 3.2 Outside Concrete Shell

#### 3.2.1 Preliminary Design.

The thickness of the outer concrete shell and the amount of external pressure exerted by the prestress wire are obtained by trial and error. Three design criteria must be satisfied in choosing the concrete thickness and amount of external pressure. The first is the compressive stress in the concrete due to prestressing and the compressive stress in the steel shell due to prestressing and wrapping must not exceed the allowable compressive stress of the concrete and steel, respectively. The second criterion is the tensile stress in the steel shell due to internal pressure must not exceed the allowable stress and the stress in the concrete must remain in compression. And the third criterion is the stress in the steel shell due to hydrostatic testing must remain within the allowable stress and any tension in the concrete shell needs to be resisted by reinforcing bars.

In order to determine the stresses in the steel and concrete, compatibility equations need to be formulated. This is accomplished by defining the radial deflection, δ, of any thick shell due to internal and external pressure as
$δ=[R2 (Pi Ri2−Po Ro2) (1−2μ)+(Pi−Po) (Ri2 Ro2) (1+μ)]/[E R (Ro2−Ri2)]$
(15)
When an internal pressure, Pi, is applied at the inside surface of a steel–concrete composite shell, an interface pressure, Pf, is developed at the interface between the outside surface of the steel cylinder and the inside surface of the concrete cylinder. The magnitude of this interface pressure is determined by the following compatibility equation:
$δsopi−δsopf=δcipf−δcipo$
(16)

where δsopi is the deflection of steel cylinder at outside surface due to internal pressure, δsopf is the deflection of steel cylinder at outside surface due to interface pressure, δcipf is the deflection of concrete cylinder at inside surface due to interface pressure, δcipo = deflection of concrete cylinder at inside surface due to outside pressure.

Substituting Eq. (15) into Eq. (16), rearranging terms, and using the terminology of Fig. 5 results in
$Pf=(Pi K5+Po K6) /(K2+K3+K4)$
(17)
Fig. 5

Steel–concrete composite shell

Fig. 5

Steel–concrete composite shell

Close modal
where
$K1=[Es (R22−R12)]/[Ec (R32−R22)]$
$K2=K1 [R22 (1−2μc)+R32 (1+μc)]$
$K3=R22 (1−2μc)$
$K4=R12 (1+μs)$
$K5=R12 (2−μs)$
$K6=K1 R32 (2−μc)$
Once the value of Pf is obtained from Eq. (17), then the circumferential stress in the steel cylinder is obtained from Lame's equation as
$σθs=[Pi R12−Pf R22+(Pi−Pf) (R12 R22/R2)]/(R22−R12)$
(18)
While the circumferential stress in the concrete cylinder is given by
$σθc=[Pf R22−Po R32+(Pf−Po) (R22 R32/R2)] /(R32−R22)$
(19)

The above equations are used repeatedly as the thickness of the concrete and the external pressure are adjusted to meet the design conditions. When the thickness of the concrete and the external pressure are found satisfactory, then the number of prestress layers is calculated as shown next.

#### 3.2.2 Required Number of Layers of Prestress Wire.

The external pressure Po calculated above is provided by the prestress wires. The wires are placed spirally with no space between them. For ease of calculations, an effective thickness is determined by smearing the wire area over 1 in. of shell length to come up with an equivalent thickness per inch of length

Number of wires per inch = 1.0/d
$tw=(πd2/4)(1/d)=πd/4$
(20)
The external pressure on the shell provided by a layer of wires is
$Po=Swtw/Ro$
(21)

where Ro =outside radius of the concrete shell for the first layer of wires and Ro = outside radius of the concrete shell plus tw for the second layer of wires, etc.

The equations for calculating the stress in the concrete and steel inner shell due to placing the first layer of prestress wires are given below. When the second layer of prestress wire is placed, a second set of calculations is performed. However, the stress in the steel and concrete shells imposed by the first set of wires is now reduced due to the added second layer, which reduces the tensile stress in the first layer. This reduction has to be accounted for as the process proceeds from one prestress layer to the other.

