**1.0 Summary of findings**

2.0 Introduction

3.0 Identification of susceptible features to be analysed

3.1 Body studs

3.2 Area behind outlet flange

4.0 Identification of operational loads

4.1 Pressure of the line fluid

4.2 Tightening of the body stud nuts

4.3 Mass of the valve, actuator and bonnet

5.0 Calculations

5.1.0 Stresses imposed on the body studs by the action of operating loads and seismic acceleration, along the horizontal axis

5.1.1 Stresses caused by the hydrostatic end thrust or gasket seating

5.1.2 Bending stress due to the actuator

5.1.3 Bending stress due to the bonnet

5.1.4 Bending stress due to the body

5.1.5 Direct stress due to the actuator weight

5.1.6 Direct stress due to the bonnet weight

5.1.7 Direct stress due to the body weight

5.1.8 Direct stress due to the actuator thrust

5.1.9 Summation of stresses

5.2.0 Stresses imposed on the body studs by the action of operating loads and seismic acceleration, along the vertical axis

5.2.1 Stresses caused by the hydrostatic end thrust or gasket seating

5.2.2 Direct stress caused by the body under the influence of acceleration due to gravity plus seismic effects

5.2.3 Direct stress caused by the actuator under the influence of acceleration due to gravity plus seismic effects

5.2.4 Direct stress caused by the bonnet under the influence of acceleration due to gravity plus seismic effects

5.2.5 Direct stress due to the actuator thrust

5.2.6 Summation of stresses

5.3.0 Stresses imposed on the area behind the outlet flange by the action of operating loads and seismic acceleration along the horizontal axis

5.3.1 Longitudinal stress caused by the internal pressure

5.3.2 Bending stress due to the actuator

5.3.3 Bending stress due to the bonnet

5.3.4 Bending stress due to the body

5.3.5 Direct stress due to the actuator weight

5.3.6 Direct stress due to the bonnet weight

5.3.7 Direct stress due to the body weight

5.3.8 Direct stress due to the actuator thrust

5.3.9 Summation of stresses

5.4.0 Stresses imposed on the area behind the outlet flange by the action of operatingloads and seismic acceleration along the vertical axis

5.4.1 Longitudinal stress caused by the Internal pressure

5.4.2 Direct stress caused by the body under the influence of gravity and seismic effects

5.4.3 Direct stress caused by the bonnet under the influence of gravity and seismic effects

5.4.4 Direct stress caused by the actuator under the influence of gravity and seismic effects

5.4.5 Direct stress due to the actuator thrust

5.4.6 Summation of stresses

6.0 Results

1.0 Summary of findings

2.0 Introduction

3.0 Identification of susceptible features to be analysed

3.1 Body studs

3.2 Area behind outlet flange

4.0 Identification of operational loads

4.1 Pressure of the line fluid

4.2 Tightening of the body stud nuts

4.3 Mass of the valve, actuator and bonnet

5.0 Calculations

5.1.0 Stresses imposed on the body studs by the action of operating loads and seismic acceleration, along the horizontal axis

5.1.1 Stresses caused by the hydrostatic end thrust or gasket seating

5.1.2 Bending stress due to the actuator

5.1.3 Bending stress due to the bonnet

5.1.4 Bending stress due to the body

5.1.5 Direct stress due to the actuator weight

5.1.6 Direct stress due to the bonnet weight

5.1.7 Direct stress due to the body weight

5.1.8 Direct stress due to the actuator thrust

5.1.9 Summation of stresses

5.2.0 Stresses imposed on the body studs by the action of operating loads and seismic acceleration, along the vertical axis

