Yield Strength Formula

Calculate pipes internal, allowable and bursting pressure

Tensile Yield Strength Unit Conversion Calculator; Unit Conversion Calculator & Converter for Tensile/Yield & Charpy values. Use the following calculator to convert yield or tensile values in ksi, Mpa, N/mm² or psi. Type the value in the box next to Mpa (using the drop down to change the unit of measurement).

1. Measuring Yield Stress Approximate yield stress measurements can be gained by plotting the shear stress values for a range of shear rates, fitting a curve to the data, and extrapolating through the stress axis. The intersect on the stress axis gives us our yield stress (figure 2).
2. Yield strength, S y, is the maximum stress that can be applied without permanent deformation of the test specimen. This is the value of the stress at the elastic limit for materials for which there is an elastic limit. Because of the difficulty in determining the elastic limit, and because many materials do not have an elastic region, yield.
3. The yield strength of a material represents the stress beyond which its deformation is plastic. Any deformation that occurs as a result of stress higher than the yield strength is permanent. Because of the linearity of elastic deformation, yield strength is also defined as the greatest stress achievable without any deviation from the.

Barlow's formula is used to determine

• internal pressure at minimum yield
• ultimate burst pressure
• maximum allowable pressure

Internal Pressure At Minimum Yield

Barlow's formula can be used to calculate the 'Internal Pressure' at minimum yield

P_y = 2 S_y t / d_o (1)

where

P_y = internal pressure at minimum yield (psig, MPa)

S_y = yield strength (psi, MPa)

t = wall thickness (in, mm)

d_o = outside diameter (in, mm)

Note! - in codes like ASME B31.3 modified versions of the Barlow's formula - like the Boardman formula and the Lame formula - are used to calculate burst and allowable pressures and minimum wall thickness.

Example - Internal Pressure at Minimum Yield

The internal pressure for a 8 inch liquid pipe line with outside diameter 8.625 in and wall thickness 0.5 in with yield strength 30000 psi can be calculated as

P_y = 2 (30000 psi) (0.5 in) / (8.625 in)

= 3478 psi

Example - Polyethylene PE pipe

The yield strength of a 110 mm polyethylene pipe is 22.1 MPa. The minimum wall thickness for pressure 20 bar (2 MPa) can be calculated by rearranging eq. 1 to

t = P_yd_o / (2 S_y)

= (2 MPa) (110 mm) / (2 (22.1 MPa))

= 5 mm

Ultimate Burst Pressure

Barlow's formula can be used to calculate the 'Ultimate Burst Pressure' at ultimate (tensile) strength as

P_t = 2 S_t t / d_o (2)

where

P_t = ultimate burst pressure (psig)

S_t = ultimate (tensile) strength (psi)

Example - Ultimate Burst Pressure

The ultimate pressure for the pipe used in the example above with ultimate (tensile) strength 48000 psi can be calculated as

P_t = 2 (48000 psi) (0.5 in) / (8.625 in)

= 5565 psi

Working Pressure or Maximum Allowable Pressure

Working pressure is a term used to describe the maximum allowable pressure a pipe may be subjected to while in-service. Barlow's formula can be used to calculate the maximum allowable pressure by using design factors as

P_a = 2 S_y F_d F_e F_t t / d_o (3)

where

P_a = maximum allowable design pressure (psig)

S_y = yield strength (psi)

F_e = longitudinal joint factor

F_t = temperature derating factor

Typical Design Factors - F_d

Yield Strength Formula Beam

• liquid pipelines: 0.72
• gas pipe lines - class 1: 0.72
• gas pipe lines - class 2: 0.60
• gas pipe lines - class 3: 0.50
• gas pipe lines - class 4: 0.40

Example - Maximum Allowable Pressure

The 'Maximum Allowable Pressure' for the liquid pipe line used in the examples above with F_d = 0.72, F_e = 1 and F_t = 1 - can be calculated as

P_a = 2 (30000 psi) 0.72 1 1 (0.5 in) / (8.625 in)

= 2504 psi

Barlow's formula is based on ideal conditions and room temperatures.

Mill Test Pressure

The 'Mill Test Pressure' refers to the hydrostatic (water) pressure applied to the pipe at the mill to assure the integrity of the pipe body and weld.

