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Minor edits #422

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7bd2112
Minor edits
mihikad2 Jan 28, 2026
13daa22
Page updates
mihikad2 Feb 3, 2026
c219709
Introduction added
mihikad2 Feb 4, 2026
9bd218c
Update design_considerations.astro
mihikad2 Feb 4, 2026
0522df7
Update intro.astro
mihikad2 Feb 4, 2026
04328f8
Updates
mihikad2 Feb 18, 2026
ff5ab62
Update design_considerations.astro
mihikad2 Feb 18, 2026
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8 changes: 4 additions & 4 deletions src/components/Navbar.astro
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Expand Up @@ -221,7 +221,7 @@ const path = Astro.url.pathname;
}

.solids-menu{
columns: 2;
columns: 1;
}

@media (width <= 578px){
Expand Down Expand Up @@ -426,7 +426,7 @@ const path = Astro.url.pathname;
</li>
<li class="dropdown mega nav-item " class-value="sol">
<a class="nav-link dropdown-toggle" aria-haspopup="true" aria-expanded="false" aria-label="About" class-value="sol">
<span>Solid mechanics</a></span>
<span>Solid mechanics</span>
</a>
<div class="dropdown-menu tile-list px-2" id="mainnav-solids">
<div class="d-flex" >
Expand All @@ -443,7 +443,7 @@ const path = Astro.url.pathname;
</section>
<section class = "tile menu white-box col">
<h2><a href = "/dyn" aria-label = "About">Simple Loading</a></h2>
<ol style = "column-fill: balance-all;" class = "course-menu dynamics-menu">
<ol style = "column-fill: balance-all;" class = "course-menu solids-menu">
<li><a href="/sol/overview?origin=sidebar">Overview</a></li>
<li><a href="/sol/axial_loading?origin=sidebar">Axial loading</a></li>
<li><a href="/sol/torsion?origin=sidebar">Torsion</a></li>
Expand All @@ -453,7 +453,7 @@ const path = Astro.url.pathname;
</section>
<section class = "tile menu white-box col">
<h2><a href = "/dyn" aria-label = "About">Combined Loading</a></h2>
<ol style = "column-fill: balance-all;" class = "course-menu dynamics-menu">
<ol style = "column-fill: balance-all;" class = "course-menu solids-menu">
<li><a href="/sol/shear_&_moment_diagrams?origin=sidebar">Shear & moment diagrams</a></li>
<li><a href="/sol/beam_deflection?origin=sidebar">Beam deflection</a></li>
<li><a href="/sol/pressure_vessels?origin=sidebar">Pressure vessels</a></li>
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6 changes: 5 additions & 1 deletion src/pages/sol.astro
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Expand Up @@ -16,7 +16,11 @@ import "../../public/static/css/course_home_pages.css"
</h1>

<h2 class="site-title">Introduction/Big Picture:</h2>

<section class="mt-sm-4 mt-2">
<ol>
<li><a href="/sol/intro?origin=coursemenu">Introduction</a></li>
</ol>
</section>

<h2 class="site-title">Material Behavior:</h2>
<section class="mt-sm-4 mt-2">
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33 changes: 0 additions & 33 deletions src/pages/sol/axial_bending.astro
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2 changes: 1 addition & 1 deletion src/pages/sol/axial_loading.astro
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Expand Up @@ -29,7 +29,7 @@ import DisplayEquation from "../../components/DisplayEquation.astro"

<Section title="Axial Loading" id="axial_loading"></Section>

<SubSection title="Pure Axial Loading Tensor" id="tensor">
<SubSection title="Stress Tensor from Pure Axial Loading" id="tensor">
<p>
For a scenario with only axial loading conditions, the stress tensor can be simplified as shown below.
</p>
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2 changes: 1 addition & 1 deletion src/pages/sol/bending.astro
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Expand Up @@ -49,7 +49,7 @@ A beam in bending will develop normal (tensile and compressive) bending stresses

</Section>

<SubSection title="Pure Bending Tensor" id="tensor">
<SubSection title="Stress Tensor from Pure Bending" id="tensor">
<p>
For pure bending loading conditions, the stress tensor can be simplified as shown below, depending on whether bending occurs around the y or z axis.
</p>
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122 changes: 117 additions & 5 deletions src/pages/sol/design_considerations.astro
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Expand Up @@ -9,22 +9,133 @@ import Item from "../../components/Item.astro"
import InlineEquation from "../../components/InlineEquation.astro"
import DisplayEquation from "../../components/DisplayEquation.astro"
import BlueText from "../../components/BlueText.astro"
import Example from "../../components/Example.astro"