5.2.1 Stresses caused by the hydrostatic end thrust or gasket seating

5.2.2 Direct stress caused by the body under the influence of acceleration due to gravity plus seismic effects

5.2.3 Direct stress caused by the actuator under the influence of acceleration due to gravity plus seismic effects

5.2.4 Direct stress caused by the bonnet under the influence of acceleration due to gravity plus seismic effects

5.2.5 Direct stress due to the actuator thrust

5.2.6 Summation of stresses

5.3.0 Stresses imposed on the area behind the outlet flange by the action of operating loads and seismic acceleration along the horizontal axis

5.3.1 Longitudinal stress caused by the internal pressure

5.3.2 Bending stress due to the actuator

5.3.3 Bending stress due to the bonnet

5.3.4 Bending stress due to the body

5.3.5 Direct stress due to the actuator weight

5.3.6 Direct stress due to the bonnet weight

5.3.7 Direct stress due to the body weight

5.3.8 Direct stress due to the actuator thrust

5.3.9 Summation of stresses

5.4.0 Stresses imposed on the area behind the outlet flange by the action of operatingloads and seismic acceleration along the vertical axis

5.4.1 Longitudinal stress caused by the Internal pressure

5.4.2 Direct stress caused by the body under the influence of gravity and seismic effects

5.4.3 Direct stress caused by the bonnet under the influence of gravity and seismic effects

5.4.4 Direct stress caused by the actuator under the influence of gravity and seismic effects

5.4.5 Direct stress due to the actuator thrust

5.4.6 Summation of stresses

6.0 Results

1.0 Summary of findings

The 16" angle control valve will perform it's intended duty during an earthquake having a seismic acceleration of 0.81g in the horizontal direction, and during an earthquake having a seismic acceleration of 0.81g in the vertical direction. There will be no rupture of the valve body nor failure of the studs at the valve body/ bonnet joint.

**2.0 Introduction**

I consider the performance of a 16" angle control valve subjected to both horizontal and vertical seismic forces together with normal operating loads. Two regions are identified as being susceptible to damage during seismic events.

The maximum tensile stress is calculated for the two susceptible areas for normal operating loads plus seismic loading along the horizontal axis and for normal operating loads plus seismic loading along the vertical axis.

Component stresses are determined by accepted axial loading stress theory, bending stress theory, cylinder stress theory and bolt load theory.

These stresses are summated and compared with the yield stress of the material being considered to show that the total tensile stress is not in excess of the yield stress for non-pressurised components and not in excess of 90% of the yield stress for pressurised components.

The following assumptions are made in this analysis :

(1) The design seismic acceleration of 0.81g acts in the horizontal direction or vertical direction separately and not simultaneously.

(2) The pipe work and equipment adjacent to the valve exert no force or moment to it.

(3) The component stresses are all tensile and not compressive.

(4) The changes of section near to the region under consideration are such that negligable concentration of stress occurs.

**3.0 Identification of susceptible features to be analysed**

The two areas that we consider to be susceptible to seismic stresses are the body studs and the area behind the outlet flange.

**3.1 Body studs**

The body studs are manufactured in chromium-molybdenum steel ASTM A320 Grade L7. This material has a minimum yield stress of 105,000 psi and a minimum tensile strength of 125,000 psi There are 24 studs on a PCD (pitch circle diameter) of 30-1/2"

**3.2 Area behind the outlet flange**

The valve body is manufactured in carbon steel ASTM A350 LF2. This material has a minimum yield stress of 36,000 psi and a minimum tensile strength of 70,000 psi.

**4.0 Identification of operational loads**

The valve would be subject to stresses caused by the pressure of the line fluid, tightening of the body stud nuts and the mass of the valve body, bonnet and actuator.

**4.1 Pressure of the line fluid**

The maximum line pressure of the fluid is 1230 psig and this will act on all 'wetted parts'.

**4.2 Tightening of the body stud nuts**

A torque is applied to the body stud nuts which is sufficient to provide the body/bonnet seal by loading the body studs.

**4.3 Mass of the valve body, valve bonnet and actuator**

The mass of the valve body is 11,000 pounds and under the influence of acceleration due to gravity and earthquakes, this would produce a force and moment.

