Portland Community College | Portland, Oregon

Upon completion of the course students will be able to:

• Analyze a simple mechanical design or system to determine external (input) and reaction forces using computer aided engineering (CAE) tools and hand calculations.  
• Apply knowledge of how applied forces and loads affect a mechanical design and the resulting internal stresses.  
• Evaluate internal stresses in a mechanical design and determine if a design has sufficient factor of safety to eliminate design failures.  
• Apply good mechanical and product design practices to achieve design optimization relating to material usage, weight, cost and factor of safety.
• Correlate hand calculations and assumptions relating to internal stresses of a mechanical design to computer aided analysis. 
• Communicate and understand technical design topics related to statics and mechanics of materials with engineering and technical product development teams.  

• Define a force vector and how forces and reactions equate to static equilibrium on a physical system. Use mathematical (trigonometric) and graphical CAD techniques to resolve forces into rectangular components (and the resultant of distributed loads) to solve for the resultant forces.  Apply equations of equilibrium to solve for any unknown reactions.

• Create a free body diagram of forces on a static physical system and rigid bodies with various supports acted upon by external forces including rotational (moments and couples) and friction effects.   

• Establish center of gravity and centroids of various geometries using hand calculations and CAD/CAE.  Define and calculate, by hand, the moment of inertia for various simple geometries.  Determine moments of inertias for complex geometries using CAD for structural and mechanical analysis.   

• Define stress, allowable stress and calculate internal reactions and induced stresses at various locations within an object.  Calculate the factor of safety for a static loaded system in equilibrium.  Apply various design techniques to reduce internal stresses.  

• Apply Hooke’s law and demonstrate graphically and mathematically the linear and nonlinear relationships between stress and strain.  Define and explain the critical points of interest on a stress/strain diagram for ductile and brittle materials and how it relates to the strength of the material and how designs are affected under loads.  Use best design practices to improve a design for internal stress reduction.  Define Young’s modulus and its application.  

• Calculate the torsional shear stresses and deformations in solid shafts, hollow shafts and other mechanical components used for power transmission.  Use best design practices to improve a design for internal stress reduction reduction of material usage related to cost.  

• Using CAD/CAE analysis and/or tables of data for different geometries, use equations to calculate various beam deflections (including cantilever and simply supported beams).  Determine Von Mises equivalent stress on various static systems using CAD and how it relates to the material strength properties and factor of safety.  

• Complete activities, assignments, and exams, which show an understanding of the connection between external forces and the resultant internal stresses and possible deformation of members in a static system.  

• Complete assignments, projects, test or quiz problems, and class activities which apply real-life situations to statics and mechanics of materials and factor of safety for simple designs.  

• Show an understanding of statics and mechanics of materials in a variety of forms through the use of activities, exam problems, design projects and/or discussions, multiple representations.

• Participate in, and contribute to, class discussions and activities.

• Take all scheduled examinations.

The following must be assessed in a proctored, (allowing one page/one sided formulas and note sheet) setting:

• Find the resultant of concurrent forces

• Create a free body diagram (FBD) of a design system showing external and reaction forces

• Calculate internal stresses and any deformations due to external forces.  

• Determine internal stresses and the factor of safety for a system in static equilibrium

At least two proctored, closed-book, one page/one sided formula notes, examinations (one of which is the comprehensive final) must be given. These exams must consist primarily of free response questions although a limited number of multiple choice and/or ll in the blank questions may be used where appropriate.

Assessment must include evaluation of the students ability to arrive at correct conclusions using proper mathematical procedures and notation. Additionally, each student must be assessed on their ability to use appropriate organizational strategies and write appropriate conclusions. Application problems must be answered in complete sentences.

At least two of the following additional measures must also be used

• Take-home examinations

• Graded homework

• Quizzes

• Projects

• In-class activities

• Portfolios

THEMES:

• The relationship between external forces and induced stresses for systems in equilibrium.  

• Importance of preventing catastrophic failures in design through use of statics and mechanics of materials.  Use of best design practices to reduce internal stresses or deformations and optimize amount of material used.  

• Problem solving

• Effective communication

• Critical thinking

SKILLS:

FORCE RESULTANTS AND EQUILIBRIUM

• Determine components (x and y direction) of a vector using trigonometry and CAD 2D graphical techniques via angles and constraints.  Note the directions of the resultant components and how it relates to the equilibrium equation sign convention.  (Such as sum of forces in x-direction is positive to the right)

• Draw a free body diagram showing forces acting on a system in equilibrium for systems and rigid bodies.  

• Compute the moment of a force, forces that form a couple.  Application of units for moments (such as ft-lbs).  

• Determine the magnitude and location of the resultant loads for uniform and triangular distributed loads.  Divide geometry into simpler shapes (triangles, rectangles) to determine areas for calculations and location for the equivalent force. 

• Apply algebra to solve the equations of equilibrium for systems and rigid bodies and determine reaction forces for supports.  The forces in the x-direction, y-direction and sum of moments must equate to zero.  Know standard support reactions for rollers, pins, fixed joints, etc.  

  CENTER OF GRAVITY, CENTROIDS AND MOMENTS OF INERTIA OF AREAS

• Locate the centroid of simple geometries.  This could be done by inspection and/or analysis.  

• Use CAD and tables of data to determine moment of inertias of complex geometries and standard structural beam cross sections.  

• Correlate hand calculations with those done on CAD using FEA.

   INTERNAL REACTIONS FOR AXIAL LOADS: STRESS AND STRAIN

• Determine the internal reactions --axial forces, shear forces, and bending moments created in objects that are acted on by external loads.  

• Sketch a stress strain diagram of a typical steel material.  Label the critical points such as elastic limit, proportional limit, yield point, ultimate strength, etc.  Explain why and how these critical points may affect a design under applied loads.  

   SHEAR STRESS AND STRAIN: TORSION     

• Define and calculate the material property, modulus of rigidity.  

• Compute shear stresses and angle of twist of a hollow shaft, determine if suitable for meeting design parameters.  

• Analyze shafts, keys, bolted flanges and couplings in a typical power transmission system.  Use good design practices to reduce stress risers in a system.  

 BEAM DEFLECTION, FACTOR OF SAFETY AND COMBINED STRESSES

• Use the beam bending moment equation to determine deflection of a cantilever and simply supported beam acted upon by an outside force.  Correlate results with computer software (CAD).  

• Identify what factor of safety is appropriate for various designs in different applications (aerospace versus construction).  

• Use Von Mises equivalent stress to determine if a design meets factor of safety relative to material strength, availability, cost and space constraints.