{"id":2229,"date":"2019-09-26T21:22:46","date_gmt":"2019-09-26T20:22:46","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2229"},"modified":"2024-03-09T08:59:12","modified_gmt":"2024-03-09T07:59:12","slug":"how-to-calculate-and-solve-for-bulk-modulus-of-elasticity-e-rock-mechanics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/09\/26\/how-to-calculate-and-solve-for-bulk-modulus-of-elasticity-e-rock-mechanics\/","title":{"rendered":"How to Calculate and Solve for Bulk Modulus of Elasticity (E) | Rock Mechanics"},"content":{"rendered":"

To calculate bulk modulus of elasticity (E), two essential parameters are needed, and these parameters are young\u2019s modulus<\/a> (E)\u00a0<\/strong>and\u00a0Poisson\u2019s ratio (v).<\/strong><\/p>\n

The formula for calculating the bulk modulus of elasticity (E):<\/strong><\/h4>\n

k =\u00a0E<\/sup>\u00a0\/\u00a03(1 – 2v)<\/sub><\/p>\n

Where:<\/p>\n

k = Bulk Modulus of Elasticity (E)
\nE = Young’s Modulus
\nv = Poisson’s Ratio<\/p>\n

Let’s solve an example;
\nFind the bulk modulus of elasticity (E) when the young’s modulus is 66 and the Poisson’s ratio is 58.<\/p>\n

This implies that;<\/p>\n

E = Young’s Modulus = 66
\nv = Poisson’s Ratio = 58<\/p>\n

k =\u00a0E<\/sup>\u00a0\/\u00a03(1 – 2v)<\/sub>
\nk = 66<\/sup>\u00a0\/\u00a03(1 – 2(58))<\/sub>
\nThen, k = 66<\/sup>\u00a0\/\u00a03(1 – 116)<\/sub>
\nk =\u00a066<\/sup>\u00a0\/\u00a03(-115)<\/sub>
\nSo, k = 66<\/sup>\u00a0\/\u00a0-345<\/sub>
\nk = -0.19<\/p>\n

Therefore, the\u00a0bulk modulus of elasticity (E)\u00a0<\/strong>is\u00a0-0.19.<\/strong><\/p>\n

Calculating the Young’s Modulus when the Bulk Modulus of Elasticity (E) and the Poisson’s Ratio are Given<\/strong><\/h3>\n

E = k (3 – 6v)<\/p>\n

Where:<\/p>\n

E = Young’s Modulus
\nk = Bulk Modulus of Elasticity (E)
\nv = Poisson’s Ratio<\/p>\n

Let’s solve an example;
\nFind the young’s modulus when the bulk modulus of elasticity (E) is 22 and the Poisson’s ratio is 18.<\/p>\n

This implies that;<\/p>\n

k = Bulk Modulus of Elasticity (E) = 22
\nv = Poisson’s Ratio = 18<\/p>\n

E = k (3 – 6v)
\nE = 22 (3 – 6(18))
\nSo, E = 22 (3 – 108)
\nE = 22 (-105)
\nE = -2376<\/p>\n

Therefore, the\u00a0young’s modulus\u00a0<\/strong>is\u00a0-2376.<\/strong><\/p>\n

Calculating the Poisson’s Ratio when the Bulk Modulus of Elasticity (E) and the Young’s Modulus are Given<\/strong><\/h3>\n

v = -(E – 3k<\/sup> \/ 6k<\/sub>)<\/p>\n

Where:<\/p>\n

v = Poisson’s Ratio
\nk = Bulk Modulus of Elasticity (E)
\nE = Young’s Modulus<\/p>\n

Let’s solve an example;
\nFind the Poisson’s ratio when the bulk modulus of elasticity (E) is 12 and the young’s modulus is 40.<\/p>\n

This implies that;<\/p>\n

k = Bulk Modulus of Elasticity (E) = 12
\nE = Young’s Modulus = 40<\/p>\n

That is, v = -(E – 3k<\/sup> \/ 6k<\/sub>)
\nv = -(40 – 3(12)<\/sup> \/ 6(12)<\/sub>)
\nv = -(40 – 36<\/sup> \/ 72<\/sub>)
\nSo, v = -(4<\/sup> \/ 72<\/sub>)
\nv = -(0.055)
\nv\u00a0 = -0.055<\/p>\n

Therefore, the\u00a0Poisson’s ratio\u00a0<\/strong>is\u00a0-0.055.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Bulk Modulus of Elasticity (stress) | Rock Mechanics<\/a><\/p>\n

How to Calculate Bulk Modulus of Elasticity (E) Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the bulk modulus of elasticity (E).<\/p>\n

To get the answer and workings of the bulk modulus of elasticity (E) 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>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to 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>
\nApple (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\u00a0Geology<\/strong>\u00a0<\/strong>under\u00a0Add-on.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Rock Mechanics<\/strong>\u00a0<\/strong>under\u00a0Geology<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Bulk Modulus of Elasticity (E)<\/strong>\u00a0under\u00a0Rock Mechanics<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the bulk modulus of elasticity (E) according to the respective parameters which are the young\u2019s modulus (E)\u00a0<\/strong>and\u00a0Poisson\u2019s ratio (v).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the young\u2019s modulus (E)\u00a0<\/strong>is 66 <\/strong>and\u00a0Poisson\u2019s ratio (v)<\/strong> is 58<\/strong>.<\/p>\n

\"How<\/p>\n

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

\"How<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the bulk modulus of elasticity (E) and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"To calculate bulk modulus of elasticity (E), two essential parameters are needed, and these parameters are young\u2019s modulus…","protected":false},"author":5,"featured_media":13188,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Bulk Modulus of Elasticity (E)","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn the steps, guidelines, workings, and formula on How to Calculate and Solve for Bulk Modulus of Elasticity (E) | Rock 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