The mass of the actuator is 1,330 pounds and this also would produce a force and moment due to the above.

The mass of the valve bonnet is 1,200 pounds and under the influence of acceleration due to gravity and earthquakes, this would produce a force and moment.

**5.0 Calculations**

Firstly, we consider the stresses imposed on the body studs by the action of operating loads and seismic acceleration along the horizontal and vertical axis.

Secondly, we consider the stresses imposed on the area behind the outlet flange by the action of the above loads.

**5.1 Stresses imposed on the body studs by the action of operating loads and seismic acceleration along the horizontal axis**

The body studs are subject to stresses caused by the hydrostatic end thrust or gasket seating, bending due to the actuator, bending due to the bonnet, bending due to the body, force due to the actuator, force due to the bonnet, force due to the body and force due to the actuator thrust.

**5.1.1 Stress causedby the hydrostatic end thrust or gasket seating**

Using the method as described in Appendix 2 of the 'ASME Boiler and Pressure vessel code - Section VIII, Division I', calculations shall be made for each of the two design conditions of operating and gasket seating and the more severe will control.

The minimum required bolt load for operating conditions,

Wm1 = 0.785G^2 x p + (2b x 3.14 GmP)

where,

G = 27.050

P = 1,150 psig

b = 0.3186

m = 3.75

Wm1 = 0.785 x 27.050^2 x 1150 + (2 x 0.3186 x 3.14 x 27.050 x 3.75 x 1150)

Wm1 = 893,945 lbf

The minimum required bolt load for gasket seating,

Wm2 = 3.14 bGy

Where,

b = 0.3186 in

G = 27.050 in

Y = 7,600 psi

Wm2 = 3.14 x 0.3186 x 27.050 x 7,600

Wm2 = 205,663 lbf

As the larger of the two loads is due to the operating conditions, we consider the stress imposed on the studs due to hydrostatic end thrust,

S1 = Wm1 / A

Where,

Wm1 = 893,945 lbf

A = bolt area, 24 x 1.78 = 42.72 in^2

S1 = 893,945 / 42.72

S1 = 20,926 Ibf/in^2

**5.1.2 Bending stress due to the actuator**

The bending stress due to the actuator under the influence of seismic acceleration is given by,

S2 = (M / I) / Y

Where,

M = bending moment at stud, lbf in

= mass of actuator x seismic acceleration x distance

= (1330 / 32.2) x (0.81 x 32.2) x 59.25

= 63,830 lbf in

Y = distance from neutral axis to outermost fibre, in

= 16.063 in

I = second moment of area of twenty four studs, in^4

=(1 + AL^2)

= 24 x 0.2302 + 4 (1.78 x (1.9905^2 +5.8359^2 + 9.2836^2 + 12.0986^2 + 12.0986^2 + 14.08916^2 + 15.1195^2 ))

= 4,973 in^4

S2 = (63,820 / 4,973) x 16.063

S2 = 206 lbf/in^2

**5.1.3 Bending stress due to the bonnet**

The bending stress due to the bonnet under the influence of seismic acceleration is given by,

S3 = (M / I) Y

Where,

M = bending moment of stud, ibf in

= mass of bonnet x seismic acceleration x distance

= (1,200 / 32.2) x (0.81 x 32.2) x 4

= 3,888 lbf in

Y =16.063 in

I = 4,973 in^4

S3 = (3,888 / 4,973) x 16.063

S3 = 13 lbf/in^2

**5.1.4 Bending stress due to the body**

The bending stress dueto the body under the influence of seismic acceleration is given by,

S4 = (M / I) Y

Where,

M = bending moment at stud, Ibf in

= mass of body x seismicacceleration x distance

= (11,000 x 32.2) x (0.81 x 32.2) x 17.75

= 158,153 lbf in

Y = 16.063 in

I = 4,973 in^4

S4 = (158,153 / 4,973) x 16.063

S4 = 511 Ibf/in^2

**5.1.5 Direct stress due to actuator weight**

The direct stress imposed on the studs by the weight of the actuator is given by,

