added HW2-4 for MEE342

Author: antantantant

mee342_hw2_2026.md

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+---
+layout: default
+title: MEE342 Homework 2 2026
+---
+
+### Problem 1
+Let's use an *overly simplified* model to investigate the difference in side impact safety 
+between a convertible and a regular car. Specifically, we consider the side panels and the roof
+panel as beams, each with length $l$, second-area moment $I$, cross-section area $A$, and Young's 
+modulus $E$. 
+	
+* Derive the spring rate $k$ for the convertible. ($k=F/\delta$, where $\delta$ is the deflection 
+due to $F$.)
+* Derive the free-body diagram for the regular car.
+* Derive the spring rate for the regular car, by assuming that the horizontal beam does not buckle.
+Note: Need to take into account the compression of the horizontal beam.
+
+<img src="/_images/mechdesign/hw2_car.png" alt="Drawing" style="height: 400px;"/> 
+
+
+### Problem 2
+Consider the bridges in the figure. Assume all joints are frictionless (truss element).
+Find the deflections at the loading point given the loading and the truss members' Young's 
+modulus and cross section area. If truss members fail due to large tensional stress, which bridge is a better design?
+
+<img src="/_images/mechdesign/hw2_bridge.png" alt="Drawing" style="height: 400px;"/> 
+
+<script>
+  window.MathJax = {
+    tex: { inlineMath: [['$', '$'], ['\\(', '\\)']] }
+  };
+</script>
+<script defer src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>

mee342_hw3_2026.md

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+---
+layout: default
+title: MEE342 Homework 3 2026
+---
+
+### Disclaimer
+Images for Problems are taken from Shigley's (9th edition).
+
+### Problem 1
+
+A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa.
+Using the distortion-energy and maximum-shear-stress theories determine the factors of safety
+for the following principal stresses:
+
+* $\sigma_A = 100 MPa$, $\sigma_B = 100 MPa$
+* $\sigma_A = 100 MPa$, $\sigma_B = -100 MPa$
+* $\sigma_A = -50 MPa$, $\sigma_B = -100 MPa$
+
+### Problem 2
+
+A ductile material has the properties 
+$S_{yt}=60ksi$, $S_{yc}=75ksi$ Using the ductile Coulomb-Mohr theory, 
+determine the factor of safety for the states of stress given below:
+
+* $\sigma_x = 25 kpsi$, $\sigma_y = 15 kpsi$
+* $\sigma_x = -12 kpsi$, $\sigma_y = 15 kpsi$, $\tau_{xy} = -9 kpsi$
+
+### Problem 3
+
+A brittle material has the properties $S_{ut} = 30 kpsi$, $S_{uc} = 90 kpsi$. 
+Using the brittle Coulomb-Mohr and modified-Mohr theories, 
+determine the factor of safety for the following states of
+plane stress.
+
+* $\sigma_x = -15 kpsi$, $\sigma_y = 10 kpsi$, $\tau_{xy} = -15 kpsi$
+* $\sigma_x = 15 kpsi$, $\sigma_y = -15 kpsi$
+
+
+### Problem 4 
+
+Determine the actual factor of safety for yielding for problem 2 from 
+[HW1](/mechdesign_homework/2018/01/16/homework1.html). 
+Use the distortion-energy theory. The material is 1018 CD steel.
+
+### Problem 5
+
+The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C. The
+forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made of
+AISI 1035 CD steel. Using distortion-energy theory with a design factor of 2, determine the
+minimum shaft diameter to avoid yielding.
+
+<img src="/_images/mechdesign/hw2_1.png" alt="Drawing" style="height: 400px;"/>
+
+<script>
+  window.MathJax = {
+    tex: { inlineMath: [['$', '$'], ['\\(', '\\)']] }
+  };
+</script>
+<script defer src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>

mee342_hw4_2026.md

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+---
+layout: default
+title: MEE342 Homework 4 2026
+---
+
+### Disclaimer
+Images for Problems are taken from Shigley's (9th edition).
+
+### Problem 1
+
+Two steels are being considered for manufacture of as-forged connecting rods subjected to 
+bending loads. One is AISI 4340 Cr-Mo-Ni steel capable of being heat-treated to a tensile 
+strength of 260 ksi. The other is a plain carbon steel AISI 1040 with a ultimate strength of 
+113 ksi. Each rod is to have a size giving an equivalent diameter of 0.75 in. Determine the 
+endurance limit for each material. Is there any advantage to using the alloy steel for this 
+fatigue application?
+
+### Problem 2
+
+A 1-in-diameter solid round bar has a groove 0.1-in deep with a 0.1-in radius machined into it.
+ The bar is made of AISI 1020 CD steel and is subjected to a purely reversing torque of 1800 
+ lb-in. For the S-N diagram of this material, let f=0.9.
+ 
+* Estimate the number of cycles to failure.
+
+* If the bar is also placed in an environment with a temperature of 750 F, estimate the 
+number of cycles to failure.
+
+### Problem 3
+The cold-drawn AISI 1040 steel bar shown in the figure is subjected to an axial load 
+fluctuating between 0kN and 28kN. Estimate the fatigue factor of safety based on achieving 
+infinite life using modified Goodman criterion and the yielding factor of safety. 
+If infinite life is not predicted, estimate the number of cycles to failure.
+
+<img src="/_images/mechdesign/hw3_1.png" alt="Drawing" style="height: 400px;"/> 
+
+### Problem 4
+First, complete [this tutorial](https://courses.ansys.com/index.php/courses/plate-with-a-hole-optimization/lessons/problem-specification-lesson-1-30/) to get familiar with structure design in ANSYS. 
+For more explanations on ANSYS Optimization, please check [this tutorial](https://designinformaticslab.github.io/productdesign_tutorial/2016/11/20/ansys.html).
+
+Then choose one of the following structure design problems to solve using ANSYS.
+1. The "Chopsticks" that catch SpaceX BFRs during their landing.
+2. A bridge. To narrow down the design specifications, you could refer to any famous bridges, e.g., the Mathematical Bridge at Cambridge. 
+
+For the problem of your choice: 
+* Clearly explain your design objectives, variables, constraints, and assumptions.
+* Find and validate the optimal design.
+   
+<script>
+  window.MathJax = {
+    tex: { inlineMath: [['$', '$'], ['\\(', '\\)']] }
+  };
+</script>
+<script defer src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>