---
<Layout title="Design Considerations">

<div slot="navtree">
<ul class='list-group list-group-flush py-0'>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#limit_states'>Limit States</a>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#failure_modes'>Limit States</a>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#allowable_strength_design'>Allowable Strength Design</a>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#load_resistance_factor'>Load Resistance Factor</a>
</li>
</ul>
</div>

<Section title="Design Considerations" id="design_considerations"></Section>
<SubSection title="Limit States" id="limit_states"> </SubSection>
<SubSection title="Failure Modes" id="failure_modes">
<p>
Broadly speaking, the goal of a design is to prevent unwanted behaviors (or
failure modes) from occurring. There can be, and usually are, many different
failure modes which need to be considered simultaneously.
</p>

<p>
For example, consider just 2 plates bolted together and loaded to failure:

<Itemize>
<Item><iframe src="https://www.youtube.com/embed/5EjQUEBQyuY" class="w-50" title="Normal Failure" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe></Item>
<Item><iframe src="https://www.youtube.com/embed/sTAkcSVlIWE" class="w-50" title="Shear Failure" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe></Item>
<Item><iframe src="https://www.youtube.com/embed/GrIgQAAsVsI" class="w-50" title="Bolt Failure" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe></Item>
</Itemize>
</p>

<p>
It is the job of the engineer to anticipate and design for all relevant failure modes. For a given design, successful operation may require:
<Itemize>
<Item> Stresses stay below material limits (see <a href = "https://www.mechref.org/sol/failure_theories/?origin=coursemenu#von-mises"> Von Mises failure criteria </a>) </Item>
<Item> Stress from cyclic loading stays below the fatigue limit (see the <a href = "https://www.mechref.org/mf/Fatigue/?origin=coursemenu"> Fatigue reference page </a>) </Item>
<Item> Buckling is prevented (see the <a href = "https://www.mechref.org/sol/buckling/?origin=coursemenu"> Buckling reference page </a>) </Item>
<Item> Deformation stays below a prescribed limit (see the <a href = "https://www.mechref.org/sol/beam_deflection/?origin=coursemenu"> Beam Deflection reference page </a>) </Item>
<Item> Vibration deformation from dynamic loads stays below a prescribed limit <!-- (see ME340 page doesn’t exist yet) --!> </Item>
<Item> And more </Item>
</p>

<p>
Any way a product or component can fail to meet the desired performance can be referred to as a failure mode. These are occasionally categorized as
<Itemize>
<Item> <strong> Strength: </strong> exceeding the limit state results in material failure </Item>
<Item> <strong> Stability: </strong> exceeding the limit state results in a stability failure (like
<a href = "https://www.mechref.org/sol/buckling/?origin=coursemenu"> buckling</a> or
<a href="https://www.mechref.org/sta/friction/?origin=coursemenu#tip_slip"> overturning</a>) </Item>
<Item> <strong> Serviceability: </strong> exceeding the limit state results in compromised performance (excessive deflection) </Item>
</Itemize>
</p>

<p>
It can be very difficult to anticipate every possible failure mode. This broad view
of component performance is discussed in the <a href = "https://www.mechref.org/design/pds/?origin=coursemenu"> Product Design Specifications reference</a> page. In solid
mechanics, we’ll focus on the strength failure modes.

<p>
Note that the nomenclature can vary between industries, but the intent is the
same, to identify potential failures and design to prevent them, or reduce the risk
(probability x severity) to an acceptably low level.
</p>

<Example id="auto" title="Automotive" solution="False">
<div class="d-flex flex-column">
<p class="w-100">

<em> Design Failure Mode and Effects Analysis: </em>
Design FMEA is a type of FMEA that analyzes the product design, focusing on potential design-related
deficiencies, with emphasis on improving the design and ensuring product operation is safe and reliable
during useful life.
<div class="mb-2 w-100"></div>

For more information, check out: <a href = "https://saemobilus-sae-org.proxy2.library.illinois.edu/standards/j1739_202101-potential-failure-mode-effects-analysis-fmea-including-design-fmea-supplemental-fmea-msr-process-fmea"> SAE J1739_202101 </a>
<div class="mb-3 w-100"></div>
</p>
</div>
</Example>

<Example id="aero" title="Aerospace" solution="False">
<div class="d-flex flex-column">
<p class="w-100">
<em> Failure Mode and Effects Analysis (FMEA): </em>
A procedure by which each potential failure mode or fault of a system is analyzed to determine the
consequences or effects thereof on the system, to classify each potential failure mode according to its
severity, and to recommend actions to eliminate, or compensate for, unacceptable effects.
<div class="mb-2 w-100"></div>