S5 = W2 / A

Where,

W2 = Weight of actuator, 1,330 lbf

A = bolt area, 42.72 in^2

S5 = 1330 / 42.72

S5 = 31 Ibf/in^2

**5.1.6 Direct stress due to bonnet weight**

The direct stress imposed on the studs by the weight of the bonnet is given by,

S6 = W3 / A

Where,

W3 = weight of bonnet, 1,200 lbf

A = bolt area, 42.72 in^2

S6 = 1200 / 42.72

S6 = 28 lbf / in2

**5.1.7 Direct stress due to the body weight**

The direct stress imposed on the studs by the weight of the body is given by,

S7 = W1 / A

Where,

W1 = weight of body, 11,000 lbf

A = bolt area, 42.72 in^2

S7 = 11,000 / 42.72

S7 = 258 Ibf/in^2

**5.1.8 Direct stress due to actuator thrust**

The direct stress on the studs caused by the thrust of the actuator when the valve is in the closed position and the valve is not filled with line fluid is given by,

S8 = F / A

Where,

F = maximum thrust of actuator, 15,600 lbf

A = bolt area 42.72 in^2

S8 = 15,600 / 4,272

S8 = 365 Ibf/in^2

**5.1.9 Summation of stresses**

Addition of the eight component stresses yields a total stress of :

S = S1 + S2 + S3 + S4 + S5 + S6 + S7 + S8

= 20,926 + 206 +13 + 511 + 31 + 28 + 258 + 365

= 22,338 lbf/in^2

. .

The value of the total stress is less than 22% of the yield-stress for this non-pressurised component.

**5.2 Stresses imposed on the body studs by the action of operating loads and seismic acceleration along the vertical axis**

The body studs are subject to stresses caused by the hydrostatic end thrust or gasket seating, force due to the actuator, bonnet, body and actuator thrust.

**5.2.1 Stress caused by the hydrostatic end thrust or gasket seating**

The direct stress caused by the hydrostatic and thrust or gasket seating calculation is as detailed in 5.1.1 yielding a stress of 20,926 lbf/in2.

**5.2.2 Direct stress caused by the bodyunder the influence of acceleration due to gravity plus seismic effects**

The direct stress is given by,

S9 = F / A

Where,

F = effective force due to body, Ibf

=11,000 + (11,000 / 32.2) x (0.81 x 32.2)

=19,910 lbf

A = bolt area, 42.72 in^2

S9 = 19,910 / 42.72

S9 = 466 Ibf/in^2

**5.2.3 Direct stress caused by the actuator under the influence of acceleration due to gravity and seismic effects**

The direct stress is given by,

S10 = F / A

Where,

F = effective force due to actuator, lbf

= 1,330 + (1,330 / 32.2) x (0.81 x 32.2)

= 2,407 lbf

A = bolt area, 42.72 in^2

S10 = 2,407 / 42.72

S10 = 56 lbf/in^2

**5.2.4 Direct stress caused by the bonnet under the influence of acceleration due to gravity and seismic effects**

The direct stress is given by,

S11 = F / A

Where,

F = effective force due to bonnet, lbf

=1,200 + (1,200 / 32.2) x (0.81 x 32.2)

= 2,172 lbf

A = bolt area, 42.72 in^2

S11 = 2,172 / 42.72

S11 = 51 lbf/in^2

**5.2.5 Direct stress due to the actuator thrust**

The direct stress on the studs, caused by the thrust of the actuator when the valve is in the closed position and the valve is not filled 2 with line fluid, is as detailed in 5.1.8 yielding a stress of 365 lbf/in^2.

