Steam Boiler: Design Calculation

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Can You Calculate Tube thickness?

Can you calculate tube thickness is one of question must be answered by mechanical engineer who involve in design steam boiler. Basically the calculation of tube thickness is really simple but if we don’t know, it will be difficult off course.

Basically you only need knowledge about the theory of longitudinal stress in cylindrical part and circumferential stress cylindrical part as my previous post. The following below is formula to calculate tube thickness because of these stresses:

t_L = P D / 2 S_L (equation 1)

t_C = P D / 4 S_C (equation 2)

where:

t_L = tube thickness because of longitudinal stress

t_C = tube thickness because of circumferential stress

P = design pressure

D = inside diameter

S_C = circumferential stress

S_L = longitudinal stress

From the equation above, thickness because of longitudinal stress is always greater than thickness because of circumferential stress. Therefore you can simply choose the equation 1 to calculate tube thickness.

However, if the tube is used in boiler plant, the calculation should refer to ASME BPV Code Section I Part PG 27.2.1 as following formula:

t = (P D / 2 S) + 0.005D + e + Ca

where:

t = minimum required tube thickness

P = maximum allowable working pressure

D = outside diameter

S = maximum allowable stress value at certain temperature in each material, the table can be found in ASME BPV Code Section IID.

e = thickness factor for expanded tube ends

Ca = Corrosion allowance.

To make easy to calculate tube thickness, I had made a spreadsheet of tubethickness calculation, you just enter input data such as pressure, outside diameter, e, Ca and S value.

So if you get question “can you calculate tube thickness?” just answer it, I can do it for 5 minutes only, he..he.. but if you have already ASME BPV Code Section IID to find S value.

Maximum Allowable Working Pressure Calculation

The maximum allowable working pressure (MAWP) of a steam boiler is an absolute restriction of pressure within psig unit for a steam boiler is allowed to run. The ASME BPV Code (American Society of Mechanical Engineers Boiler and Pressure Vessel) says that absolutely no steam boiler should be run at a pressure above the MAWP with the exception of the safety valve is operated to discharge excessive pressure. Steam boiler has some technical terms that be generally used. One of them is MAWP (Maximum Allowable Working Pressure) which means that all of working pressure at the pressure part shall not exceed MAWP. MAWP on the header or drum can be calculated based on the equation below:

MAWP = (t x E x TS) / (R x SF)

Abbreviation of the equation above is:

MAWP = Maximum Allowable Working Pressure in the drum or header.

E = Joint efficiency of welding in the drum or header

t = Thickness of header or drum

TS = Tensile strength of the material, can be looked at ASME BPV Section II D

SF = Design safety factor, the value which is commonly used is five

R = Inside radius of header or drum either steam drum or water drum

Circumferential Stress in Cylindrical Part

Pipes, headers, drums and tubes are pressure parts in steam boiler which has cylindrical shape. Design calculation must consider stress either longitudinal stress or circumferential stress. Circumferential stress is impact from internal pressure or loads which acting around in its circumstance of cylindrical part.

Circumferential stress is designed and calculated on that part to prevent the material split or break circumferentially. Resistance force should minimum equal than circumferential force. The following formula below is the step by step to get equation of circumferential stress:

Circumferential Force = Internal Pressure x Projection Area

= Internal Pressure x phi x Square of Inside Diameter / 4

= P x π x D² / 4

Resistance Force = Circumferential Stress x Projection Area

= Circumferential Stress x phi x Inside Diameter x Thickness

= SC x π x D x t

Résistance Force = Circumferential Force

SC x π x D x t = P x π x D² / 4

SC = PD / 4t

The equation of circumferential stress is PD / 4t while the longitudinal stress is PD / 2t. This comparison show that amount of stress longitudinal is twice higher than circumferential.

Cylindrical Part under Longitudinal Stress

Design calculation is one of important steps to build new steam boiler. Cylindrical parts such as water wall tubes, header, downcomer pipe, riser, and drum are designed under stress both external pressure and internal pressure. One of them is longitudinal stress which is caused by load from internal pressure that performs along the lengthwise or long axis of tube, pipe or other cylindrical parts.

Material should be designed to resist longitudinal stress unless the material will impact to break material and split along the long axis (please see Figure 1 and Figure 2). The following below is an approach to get the formula of longitudinal stress.

From figure 1 above, longitudinal force is resisted by resistance force. Cylindrical part should have enough strength to resist longitudinal force, so minimum requirement of resistance force value should has minimum equal, not less than longitudinal force unless the material will be crack along longitudinal axis (see Figure 2).