The pertinent equations needed for the analysis are based on Eqs. (15), (18), and (19) and the details are shown in Fig. 6. The derivation of the equations is shown below.

Fig. 6
Fig. 6
Close modal
In Fig. 6, the outer steel layer shown represents the prestressing wires that are already in place and po is the pressure on them from a new additional wire. The two unknowns in the figure are interface pressures p1 and p2. These are obtained from the deflection, δ, compatibility equations
$δ of the outer surface of the inner steel shell=δ of the inner surface of the concrete shell$
(22)
Substituting Eq. (15) into Eq. (22), rearranging terms, and using the terminology of Fig. 6 results in
$P1(C1+C2)−C3P2=C4$
(23)
Similarly
$δ of the outer surface of the concrete shell=δ of the inner surface of the outer steel shell$
(24)
Substituting Eqs. (15) into Eq. (24), rearranging terms, and using the terminology of Fig. 6 gives
$C5P1– P2(C6+C7)=C8$
(25)
Solving Eqs. (23) and (25) for P1 and P2 results in
$P1=C11/C12 and P2=C9/C10$
(26)
where
$C1=(Ec/Es)(R22−R12)(R1)[(R12+Ri2)−μs(R12−Ri2)]$
$C2=(R12−Ri2)(R1)[(R22+R12)+μc(R22−R12)]$
$C3=2(R12−Ri2)R1R22$
$C4=2(Ec/Es)(R22−R12)piRi2R1$
$C5=2(Ro2−R22)R12R2$
$C6=(Ro2−R22)(R2)[(R22+R12)−μc(R22−R12)]$
$C7=(Ec/Es)(R22−R12)(R2)[(Ro2+R22)+μs(Ro2−R22)]$
$C8=−2(Ec/Es)(R22−R12)poR2Ro2$
$C9=C8 (C1+C2)−C4 C5$
$C10=C3 C5−(C1+C2) (C6+C7)$
$C11=C4+(C3 C9/C10)$
$C12=C1+C2$
Equations (26), (18), and (19) are used to obtain the stress in the inner steel shell, the concrete shell, and the prestress wires.

### 3.3 Discontinuity Stress Between Head and Steel–Concrete Shell.

The discontinuity forces are shown in Fig. 7. Total unknown forces are H1, H2, H3, M1, M2, and Pf. The six equations (two equilibrium and four compatibility) required to solve these six unknown forces are
$H1−H2−H3=0$
(27)
$M1−M2=0$
(28)
$δs=δh$
(29)
$δs=δc$
(30)
$θs=θh$
(31)
$θs=θc$
(32)
Fig. 7
Fig. 7
Close modal
$δh=δhPi−δhH1+δhM1$
(33)
$θh=θhPi+θhH1−θhM1$
(34)

where

$=Pi Rh2 (1−μh)/(2 Eh th)$
$=H1 Rh (2λ)/(Eh th)$
$=2 M1 λ2/(Eh th)$
θhPi = rotation of head due to internal pressure Pi
$=0$
θhH1 = rotation of head due to shear force H1
$=2 H1 λ2/(Eh th)$
θhM1 = rotation of head due to bending moment M1
$=4 M1 λ3/(Eh Rh th)$

and where, $λ=[3(1−μh2)(Rh/th)2]0.25$

Steel shell equations
$δs=δsPi−δsPf+δsH2+δsM2$
(35)
$θs=θsPi+θsPf+θsH2−θsM2$
(36)
where
δsPi = radial deflection of steel shell due to internal pressure Pi
$=Pi Rs2 [1−(μs/2)]/(Es ts)$
δsPf = radial deflection of steel shell due to interface pressure Pf
$=Pf Rs2/(Es ts)$
δsH2 = radial deflection of steel shell due to shear force H2
$=H2/(2 βs3 Ds)$
δsM2 = radial deflection of steel shell due to bending moment M2
$=M2/ (2 βs2 Ds)$
θsPi = rotation of steel shell due to internal pressure Pi
$=0$
θsPf = rotation of steel shell due to external pressure Pf
$=0$
θsH2 = rotation of steel shell due to shear force H2
$=H2/(2 βs2 Ds)$
θsM2 = rotation of steel shell due to bending moment M2
$=M2/(βs2 Ds)$
and where
$βs=[3(1−μs2)/(Rs ts)2]0.25 and Ds=Es ts3/[12(1−μs2)]$
Concrete shell equations
$δc=δcPf−δcPo+δcH3$
(37)
$θc=θcPf+θcPo+θcH3$
(38)