P_t = 2 S_t t / d_o (4)

where

P_t = test pressure (psig)

S_t = specified yield strength of material - often 60% of yield strength (psi)

Wall Thickness

Barlow's formula can be useful to calculate required pipe wall thickness if working pressure, yield strength and outside diameter of pipe is known. Barlow's formula rearranged:

t_min = P_i d_o / (2 S_y) (5)

where

t_min = minimum wall thickness (in)

P_i = Internal pressure in pipe (psi)

Example - Minimum Wall Thickness

The minimum wall thickness for a pipe with the same outside diameter - in the same material with the same yield strength as in the examples above - and with an internal pressure of 6000 psi - can be calculated as

Calculating Yield Strength Formula

t = (6000 psi) (8.625 in) / (2 (30000 psi))

= 0.863 in

From table - 8 inch pipe Sch 160 with wall thickness 0.906 inches can be used.

Material Strength

The strength of a material is determined by the tension test which measure the tension force and the deformation of the test specimen.

• the stress which gives a permanent deformation of 0.2% is called the yield strength
• the stress which gives rupture is called the ultimate strength or the tensile strength
  

Typical strength of some common materials:

• 1 psi (lb/in²) = 6,894.8 Pa (N/m²) = 6.895x10^-2 bar
• 1 MPa = 10⁶ Pa

Barlow's Pressure Calculator

The Barlow's formula calculator can be used to estimate

• internal pressure at minimum yield
• ultimate burst pressure
• maximum allowable pressure

Outside diameter (in)

Wall thickness (in)

Yield strength (psi)

Ultimate (tensile) strength (psi)

Total Design Factor

Barlow's Wall Thickness Calculator

The Barlow's formula calculator can be used to estimate minimum wall thickness of pipe.

Outside diameter (in, mm)

Yield strength (psi, MPa)

Internal pressure (psi, mm)

Example - A53 Seamless and Welded Standard Pipe - Bursting Pressure

Bursting pressure calculated with Barlow's formula (2) for A53 Seamless and Welded Standard Pipe Grade A with ultimate (tensile) strength 48000 psi. Pipe dimensions - outside diameter and wall thickness according ANSI B36.10.

• 1 in (inch) = 25.4 mm
• 1 MPa = 10³ kPa = 10⁶ Pa

Related Topics

• Pressure Ratings - Pressure ratings of pipes and tubes and their fittings - carbon steel , stainless steel, plastic, copper and more

Related Documents

• Aluminum Tubing - Allowable Pressure - Allowable pressure for aluminum tubes
• ASME 31.3 Allowable Pressure Calculator - Calculate ASME 31.3 allowable pressure
• ASTM A53 B Carbon Steel Pipes - Allowable Pressure - Maximum working pressure of carbon steel pipe at temperature 400^oF
• Bursting and Collapsing Pressures of ASTM A312 Stainless Steel Pipes - The theoretic bursting and collapsing values of stainless steel pipes - ASTM A312
• CTS Sized CPVC Tubes - Pressure and Temperature Ratings - CTS - Copper Tube Sized CPVC (Chlorinated Poly Vinyl Chloride) tubes - temperature and pressure ratings
• Pressure and Temperature Ratings ASTM A-53, A-106 and API 5L Grade B Carbon Steel Pipes - Metric Units - Pressure (kPa) and temperature (^oC) ratings of ASTM A-106, API 5L and ASTM A-53 Seamless Carbon Steel Pipes - temperatures ranging -29 ^oC - 450 ^oC
• Pressure and Temperature Ratings of A-53 B, A-106 B, A333, A334 and API 5L Carbon Steel Pipes - Imperial Units - Pressure (psig) and temperature (deg F) ratings for A-53 B and A-106 B, A333, A334 and API 5L carbon steel pipes - temperatures ranging 100 ^oF - 700 ^oF
• Steel Tubes - Working Pressures - Normal maximum working pressures for steel tubes - in psi (lb/in²) and kPa (kN/m²)
• Steels - Endurance Limits and Fatigue Stress - Endurance limits and fatigue stress for steels
• Stress in Thick-Walled Cylinders - or Tubes - Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure
• Surge - Water Hammer - Rapidly closing or opening valves - or starting stopping pumps - may cause pressure transients in pipelines known as surge or water hammers
• Temperature and Strength of Metals - Influence of temperature on strength of metals
• Working Pressure Copper Tubes Type K, L and M - ASTM B88 seamless copper water tubes - working pressures
• Wrought Steel Pipe - Bursting Pressures - Theoretical bursting and working pressure of wrought steel standard, extra strong and double extra strong pipes
• Young's Modulus - Tensile and Yield Strength for common Materials - Young's Modulus or Tensile Modulus alt. Modulus of Elasticity - and Ultimate Tensile and Yield Strength for steel, glass, wood and other common materials

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In engineering, shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear.