**5.2.6 Summation of stresses**

Addition of the five component stresses yields a total stress of :

S = S1 + S9 + S10 + S11 + S8

= 20,926 + 466 + 2,407 + 51 + 365

= 24,215 lbf/in^2

The value of the total stress is less than 23% of the yield stress for this non-pressurised component.

**5.3 Stresses imposed on the area behind the outlet flange by the action of operating loads and seismic acceleration along the horizontal axis**

The area behind the outlet flange is subject to stresses caused by the internal pressure, moment of the actuator,moment of the bonnet, moment of the body, force due to the actuator, force due to the bonnet, force due to the body and force due to the actuator thrust.

**5.3.1 Longitudinal stress caused by internal pressure**

The longitudinal stress caused by the internal pressure is given by,

S12 = P (AI / AM)

Where,

P = Maximum working pressure, 1,150 psig

AI = inside areaof cross section in^2

= Pi x (14.75^2 / 4)

= 170.9 in^2

Am = metal area of cross-section in^2

= ( ((Pi x 19.25^2) / 4)) - ((Pi x 14.75^2) / 4)) )

= 120.1 in^2

S12 = 1,150 x (170.9 / 120.1)

S12 = 1,636 lbf/in^2

**5.3.2 Bending stress due to the actuator**

The bending stress due to the actuator, under the influence of seismic acceleration is given by,

S13 = (M / Y) I

Where,

M = bending moment at cross-section, Ibf in

= mass of actuator x seismic acceleration x distance

= (1,330 / 32.2) x (0.81 x 32.2) x 91

= 98,034 lbf in

Y= distance from neutral axis to outermost fibre, in

= 9.625 in

I= second moment of area at cross section, in^4

= Pi (19.25^4 - 14.75^4) / 64

= 4,417 in^4

S13 = (98,034 / 4,417) x 9.625

S13 = 214 lbf in^2

**5.3.3 Bending stress due to the bonnet**

The bending stress due to the bonnet under the influence of seismic acceleration is given by,

S14 = (M / I) Y

Where,

M = bending moment at cross -section, Ibf in

= mass of bonnet x seismic acceleration x distance

= (1,200 / 32.2) x (0.81 x 32.2) x 35.75

= 34,749 Ibf in

Y = 9.625 in

I = 4,417 in^4

S14 = (34,749 / 4,417) x 9.625

S14 = 76 lbf/in^2

**5.3.4 Bending stress due to the body**

The bending stress due to the body under the influence of seismic acceleration is given by,

S15 = (M / I) Y

Where,

M = bending moment at cross section, Ibf in

= mass of body x seismic acceleration x distance

= (11,000 x 32.2) x (0.81 x 32.2) x 20.375

= 181,541 lbf in

Y = 9.625 in

I = 4417 in^4

S15 = (181,541 / 4,417) lbf in x 9.625

S15 = 396 lbf/in^2

**5.3.5 Direct stress due to the actuator weight**

The direct stress due to the actuator weight is given by,

S16 = W2 / A

Where,

W2 = weight of actuator, 1,330 lbf

A = area of cross-section, 120 in^2

S16 = 1,330 / 120

S16= 11 lbf/in^2

**5.3.6 Direct stress due to bonnet weight**

The direct stress due to bonnet weight is given by,

S17 = W3 / A

Where,

W3 = weight of bonnet, 1,200 lbf

A = 120 in2

S17 = 1,200 / 120

S17 = 10 lbf/in^2

**5.3.7 Direct stress dueto body weight**

The direct stress due to the body weight is given by,

S18 = W1 / A

Where,

W = weight of body, 11,000 lbf

A = 120 in^2

S18 = 11,000 / 120

S18 = 92 lbf/in^2

**5.3.8 Direct stress due to actuator thrust**

The direct stress on the cross-section caused by the thrust of the actuator when the valve is in the closed position and the valve is not filled with line fluid is given by,

S19 = F / A

Where,

F = maximum thrust of actuator, 15,600 lbf

A = 120 in^2

S19 = 15,600 / 120

S19 = 130 lbf/in^2

**5.3.9 Summation of stresses**

Addition of the eight component stresses yields a total stress of,

S = S12 + S13 + S14 + S15 + S16 + S17 + S18 + S19

= 1,636 + 214 + 76 + 396 + 11 + 10 + 92 + 130

= 2,565 Ibf/in^2

The value of the total stress is less than 8% of the yield stress for this pressurised cross-section.

