Study Guide for MEAT-3624 Exam 1

EXAM 1 REVIEW MEAT-3624 E-351 INTRODUCTION TO POLYMERIC MATERIALS

  • Instructor: Prof. Michael Bartlett

  • Department: Mechanical Engineering

  • Institution: Iowa State University

EXAM 1 DETAILS

  • Duration: 75 minutes

  • Requirements:

    • Complete the exam independently.

    • No books or notes allowed.

    • One handwritten equation sheet permitted, size 8.5 x 11 inches, single sided.

    • Note: Include units in all answers.

EXAM FORMAT

  • Section A: Multiple Choice

  • Section B: Short Answer Questions

  • Section C: Quantitative Problems

TOPICS COVERED

  • Schedule of topics with readings to be studied:

    • 8-25 T: Introduction, Course Information, Design, Safety Factor, Free Body Diagram (FBD), Reading: 1-7 through 1-11, 1-14, 1-16

    • 8-27 Th: Shear and Moment Diagrams, Stress, Strain, Mohr's Circle, Reading: 3-1 through 3-2, 3-4 through 3-8

    • 9-01 T: Normal Stress (Axial, Bending), Shear Stress (Torsional Shear, Torsion), Reading: 3-9 through 3-12

    • 9-03 Th: Combined Stresses (2-Plane Bending), Stress Concentration, Reading: 3-12 through 3-13

    • 9-08 T: Pressure Vessels, Press and Shrink Fits, Reading: 3-14, 3-16

    • 9-10 Th: Thermal Strain, Contact Stresses, Reading: 3-17, 3-19

    • 9-15 T: Static Failure Theory: Ductile (MNST, MSS, DE), Reading: 2-1 through 2-3, 2-8, 5-1 through 5-7

    • 9-17 Th: Static Failure Theory: Brittle (MNS, BCM, M1M), Reading: 5-8 through 5-10

    • 9-22 T: Fracture Mechanics, Reading: 5-11, 5-12

    • 9-24 Th: Buckling: Euler, Johnson, Buckling Design, Eccentric Loading, Reading: 4-11 through 4-16

STRESSES AND MOHR CIRCLE

  • Context of stress analysis covered was based on Mohr's Circle principles.

FREE-BODY DIAGRAM EXAMPLE

  • See Example (3–1(2)) for contextual understanding.

STRESS ANALYSIS

  • Key focus includes fundamental aspects of stress and strain analysis related to materials.

STRESS ELEMENT

  • Defined by:

    • Figure 3–8: Displays general three-dimensional stress and plane stress configuration.

    • Represents stress at a designated point, with arbitrary coordinate directions, emphasizing that choice of coordinates can yield principal stresses by nullifying shear stress.

BIAXIAL STRESS STATES

  • Analytical approach for determining stress along various directions in similar systems is indicated by angular dependence.

PRINCIPAL STRESSES: PLANE STRESS

  • Maximum and minimum shear stresses occur 45° from the principal axes, which is a critical calculation point. Description of shear variations is explored in principle mechanics.

MOHR’S CIRCLE DIAGRAM

  • Figure 3−10: Contextualizes stress analysis implementation using graphical Mohr's Circle, illustrating principal and shear stresses in relation to mechanical design principles.

BEAM BENDING AND TORSION

  • Subject outlines maximum bending stress calculations and the equations related.

    • Normal stresses for beams in bending:

      • Maximum bending stress occurs where the distance 'y' is greatest.

      • Notation used includes:
        ext{Max Stress} = rac{M c}{I} (Equation 3 - 26)

      • Section modulus denoted as:
        Z = rac{I}{c}

TRANSVERSE SHEAR STRESS

  • Analysis includes:

    • Subjected to the accompanying bending stress.

    • Equations include:
      au = rac{V Q}{I b} (Equation 3 - 31)

SIGNIFICANCE OF TRANSVERSE SHEAR COMPARED TO BENDING

  • Evaluations based on cantilever beams with rectangular cross-sections to define maximum shear stresses as related to bending stresses.

    • Normalization leads to the equation describing combined maximum shear through calculations represented in graphs and dimensional analysis.

TORSIONAL SHEAR STRESS

  • Established that for round bars in torsion, the shear stress is proportional to the radius, with maximum stress present at the outer surface, leading to:
    au = rac{T r}{J}
    ext{Max shear} au_{max} = T rac{r}{J}

TWO-PLANE BENDING

  • Analyzed configurations of bending in both x-y and x-z planes.

    • Derivation includes complex relationships between maximum bending stress across cross-section configurations.

EXAMPLE OF BENDING AND STRESS

  • Example calculations introduced with the load and stress identification based on given geometries and applied forces, including:

    • Reactions, bending moments indicated in both xy and xz planes.

    • Notations for moments were given as:
      M{xy} ext{ and } M{xz}

STRESS CONCENTRATIONS

  • Inglis Expression:

    • Given with parameters indicating dependency on the flaw size and type leading to defining maximum stress concentration at a point.

PRESSURE VESSELS AND FITTINGS

  • Focused studies on internal pressure within cylinders, leading to stress evaluations characterized through established equations.

    • For thin-walled vessels:

      • Relationships defined alongside assumptions of uniform stress distribution. Equations derived include:
        au{t} = rac{p{i} d}{2t}

PRESS AND SHRINK FITS

  • Delves into the contact stresses arising due to radial interference, dependent on both geometrical and material considerations.

THERMAL STRAIN

  • Investigation into temperature-induced normal strain and resultant thermal stresses, capturing the equations:
    rac{
    ho}{E} = rac{ au}{ rac{eta}{ ext{dT}}}

CONTACT STRESSES

  • Analysis provided focusing on spherical contact stresses with formulas pertinent to geometrical configurations and applied forces.

    • Maximum pressures modeled through averaging methods yielding to equations based on stress distributions.

MATERIAL STRENGTH AND STIFFNESS

  • Provided discourse on stress-strain diagrams and definitions for yield strength and ultimate strength.

    • Illustrative diagrams indicate behaviors across elastic to plastic deformation ranges and define methods to ascertain these measurements.

FAILURE CRITERIA

  • Explores the need for static failure theories dealing with both uniaxial and multi-axial stress states.

    • Maximum Shear Stress Theory (MSS) summarized alongside distortion energy theory indicating operational philosophy towards constructing safe designs.

FRACTURE MECHANICS

  • Introduces fracture descriptors and stress intensity factors with detailed equations derived for standard and non-standard configurations relevant to engineering design principles.

    • Foundational equations define critical stresses exceeding material capacities, emphasizing design safety.

BUCKLING OF COLUMNS

  • Analyzed through theoretical constructs of Euler’s formula for pin-ended columns established with critical loads.

    • Calculated conditions characterized by end conditions, leading to specified constants intended for conservative structural designs.