Figure 1: Working Principal of Cylindrical Part

Longitudinal Force = Internal Pressure x Projection Area

= Internal Pressure x Inside Diameter x Length

= P x D x L

Resistance Force = Longitudinal Stress x Projection Area

= Longitudinal Stress x Thickness x Length x 2

= SL x t x L x 2

Résistance Force = Longitudinal Force

SL x t x L x 2 = P x D x L

SL = PD / 2t

So the formula of longitudinal stress in the cylindrical part is PD / 2t

Figure 2: Sample of Longitudinal Cracking in Cylindrical Part

Cylindrical Part under Stress

Figure 1: Cylindrical Part Under Pressure

Steam boiler consist a lot of cylindrical parts such as tube, pipe, header and drum. All cylindrical parts are performed under stress. Designer steam boiler shall have good knowledge to design and calculate stress on these parts. Based on location, stress can be classified by two types; internal stress and external stress. Internal stress is stress which is occurring inside cylindrical part while external stress occurs because of load from outside cylindrical parts.

Tube, pipe, header and drum must be designed and calculate internal pressure first to prevent deformation on that parts. Internal stress consists of two types, longitudinal stress and circumferential stress. Longitudinal stress is caused by lengthwise of axial load and circumferential stress can be called as hoop stress is caused pressure which working cylindrically. For illustration please see figure 1.

The formula of longitudinal stress can be expressed as: SL = P D / 2 t

The formula of circumferential stress can be expressed as: SC = P D / 4 t

SL = Longitudinal Stress (psi)

SC = Circumferential Stress (psi)

D = Outside Diameter Cylindrical Part (in)

P = Internal Pressure (psi)

T = Thickness of Cylindrical Part (in)

Requirement ASME for Design Calculation

Design calculation of steam boiler should be performed carefully. Engineers who have responsibility to design steam boiler shall have good understanding about requirement ASME BPV Section I not only for materials, but also for design calculation.

Design calculation ideally should follow ASME Code. The following below is summary of requirement ASME for design calculation:

- General Design, see ASME BPV Section I sub chapter PG 16
- Maximum Allowable Working Pressure, see ASME BPV Section I sub chapter PG 21
- Loading on Steam Boiler, see ASME BPV Section I sub chapter PG 22
- Stress Value for Calculation Formula, see ASME BPV Section I sub chapter PG 23 and ASME BPV Section II Part D
- Calculation Formula for Tube Up To 5 in Outside Diameter, see ASME BPV Section I sub chapter PG 27.2.1
- Calculation Formula for Piping, Drums and Headers, see ASME BPV Section I sub chapter PG 27.2.2
- Thickness Greater Than One-Half the Inside Radius of Component, see ASME BPV Section I sub chapter PG 27.2.3
- Welded Access or Inspection Openings under External Pressure, see ASME BPV Section I sub chapter PG 28
- Dished Head Design and Calculation, see ASME BPV Section I sub chapter PG 29
- Design Stayed Dished Head, see ASME BPV Section I sub chapter PG 30
- Design Unstayed Flat Heads and Covers, see ASME BPV Section I sub chapter PG 31
- Design Calculation for Opening in Shells, Headers, and Heads, see ASME BPV Section I sub chapter PG 32.1
- Design Shape of Opening, see ASME BPV Section I sub chapter PG 32.2
- Design Size of Opening, see ASME BPV Section I sub chapter PG 32.3
- Design Compensation Required for Opening in Shells and Formed Heads, see ASME BPV Section I sub chapter PG 33
- Design Flanged in Openings in Formed Heads, see ASME BPV Section I sub chapter PG 34
- Design Compensation Required for Opening in Flat Heads, see ASME BPV Section I sub chapter PG 35
- Design Limit of Metal Available for Compensation, see ASME BPV Section I sub chapter PG 36
- Design Strength of Compensation, see ASME BPV Section I sub chapter PG 37
- Design Compensation for Multiple Openings, see ASME BPV Section I sub chapter PG 38
- Minimum Thickness and Maximum Working pressure for Stayed Flat Plates, see ASME BPV Section I sub chapter PG 46.1
- Design Calculation of Ligaments, see ASME BPV Section I sub chapter PG 52 and PG 53
- Boiler External Piping and Boiler Proper Connection, see ASME BPV Section I sub chapter PG 58
- Nondestructive Examination Requirements, see ASME BPV Section I sub chapter PW 11
- Heat Treatment Process, see ASME BPV Section I sub chapter PW 38 and PW 39