{"id":8538,"date":"2023-01-05T22:15:49","date_gmt":"2023-01-05T21:15:49","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=8538"},"modified":"2024-06-08T18:34:58","modified_gmt":"2024-06-08T17:34:58","slug":"how-to-calculate-and-solve-for-linear-elastic-modulus-of-resilience-mechanical-properties","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2023\/01\/05\/how-to-calculate-and-solve-for-linear-elastic-modulus-of-resilience-mechanical-properties\/","title":{"rendered":"How to Calculate and Solve for Linear Elastic Modulus of Resilience | Mechanical Properties"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents linear elastic modulus of resilience. To calculate linear elastic modulus of resilience, two essential parameters are needed and these parameters are Stress at y-direction (\u03c3y<\/sub>)\u00a0<\/strong>and\u00a0Strain at y-direction (\u03b5y<\/sub>).<\/strong><\/p>\n

The formula for calculating linear elastic modulus of resilience:<\/strong><\/h3>\n

Ur<\/sub>\u00a0= 0.5\u03c3y<\/sub>\u03b5y<\/sub><\/p>\n

Where:<\/p>\n

Ur<\/sub>\u00a0= Linear Elastic Modulus of Resilience
\n\u03c3y<\/sub>\u00a0= Stress at y-direction
\n\u03b5y<\/sub>\u00a0= Strain at y-direction<\/p>\n

Given an example;
\nFind the linear elastic modulus of resilience when the stress at y-direction is 33 and the strain at y-direction is 11.<\/p>\n

This implies that;<\/p>\n

\u03c3y<\/sub> = Stress at y-direction = 33
\n\u03b5y<\/sub> = Strain at y-direction = 11<\/p>\n

Ur<\/sub>\u00a0= 0.5\u03c3y<\/sub>\u03b5y<\/sub>
\nThat is, Ur<\/sub> = 0.5(33)(11)
\nUr<\/sub> = 0.5(363)
\nUr<\/sub> = 181.5<\/p>\n

Therefore, the\u00a0linear elastic modulus of resilience\u00a0<\/strong>is\u00a0181.5 Pa.<\/strong><\/p>\n

Calculating the Stress at y-direction when the Linear Elastic Modulus of Resilience and the Strain at y-direction are Given<\/strong><\/h3>\n

\u03c3y<\/sub> = Ur<\/sub><\/sup> \/ 0.5\u03b5y<\/sub><\/sub><\/p>\n

Where:<\/p>\n

\u03c3y<\/sub>\u00a0= Stress at y-direction
\nUr<\/sub>\u00a0= Linear Elastic Modulus of Resilience
\n\u03b5y<\/sub>\u00a0= Strain at y-direction<\/p>\n

Let’s solve an example;
\nFind the stress at y-direction when the linear elastic modulus of resilience is 40 and the strain at y-direction is 20.<\/p>\n

This implies that;<\/p>\n

Ur<\/sub> = Linear Elastic Modulus of Resilience = 40
\n\u03b5y<\/sub> = Strain at y-direction = 20<\/p>\n

\u03c3y<\/sub> = Ur<\/sub><\/sup> \/ 0.5\u03b5y<\/sub><\/sub>
\nThen, \u03c3y<\/sub> = 40<\/sup> \/ 0.5(20)<\/sub>
\n\u03c3y<\/sub> = 40<\/sup> \/ 10<\/sub>
\n\u03c3y<\/sub> = 4<\/p>\n

Therefore, the\u00a0stress at y-direction\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Hooke’s Law Linear Elastic Modulus of Resilience | Mechanical Properties<\/a><\/p>\n

Calculating the Strain at y-direction when the Linear Elastic Modulus of Resilience and the Stress at y-direction are Given<\/strong><\/h3>\n

\u03b5y<\/sub> = Ur<\/sub><\/sup> \/ 0.5\u03c3y<\/sub><\/sub><\/p>\n

Where:<\/p>\n

\u03b5y<\/sub>\u00a0= Strain at y-direction
\nUr<\/sub>\u00a0= Linear Elastic Modulus of Resilience
\n\u03c3y<\/sub> = Stress at y-direction<\/p>\n

Let’s solve an example;
\nFind the strain at y-direction when the linear elastic modulus of resilience is 24 and the stress at y-direction is 12.<\/p>\n

This implies that;<\/p>\n

Ur<\/sub> = Linear Elastic Modulus of Resilience = 24
\n\u03c3y<\/sub> = Stress at y-direction = 12<\/p>\n

\u03b5y<\/sub> = Ur<\/sub><\/sup> \/ 0.5\u03c3y<\/sub><\/sub>
\n\u03b5y<\/sub> = 24<\/sup> \/ 0.5(12)<\/sub>
\nSo, \u03b5y<\/sub> = 24<\/sup> \/ 6<\/sub>
\n\u03b5y<\/sub> = 4<\/p>\n

Therefore, the\u00a0strain at y-direction\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

How to Calculate Linear Elastic Modulus of Resilience With Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the linear elastic modulus of resilience.<\/p>\n

\n

To get the answer and workings of the linear elastic modulus of resilience using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><\/p>\n

Apple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n<\/div>\n

<\/p>\n

Now, Click on\u00a0Mechanical Properties<\/strong>\u00a0<\/b>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on Linear Elastic Modulus of Resilience <\/b>under\u00a0Mechanical Properties<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the linear elastic modulus of resilience according to the respective parameter which is the Stress at y-direction (\u03c3y<\/sub>)\u00a0<\/strong>and\u00a0Strain at y-direction (\u03b5y<\/sub>).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Stress at y-direction (\u03c3y<\/sub>)<\/strong> is 33 <\/strong>and Strain at y-direction (\u03b5y<\/sub>)<\/strong> is 11<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the linear elastic modulus of resilience and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents linear elastic modulus of resilience. To calculate linear elastic modulus of resilience, two essential…","protected":false},"author":5,"featured_media":16641,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Linear Elastic Modulus of Resilience","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Master the steps and the formula on How to Calculate and Solve for Linear Elastic Modulus of Resilience in Mechanical 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