where

δcPf = radial deflection of concrete shell due to interface pressure Pf
$=Pf Rc2/(Ec tc)$
δcPo = radial deflection of concrete shell due to prestress pressure Po
$=Po Rc2/(Ec tc)$
δcH3 = radial deflection of concrete shell due to shear force H3
$=H3/(2 βc3 Dc)$
θcPf = rotation of concrete shell due to interface pressure Pf
$=0$
θcPo = rotation of concrete shell due to prestress pressure Po
$=0$
θcH3 = rotation of concrete shell due to shear force H3
$=H3/(2 βc2 Dc)$
and where
$βc=[3(1−μc2)/(Rc tc)2]0.25 and Dc=Ec tc3/[12(1−μc2)]$
Substituting Eqs. (33) through (38) into Eqs. (27) through (32) and rearranging terms results in the following six simultaneous equations, written in matrix form, and can be solved for the unknowns H1, H2, H3, M1, M2, and Pf
$[K][F]=[C]$
(39)
where
$[K]=1−1−10000001−10C1C20−C3C4−C50C2−C70C4−C8−C3C40C10C1100C4−C120C110$
$F=H1H2H3M1M2Pf$
$C=000C6C90$
and
$C1=2 Rh λ/(Eh th)$
$C2=1/(2 βs3Ds)$
$C3=2 λ2/(Eh th)$
$C4=1/(2 βs2Ds)$
$C5=Rs2/(Es ts)$
$C6=Pi [Rh2(1−μh)/(2 Eh th)−Rs2(1−μs/2)/(Es ts)]$
$C7=1/(2 βc3Dc)$
$C8=Rs2/(Es ts)+Rc2/(Ec tc)$
$C9=−Pi [Rs2(1−μs/2)/(Es ts)]−Po Rc2/(Ec tc)]$
$C10=4 λ3/(Eh Rh th)$
$C11=1/(βs Ds)$
$C12=1/(2 βc2Dc)$

Once the unknown forces are calculated from Eq. (39), the stresses are then determined from the following equations:

Longitudinal stress
$SL=Pi Rh/2th+6 M1/th2$
(40)
Circumferential stress
$SC=δh Eh/Rh+(μh)(6 M1/th2)$
(41)
Layered steel shell
Longitudinal stress
$SL=Pi Rs/2ts+6 M2/ts2$
(42)
Circumferential stress
$SC=δs Es/Rs+(μs)(6 M2/ts2)$
(43)

Concrete shell

Longitudinal stress
$SL=0$
(44)
Circumferential stress
$SC=δc Ec/Rc$
(45)
where
$δh=(1/Eh th)[(0.5) (Pi Rh2)(1−μh)−2H1 Rh λ+2M1 λ2]$
$δs=(Pi Rs2)(1−μs/2)/(Es ts)−(Pf Rs2)/(Es ts)+H2/(2βs3 Ds)+M2/(2βs2Ds)$
$δc=(PfRc2)/(Ectc)−(PoRc2)/(Ectc)+H3/(2βc3Dc)$

### 3.4 Finite Element Analysis.

A finite element analysis of the total vessel is necessary in order to ascertain the stress levels because various loading conditions at various locations are within the allowable stress.

## 4 Venting System in the Steel Vessel

Hydrogen permeation in carbon steel is a major concern at high pressures. It can cause accelerated crack growth and possible embrittlement. Accordingly, stainless steel liners are used as a barrier. An experiment was conducted at ORNL to measure the effect of stainless steel on permeation [3,4]. Figure 8 shows a four-plate setup immersed in a hydrogen bath. Figure 9 shows the permeation rate of hydrogen in stainless steel versus carbon steel. It shows a permeation rate of carbon steel to be about ten times higher than that of stainless steel. Accordingly, a venting system is needed to dispose of the permeated hydrogen in the heads and shell to the atmosphere. This is accomplished by providing a lose type 304 stainless steel liner as a barrier. Hydrogen permeating through the stainless steel liner is vented to the atmosphere through vent holes in the heads and shell. Venting through the circumferential head-to-shell welds is more problematic. However, this can be circumvented by using a thin chill bar made of copper or titanium between the weld in the liner and weld in the steel as shown in Fig. 10.

Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

The vent holes in the layered steel shell shown in Fig. 10 are covered by the outer concrete shell. In order to provide a path for the hydrogen to vent to the atmosphere, a grooved steel shroud shown in Fig. 11 is placed on the outside surface of the steel layered shell and underneath the concrete. The grooves fit over the holes to channel the hydrogen toward the heads, which are not covered by the concrete.

Fig. 11
Fig. 11
Close modal

## 5 Mock Up Vessel

A full-scale vertical steel–concrete pressure vessel was designed and fabricated in accordance with the procedure outlined above. The design pressure was 6250 psi (43.1 MPa). The inside diameter of the vessel was 47 in. (1190 mm) and the length of the steel layered shell was 79 in. (2007 mm). A 20 in. (508 mm) manway was installed in the top head. A skirt length of 53.5 in. (1360 mm) was attached to the bottom head as shown in Fig. 12.

Fig. 12
Fig. 12
Close modal

The heads were made of SA-537 CL 2 material with a tensile strength of 75 ksi (517 MPa) and minimum thickness of 2.48 in. (63 mm) with a type 304 inner stainless steel liner. The steel-layered shell was made of SA-724 material with a tensile strength of 95 ksi (655 MPa) with a type 304 inner stainless steel liner. It consisted of four layers. The thickness of each layer was 0.583 in. (14.8 mm) thick. All pressure components, with the exception of the steel layered shell, were designed to 6250 psi (43.1 MPa). The steel-layered shell was designed to 3620 psi (25.0 MPa) pressure. The steel vessel was hydrotested at 5180 psi (35.7 MPa) and stamped in accordance with the ASME Section VIII, Division 2.

The outer concrete shell was constructed in accordance with ACI 318 and ACI 372R and consisted of high strength concrete with a compressive stress, fc, of 9000 psi (62.1 MPa). The thickness was 11.2 in. (284 mm). The prestress wires consisted of 5 layers and were ASTM A-648 Class III with a diameter of 0.192 in. (5 mm) and a tensile strength of 252 ksi (1737 MPa). The reinforcing bar cages were ASTM A-706 with a tensile strength of 80 ksi (552 MPa). Details of construction are shown in Fig. 13.

Fig. 13
Fig. 13
Close modal

The allowable stress in the prestress wires is taken as 176,400 psi (1216 MPa). The relaxation stress is taken as 35,000 psi (241 MPa). Hence, the design stress used in the analysis is 141,400 psi (975 MPa).

A thin layer of mortar was added to the outside of the prestress wires for protection as shown in Fig. 14.

Fig. 14
Fig. 14
Close modal

A finite element analysis was performed on the heads and shell. All critical stress values were within the allowable stress levels. Figure 15 shows a typical output for the analysis.

Fig. 15
Fig. 15
Close modal

The completed vessel was hydrotested at 8940 psi (61.6 MPa). The vessel, Fig. 16, was then cycled with hydrogen to prove its integrity.

