update mee342 hw1 and index.html

Author: antantantant

index.html

@@ -53,12 +53,12 @@ <h3>Selected Publications</h3>
   <h3>Current Students</h3>
   <ul>
     <li>Mukesh Ghimire (PhD, co-advised by Dr. Zhe Xu) – Differential games</li>
-    <li>Sheng Cheng (PhD, co-advised by Dr. Yezhou Yang) – AI for science</li>
     <li>Guangyu Nie (PhD) – AI for science </li>
   </ul>
 
   <h3>Past Students</h3>
   <ul>
+    <li>Sheng Cheng (PhD, co-advised by Dr. Yezhou Yang) - Amazon </li>
     <li>Lei Zhang (PhD) – Postdoc at Purdue</li>
     <li>Ruijin Cang (PhD) – Google</li>
     <li>Houpu Yao (PhD) – Google</li>

mee342_hw1_2026.md

@@ -0,0 +1,112 @@
+---
+layout: default
+title: MEE342 Homework 1 2026
+---
+
+### Instructions
+
+1. Please submit a single **PDF** file on Canvas.
+2. If you have codes, please put them in the same PDF file.
+3. This homework is **DUE on Feb. 1**.
+
+### Disclaimer
+Images for Problems 2 and 3 are taken from Shigley's.
+
+
+### Problem 1 (10 Points)
+
+For the plane stress $\sigma_x = -8MPa$, $\sigma_y = 7MPa$, $\tau_{xy} = 6MPa$ cw, 
+draw a Mohr's circle diagram properly labeled,
+   find the principal normal and shear stresses, and determine the angle from the 
+   $x$ axis to $\sigma_1$. 
+   Draw stress elements as in Fig. 3-11c and d (Shigley's) and label all details.
+
+
+### Problem 2 (30 Points)
+
+A countershaft carrying two V-belt pulleys is shown in the figure. Pulley A receives power from a
+   motor through a belt with the belt tensions shown. The power is transmitted through the shaft and
+   delivered to the belt on pulley B. Assume the belt tension on the loose side at B is 15 percent of
+   the tension on the tight side.
+   
+   * Determine the tensions in the belt on pulley B, assuming the shaft is running at a constant
+   speed.
+   
+   * Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple
+   supports.
+   
+   * Draw shear-force and bending-moment diagrams for the shaft. If needed, make one set for the
+   horizontal plane and another set for the vertical plane.
+   
+   * At the point of maximum bending moment, determine the bending stress and the torsional
+   shear stress.
+   
+   * At the point of maximum bending moment, determine the principal stresses and the maximum
+   shear stress.
+   
+<img src="/_images/mechdesign/hw1_3.png" alt="Drawing" style="height: 400px;"/> 
+
+### Problem 3 (20 Points)
+
+The cantilevered bar in the figure is made from a ductile material and is statically loaded with
+  $F_y = 200lbf$ and 
+  $F_x = F_z = 0$. Analyze the stress situation in rod AB by obtaining the following
+   information.
+   
+   * Determine the precise location of the critical stress element.
+   
+   * Sketch the critical stress element and determine magnitudes and directions for all stresses acting
+   on it. (Transverse shear may only be neglected if you can justify this decision.)
+   
+   * For the critical stress element, determine the principal stresses and the maximum shear stress.
+   
+<img src="/_images/mechdesign/hw1_4.png" alt="Drawing" style="height: 400px;"/> 
+
+### Problem 4 (20 Points for Part 1 and 2)
+
+Consider a cantilever beam as shown in the figure with length 
+$l$ and the left end fixed to a wall.
+
+1. Derive the deflection $y$  of the beam along 
+$x$ under a single downward force $F$ on the right,
+and assume that the moment of inertia $I$  is constant along 
+$x$. 
+(Show complete derivation instead of the final function 
+$y(x)$) 
+
+2. Now consider that the beam has two connected parts, with the part on the left (of length 
+$l/2$) having a moment of 
+inertia 
+$I_1$, 
+and the part on the right 
+$I_2$. 
+Derive the deflection $y$ again.
+ Ignore stress concentration.
+
+3. Further, consider that the cross-sections for the two parts are both circular, and the total volume
+of the beam is constant. What should 
+$I_1$ and 
+$I_2$ be for the beam to have minimal maximum deflection? (Optional)
+
+<img src="/_images/mechdesign/hw1_5.png" alt="Drawing" style="height: 200px;"/> 
+
+### Problem 5 (20 Points)
+
+1. *Form your project team*. Choose from one of these: (1) Shaft, (2) Gear + Bearing + key. Each team should have at most 5 people.
+
+2. *Formulate a pseudo code (flow chart) for component-wise analysis and design*. 
+
+* For shaft teams, please read Chapter 6 on Fatigue Failure Resulting from Variable Loading and 
+Chapter 7 on Shafts and Shaft Components (Sections 7-4 to 7-5). Start with Example 7-2 that runs through the whole design process, 
+list down the concepts you do not understand, and then seek answers to these questions from Chapters 6 and 7. 
+
+* For gear+ teams, please read Chapter 13 Gears-General Sections 13-1 to 13-8 and 13-13 and 
+Chapter 14 Spur and Helical Gears. For Chapter 14, start with Section 14-19 and the example within, list down 
+the concepts you do not understand, and then seek answers from the chapter. For bearing and key, 
+please read Chapter 11 on Rolling-Contact Bearings and Chapter 7 Section 7-7. 
+
+* The pseudo code should specify (1) the inputs, e.g., 
+static and dynamic loading conditions, geometry, target safety factors, (2) the outputs, e.g., 
+detailed component geometry design, material selection, performance metrics, and (3) the design flow.
+
+* As a starting point, your submission does not have to be perfect but needs to show your best effort.