{"id":5190,"date":"2021-03-08T17:23:28","date_gmt":"2021-03-08T16:23:28","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=5190"},"modified":"2024-05-01T16:36:21","modified_gmt":"2024-05-01T15:36:21","slug":"how-to-calculate-and-solve-for-modulus-of-rupture-fracture-mechanics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2021\/03\/08\/how-to-calculate-and-solve-for-modulus-of-rupture-fracture-mechanics\/","title":{"rendered":"How to Calculate and Solve for Modulus of Rupture | Fracture Mechanics"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents modulus of rupture. To calculate modulus of rupture, three essential parameters are needed and these parameters are Bending Moment (M), Distance (c)\u00a0<\/strong>and\u00a0Moment of Inertia (I).
\n<\/strong><\/p>\n

The formula for calculating modulus of rapture:<\/strong><\/h3>\n

\u03c3 = Mc<\/sup> \/ I<\/sub><\/p>\n

Where:<\/p>\n

\u03c3 = Modulus of Rupture
\nM = Bending Moment
\nc = Distance
\nI = Moment of Inertia<\/p>\n

Let’s solve an example;
\nFind the modulus of rupture when the bending moment is 22, the distance is 10 and the moment of inertia is 14.<\/p>\n

This implies that;<\/p>\n

M = Bending Moment = 22
\nc = Distance = 10
\nI = Moment of Inertia = 14<\/p>\n

\u03c3 = Mc<\/sup> \/ I<\/sub>
\nThat is, \u03c3 = 22(10)<\/sup> \/ 14<\/sub>
\n\u03c3 = 220<\/sup> \/ 14<\/sub>
\n\u03c3 = 15.71<\/p>\n

Therefore, the\u00a0modulus of rupture\u00a0<\/strong>is\u00a015.71 Pa.<\/strong><\/p>\n

Calculating the Bending Moment when the Modulus of Rupture, the Distance and the Moment of Inertia are Given<\/strong><\/h3>\n

M = \u03c3 x I<\/sup> \/ c<\/sub><\/p>\n

Where;<\/p>\n

M = Bending Moment
\n\u03c3 = Modulus of Rupture
\nc = Distance
\nI = Moment of Inertia<\/p>\n

Let’s solve an example;
\nFind the bending moment when the modulus of rupture is 22, the distance is 8 and the moment of inertia is 2.<\/p>\n

This implies that;<\/p>\n

\u03c3 = Modulus of Rupture = 22
\nc = Distance = 8
\nI = Moment of Inertia = 2<\/p>\n

M = \u03c3 x I<\/sup> \/ c<\/sub>
\nThat is, M = 22 x 2<\/sup> \/ 8<\/sub>
\nM = 44<\/sup> \/ 8<\/sub>
\nM = 5.5<\/p>\n

Therefore, the\u00a0bending moment\u00a0<\/strong>is\u00a05.5.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Young’s Modulus | Fracture Mechanics<\/a><\/p>\n

Calculating the Distance when the Modulus of Rupture, the Bending Moment and the Moment of Inertia are Given<\/strong><\/h3>\n

c = \u03c3 x I<\/sup> \/ M<\/sub><\/p>\n

Where;<\/p>\n

c = Distance
\n\u03c3 = Modulus of Rupture
\nM = Bending Moment
\nI = Moment of Inertia<\/p>\n

Let’s solve an example;
\nFind the distance when the modulus of rupture is 12, the bending moment is 4 and the moment of inertia is 16.<\/p>\n

This implies that;<\/p>\n

\u03c3 = Modulus of Rupture = 12
\nM = Bending Moment = 4
\nI = Moment of Inertia = 16<\/p>\n

c = \u03c3 x I<\/sup> \/ M<\/sub>
\nSo, c = 12 x 16<\/sup> \/ 4<\/sub>
\nc = 192<\/sup> \/ 4<\/sub>
\nc = 48<\/p>\n

Therefore, the\u00a0distance\u00a0<\/strong>is\u00a048.<\/strong><\/p>\n

Calculating the Moment of Inertia when the Modulus of Rupture, the Bending Moment and the Distance are Given<\/strong><\/h3>\n

I = Mc<\/sup> \/ \u03c3<\/sub><\/p>\n

Where;<\/p>\n

I = Moment of Inertia
\n\u03c3 = Modulus of Rupture
\nM = Bending Moment
\nc = Distance<\/p>\n

Let’s solve an example;
\nFind the moment of inertia when the modulus of rupture is 30, the bending moment is 10 and the distance is 3.<\/p>\n

This implies that;<\/p>\n

\u03c3 = Modulus of Rupture = 30
\nM = Bending Moment = 10
\nc = Distance = 3<\/p>\n

I = Mc<\/sup> \/ \u03c3<\/sub>
\nI = 10 x 3<\/sup> \/ 30<\/sub>
\nThat means, I = 30<\/sup> \/ 30<\/sub>
\nI = 1<\/p>\n

Therefore, the\u00a0moment of inertia\u00a0<\/strong>is\u00a01.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Polar Moment of Inertia | Material Selection<\/a><\/p>\n

How to Calculate Modulus of Rupture With Nickzom Calculator<\/strong><\/h3>\n

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

To get the answer and workings of the modulus of rupture using the\u00a0Nickzom 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 2,000\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\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Fracture Mechanics\u00a0<\/strong>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Modulus of Rupture\u00a0<\/strong>under\u00a0Fracture Mechanics<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the modulus of rupture according to the respective parameters which is the\u00a0Bending Moment (M), Distance (c)\u00a0<\/strong>and\u00a0Moment of Inertia (I).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the\u00a0<\/span>v<\/span>al<\/span>ue appropriately and accordingly for the parameter as required by the\u00a0<\/span>Bending Moment (M)<\/strong>\u00a0is 22<\/strong>, Distance (c)<\/strong>\u00a0is 10\u00a0<\/strong>and\u00a0Moment of Inertia (I)<\/strong>\u00a0is 14<\/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 modulus of rupture and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents modulus of rupture. To calculate modulus of rupture, three essential parameters are needed and…","protected":false},"author":5,"featured_media":14659,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[1475,537,60,1469,543,1477,1476],"class_list":["post-5190","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-bending-moment","tag-distance","tag-engineering","tag-fracture-mechanics","tag-materials-and-metallurgical","tag-modulus-of-rupture","tag-moment-of-inertia","cs-entry"],"yoast_head":"\nHow to 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