Fig. 16
Fig. 16
Close modal

## Acknowledgment

The research was sponsored by the U.S. Department of Energy with Oak Ridge National Laboratory (ORNL), managed and operated by UT-Battelle, LLC. Programmatic direction was provided by the Fuel Cell Technologies Office. Mr. Nico Bouwkamp of the CaFCP & Frontier Energy was very helpful in showing the authors the existing infrastructure and various kinds of fueling stations in the Los Angeles, California, area. The cost analysis of various configuration options was done by Mr. Mike Kelly of Irvine, California. The initial analysis of the concrete shell including Finite Element analysis was performed by Dr. Fariborz Vossoughi at the Ben Gerwick Corporation in Oakland, California. Final details of reinforcement and prestressing of the concrete were calculated by Mr. Basil Kattula of Kent, Washington. A comprehensive Finite Element Analysis was also conducted by Jian Chen at ORNL. The layered steel vessel was fabricated by Kobelco in Kobe, Japan, with Mr. Susumu Terada contributing substantially to the various phases of fabrication. Strain gage instrumentation and data acquisition during concrete placement, hydrotesting, and hydrogen cycling was conducted by Dr. Fei Ren of Temple University in Baltimore, Maryland. The prestressed and reinforced concrete shell was fabricated by the Thompson Pipe Group in Grand Prairie, Texas, with Mr. Sam Arnaout's technical assistance. Final hydrotesting and hydrogen cycling was conducted at the Harris Thermal Transfer Products in Newberg, Oregon, under the direction of Mr. Jim Nylander.

This manuscript has been co-authored by UT-Battelle LLC, under Contract No. DE-AC0500OR22725, with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.2

## Funding Data

• U.S. Department of Energy (Contract No. DE-AC05-00OR22725; Funder ID: 10.13039/100000015).

## Nomenclature

• d =

diameter of prestress wire

•
• D =

diameter of vessel

•
• E =

modulus of elasticity

•
• Ec =

modulus of elasticity of concrete

•
• Eh =

•
• Es =

modulus of elasticity of shell

•
• K =

weld shrink factor obtained experimentally

•
• L =

length of shell

•
• n =

number of weld seams in a given layer

•
• N =

number of layers of prestress wire

•
• P =

design pressure

•
• Pf =

interface pressure

•
• Pi =

internal pressure

•
• Po =

external pressure

•
• R =

•
• Rc =

•
• Rh =

•
• Ri =

•
• Ro =

•
• Rs =

•
• S =

allowable stress

•
• Sw =

allowable stress of prestress wire

•
• t =

thickness

•
• tc =

thickness of concrete shell

•
• th =

•
• ti =

thickness of all layers underneath to

•
• to =

thickness of outer layer being shrunk

•
• ts =

thickness of steel shell

•
• tw =

equivalent thickness of prestress wire

•
• w =

width of weld seam

•
• δ =

•
• δc =

•
• δh =

•
• δi =

radial deflection of the inside surface of a cylinder

•
• Δi =

radial deflection of inner layer ti due to interface pressure Pf

•
• δo =

radial deflection of the outside surface of a cylinder

•
• Δo =

radial deflection of outer layer to due to interface pressure Pf

•
• δs =

•
• δw =

radial deflection of layer to due to weld shrinkage

•
• Δw =

weld shrinkage

•
• εL =

longitudinal strain

•
• εθ =

circumferential strain

•
• θc =

rotation of concrete shell

•
• θh =

•
• θs =

rotation of steel shell

•
• μ =

Poisson's ratio

•
• μc =

Poisson's ratio of concrete shell material

•
• μh =

•
• μs =

Poisson's ratio of steel shell material

•
• σL =

longitudinal stress

•
• σθ =

circumferential (hoop) stress

•
• σθc =

circumferential stress in concrete

•
• σθs =

circumferential stress in steel

## References

1.
,
M.
,
1972
, “
Wrapping Stress and Its Effect on Strength of Concentrically Formed Playwalls
,”
ASME Paper No. 72-PVP-7.
2.
,
M.
,
2018
,
Stress in ASME Pressure Vessels, Boilers, and Nuclear Components
,
Wiley-ASME Press
,
New York
.
3.
Wang
,
Y.
,
Feng
,
Z.
,
Lim
,
Y.
,
Chen
,
J.
,
,
M.
, and
Ren
,
F.
,
2016
, “
Design and Testing of Steel-Concrete Composite Vessel for Stationary High-Pressure Hydrogen Storage
,”
International Hydrogen Conference: Materials Performance in Hydrogen Environments
,
Moran, WY
,
Sept. 11--14
, pp.
390
397
.
4.
Wang
,
Y.
,
Feng
,
Z.
,
Ren
,
F.
,
Lim
,
Y.-C.
,
Chen
,
J.
, and