**5.4 Stresses imposed on the area at he back of the outlet flange by the action of operating loads and seismic acceleration along the vertical axis**

The area at the back of the outlet flange is subject to stresses caused by internal pressure, force due to the actuator, bonnet, body and actuator thrust.

**5.4.1 Longitudinal stress caused by the internal pressure**

The longitudinal stress caused by the internal pressure is the same as that calculated in 5.3.1 and is 1,636 Ibf/in^2.

**5.4.2 Direct stress caused by the body, under the influence of acceleration due to gravity plus seismic effects**

The direct stress is given by,

S20 = F / A

Where,

F = effective force due to the body, Ibf

= 11,000 + (11,000 / 32.2) x ( 0.81 x 32.2)

= 19,910 lbf

= 120 in^2

S20 = 19,910 / 120

S20 = 166 lbf/in^2

**5.4.3 Direct stress caused by the bonnet under the influence of acceleration due to gravity plus seismic effects**

The direct stress is given by,

S21 = F / A

Where,

F= effective force due to the bonnet, Ibf

= 1,200 + (1,200 / 32.2) x (0.81 x 32.2)

= 2,172 Ibf

A = 120 in^2

S21 = 2,172 / 120

S21 = 18 lbf/in^2

**5.4.4 Direct stress caused by the actuator under the influence of acceleration due to gravity plus seismic effects**

The direct stress is given by,

S22 =F / A

Where,

F = effective force due to the actuator, Ibf

= 1,330 + (1,330 / 32.2) x (0.81 x 32.2)

= 2,407 Ibf

A2 = 120 in^2

S22 = 2,407 / 120

S22 = 20 Ibf/in^2

**5.4.5 Direct stress due to actuator thrust**

The direct stress on the cross-section caused by the thrust of the actuator when the valve is in the closed position and the valve is not filled with line fluid is the same as that calculated in section 5.3.8 and being 130 Ibf/in^2.

**5.4.6 Summation of stresses**

Addition of the five component stresses yields a total stress of :

S = S12 + S20 + S21 + S22 + S19

= 1,636 + 166 + 18 + 20 + 130

= 1,970 Ibf/in^2

The value of the total stress is less than 6% of the yield stress for this pressurised cross section.

**6.0 Results**

The calculated total tensile stress in the body studs by the action of operating loads and seismic acceleration along the horizontal axis is 22,338 lbf/in^2. Increasing this calculated value by 25% gives 27,923 lbf/in^2 which is less than 27% of the material yield stress ( 105,000 lbf/in^2).

Under the action of seismic acceleration in the vertical direction the calculated total tensile stress in the body studs is 24,215 lbf/in^2. Applying the 25% increase produces 30,269 lbf/in^2 which is less than 29% of the material yield stress (105,000 lbf/in^2).

Considering the region behind the outlet flange, our calculations produce a total tensile stress in the section of 2565 lbf/in^2, for the action of operating loads and seismic acceleration along the horizontal axis. Increasing this calculated value by 25% gives 3206 lbf/in^2 which is less than 9% of the yield stress of the material ( 36000 lbf/in^2).

The calculated total tensile stress in the region behind the outlet flange, subject to operating loads and seismic acceleration in the vertical direction is 1970 lbf/in^2. Increasing this calculated value by 25% gives 2463 lbf/in^2, which is less than 7% of the material yield stress (36000 lbf/in^2).

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