4/12/2022
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  1. Yield Strength Calculation

Torsional Yield Strength is the stress state causing material to twist or rotate which it can withstand before any twisting failure. The formula for computing the Torsional yield strength in a rod is: Torsional strength = rotational force / cross sectional area. Before the first yield point, the material will have an elastic behavior, which means that it will go back to its initial state if we release the applied strength. Beyond the elastic limit, the material will have a plastic behavior, and permanent deformation will occur.

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Mam Tor road destroyed by subsidence and shear, near Castleton, Derbyshire.
Pipe yield strength formula

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]

A shear force is applied to the top of the rectangle that deform the rectangle into a parallelogram. Having a higher shear modulus of elasticity increases the force needed to deform the rectangle.

For shear stressτ{displaystyle tau } applies

τ=σ1σ32,{displaystyle tau ={frac {sigma _{1}-sigma _{3}}{2}},}

where

σ1{displaystyle sigma _{1}} is major principal stress and
σ3{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 (τ{displaystyle tau }) is:

τ=FA=Fπrbolt2=4Fπdbolt2{displaystyle tau ={frac {F}{A}}={frac {F}{pi r_{bolt}^{2}}}={frac {4F}{pi d_{bolt}^{2}}}}
Yield Strength Formula

For average shear stress

τ(avg)=VA{displaystyle tau scriptstyle (avg)={frac {V}{A}}}

where

τ(avg){displaystyle tau scriptstyle (avg)} is the average shear stress,
V{displaystyle V} is the shear force applied to each section of the part, and
A{displaystyle A} is the area of the section.[1]

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

V=τdA{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]

MaterialUltimate Strength RelationshipYield Strength Relationship
SteelsUSS = approx. 0.75*UTSSYS = approx. 0.58*TYS
Ductile IronUSS = approx. 0.9*UTSSYS = approx. 0.75*TYS .
Malleable IronUSS = approx. 1.0*UTS
Wrought IronUSS = approx. 0.83*UTS
Cast IronUSS = approx. 1.3*UTS
AluminumsUSS = approx. 0.65*UTSSYS = approx. 0.55*TYS

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]

MaterialUltimate stress (Ksi)Ultimate stress (MPa)
Fiberglass/epoxy (23 o C)[6]7.8253.9

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.


Yield Strength Calculation

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