For more information, check out: <a href = "https://saemobilus-sae-org.proxy2.library.illinois.edu/standards/arp5580-recommended-failure-modes-effects-analysis-fmea-practices-non-automobile-applications"> SAE ARP5580 </a>
<div class="mb-3 w-100"></div>
</p>
</div>
</Example>

<Example id="civil" title="Civil" solution="False">
<div class="d-flex flex-column">
<p class="w-100">
<em> Limit State: </em>
A condition beyond which a structure or member becomes unfit for service and is judged either to be no
longer useful for its intended function (serviceability limit state) or to be unsafe (strength limit state).
<div class="mb-2 w-100"></div>

For more information, check out: <a href = "https://ascelibrary-org.proxy2.library.illinois.edu/doi/epdf/10.1061/9780784415788"> ASCE7 </a>

<div class="mb-3 w-100"></div>
</p>
</div>
</Example>

<Example id="gov" title="US Government" solution="False">
<div class="d-flex flex-column">
<p class="w-100">
<em> Failure mode and effects analysis (FMEA): </em>
A procedure by which each potential failure mode in a system is analyzed to determine the results or
effects thereof on the system and to classify each potential failure mode according to its severity.
<div class="mb-2 w-100"></div>

For more information, check out: <a href = "https://www.dsiintl.com/wp-content/uploads/2017/04/mil_std_1629a.pdf"> MIL-STD-1629A </a>

</p>
</div>
</Example>

</SubSection>

<SubSection title="Allowable Strength Design" id="allowable_strength_design">

Expand All @@ -47,9 +158,6 @@ A structure is safe if its strength exceeds the required strength.

Similarly, <DisplayEquation equation="\\sigma_{all} \\le \\frac{\\sigma_u}{FS}\\" title="Maximum allowed applied stress." background="True"/>

</SubSection>

<SubSection title="Load and Resistance Factor Design" id="load_resistance_factor">
<p>
Depending on the industry or application, the acceptability of a design may be interpreted differently.
For some applications showing a factor of safety of 4 may be sufficient.
Expand All @@ -58,6 +166,10 @@ For example, a sling used for lifting, such as the one shown below, is specified

<Image src='/sol/design_considerations/Web_Sling.png' width='8'><a href="https://www.mcmaster.com/8864T51/">Web sling</a></Image>


</SubSection>

<SubSection title="Load and Resistance Factor Design" id="load_resistance_factor">
<p>
In the civil/structural engineering industry, the variability of loading (wind, seismic, etc.) has been studied extensively.
This is also true for various structural capacities in building materials like steel, concrete wood, etc. Given a loading and resistance that are both random variables, a simple “safety factor” does not result in a consistent level of probability of failure across all structures.
Expand Down
6 changes: 4 additions & 2 deletions src/pages/sol/geometric_properties.astro
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Expand Up @@ -23,6 +23,7 @@ import DisplayTable from "../../components/DisplayTable.astro"
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#first-moi'>Centroid</a></li>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#second-moi'>Area Moment of Inertia</a></li>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#polar_moment_of_inertia'>Polar Moment of Inertia</a></li>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#simple_shapes_moi'>Simple Shapes Moment of Inertia</a></li>
<li class='list-group-item py-0'><a class='text-decoration-none subsection' href='#summary-moi'>Summary: Moment of Inertia</a></li>
</ul>
</div>
Expand Down Expand Up @@ -97,7 +98,7 @@ The moment of inertia of the area <InlineEquation equation='A' /> with respect t

</SubSection>

<SubSection title="Summary: Moment of Inertia" id="summary-moi">
<SubSection title="Moment of Inertia of Simple Shapes" id="simple_shapes_moi">

<center><em>Common shapes about the origin: <InlineEquation equation='I'/> and <InlineEquation equation='J_O'/></em></center>
<center><em>Common shapes about the centroid: <InlineEquation equation='\\bar{I}'/> and <InlineEquation equation='J_c'/></em></center>
Expand Down Expand Up @@ -226,8 +227,9 @@ The moment of inertia of the area <InlineEquation equation='A' /> with respect t
</tbody>

</DisplayTable>
</SubSection>

<SubSection title="Summary: Moment of Inertia" id="summary-moi">
<DisplayTable class_="text-center" id="inertia-table">
<thead>
<tr>
Expand Down
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