In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.g. beams, plates, or bolts). In a reinforced concrete beam, the main purpose of reinforcing bar (rebar) stirrups is to increase the shear strength.

Equations[edit]

Yield Strength Formula Calculation

For shear stress${\displaystyle \tau }$ applies

${\displaystyle \tau =\frac{{\sigma }_1-{\sigma }_3}{2},}$

where

${\displaystyle {\sigma }_1}$ is major principal stress and

${\displaystyle {\sigma }_3}$ is minor principal stress.

In general: ductile materials (e.g. aluminum) fail in shear, whereas brittle materials (e.g. cast iron) fail in tension. See tensile strength.

To calculate:

Given total force at failure (F) and the force-resisting area (e.g. the cross-section of a bolt loaded in shear), ultimate shear strength (${\displaystyle \tau }$) is:

${\displaystyle \tau =\frac{F}{A}=\frac{F}{\pi r_{bolt}^2}=\frac{4F}{\pi d_{bolt}^2}}$

Tensile Yield Strength Formula

For average shear stress

${\displaystyle \tau (avg)=\frac{V}{A}}$

where

${\displaystyle \tau (avg)}$ is the average shear stress,

${\displaystyle V}$ is the shear force applied to each section of the part, and

${\displaystyle A}$ is the area of the section.^[1]

Average shear stress can also be defined as the total force of ${\displaystyle V}$ as

${\displaystyle V=\int \tau dA}$

This is only the average stress, actual stress distribution is not uniform. In real world applications, this equation only gives an approximation and the maximum shear stress would be higher. Stress is not often equally distributed across a part so the shear strength would need to be higher to account for the estimate.^[2]

Comparison[edit]

As a very rough guide relating tensile, yield, and shear strengths:^[3]

Shear Yield Strength Formula

USS: Ultimate Shear Strength, UTS: Ultimate Tensile Strength, SYS: Shear Yield Stress, TYS: Tensile Yield Stress

There are no published standard values for shear strength like with tensile and yield strength. Instead, it is common for it to be estimated as 60% of the ultimate tensile strength. Shear strength can be measured by a torsion test where it is equal to their torsional strength.^[4][5]

When values measured from physical samples are desired, a number of testing standards are available, covering different material categories and testing conditions. In the US, ASTM standards for measuring shear strength include ASTM B831, D732, D4255, D5379, and D7078. Internationally, ISO testing standards for shear strength include ISO 3597, 12579, and 14130.^[7]

See also[edit]

References[edit]

1. ^Hibbeler, Russell. Mechanics of materials. ISBN1-292-17828-0. OCLC1014358513.
2. ^'Mechanics eBook: Shear and Bearing Stress'. www.ecourses.ou.edu. Retrieved 2020-02-14.
3. ^'Shear Strength of Metals'. www.roymech.co.uk.
4. ^'Shear Strength - Instron'. www.instron.us. Retrieved 2020-02-14.
5. ^Portl; Portl, bolt com; Bolt; Company, Manufacturing; St, Inc 3441 NW Guam; Portl; PT547-6758, OR 97210 USA Hours: Monday-Friday 6 AM to 5 PM. 'Calculating Yield & Tensile Strength'. Portland Bolt. Retrieved 2020-02-14.
6. ^Watson, DC (May 1982). Mechanical Properties of E293/1581 Fiberglass-Epoxy Composite and of Several Adhesive Systems(PDF) (Technical report). Wright-Patterson Air Force, Ohio: Air Force Wright Aeronautical Laboratories. p. 16. Retrieved 24 October 2013.
7. ^S. Grynko, 'Material Properties Explained' (2012), ISBN1-4700-7991-7, p. 38.

Pipe Yield Strength Formula