CTC / MTC 222 Strength of Materials - PowerPoint PPT Presentation

About This Presentation
Title:

CTC / MTC 222 Strength of Materials

Description:

Title: Structural Analysis Software Author: cim Last modified by: Lawrence R. Dunn Created Date: 3/22/2001 11:56:14 PM Document presentation format – PowerPoint PPT presentation

Number of Views:137
Avg rating:3.0/5.0
Slides: 21
Provided by: cim55
Category:

less

Transcript and Presenter's Notes

Title: CTC / MTC 222 Strength of Materials


1
CTC / MTC 222Strength of Materials
  • Final Review

2
Final Exam
  • Wednesday, December 12, 1015 -1215
  • 30 of grade
  • Graded on the basis of 30 points in increments of
    ½ point
  • Open book
  • May use notes from first two tests plus two
    additional sheets of notes
  • Equations, definitions, procedures, no worked
    examples
  • Also may use any photocopied material handed out
    in class
  • Work problems on separate sheets of engineering
    paper
  • Hand in test paper, answer sheets and notes
    stapled to back of answer sheets

3
Course Objectives
  • To provide students with the necessary tools and
    knowledge to analyze forces, stresses, strains,
    and deformations in mechanical and structural
    components.
  • To help students understand how the properties of
    materials relate the applied loads to the
    corresponding strains and deformations.

4
Chapter One Basic Concepts
  • SI metric unit system and U.S. Customary unit
    system
  • Unit conversions
  • Basic definitions
  • Mass and weight
  • Stress, direct normal stress, direct shear stress
    and bearing stress
  • Single shear and double shear
  • Strain, normal strain and shearing strain
  • Poissons ratio, modulus of elasticity in tension
    and modulus of elasticity in shear

5
Direct Stresses
  • Direct Normal Stress , ?
  • s Applied Force/Cross-sectional Area F/A
  • Direct Shear Stress, ?
  • Shear force is resisted uniformly by the area of
    the part in shear
  • ? Applied Force/Shear Area F/As
  • Single shear applied shear force is resisted by
    a single cross-section of the member
  • Double shear applied shear force is resisted by
    two cross-sections of the member

6
Direct Stresses
  • Bearing Stress, sb
  • sb Applied Load/Bearing Area F/Ab
  • Area Ab is the area over which the load is
    transferred
  • For flat surfaces in contact, Ab is the area of
    the smaller of the two surfaces
  • For a pin in a close fitting hole, Ab is the
    projected area, Ab Diameter of pin x
    material thickness

7
Chapter Two Design Properties
  • Basic Definitions
  • Yield point, ultimate strength, proportional
    limit, and elastic limit
  • Modulus of elasticity and how it relates strain
    to stress
  • Hookes Law
  • Ductility - ductile material, brittle material

8
Chapter Three Direct Stress
  • Basic Definitions
  • Design stress and design factor
  • Understand the relationship between design
    stress, allowable stress and working stress
  • Understand the relationship between design
    factor, factor of safety and margin of safety
  • Design / analyze members subject to direct stress
  • Normal stress tension or compression
  • Shear stress shear stress on a surface, single
    shear and double shear on fasteners
  • Bearing stress bearing stress between two
    surfaces, bearing stress on a fastener

9
Chapter Four Axial Deformation and Thermal
Stress
  • Axial strain e,
  • e d / L , where d total deformation, and L
    original length
  • Axial deformation, d
  • d F L / A E
  • If unrestrained, thermal expansion will occur due
    to temperature change
  • d a x L x ?T
  • If restrained, deformation due to temperature
    change will be prevented, and stress will be
    developed
  • s E a (?T)

10
Chapter Five Torsional Shear Stress and
Deformation
  • For a circular member, tmax Tc / J
  • T applied torque, c radius of cross section,
    J polar moment of inertia
  • Polar moment of Inertia, J
  • Solid circular section, J p D4 / 32
  • Hollow circular section, J p (Do4 - Di4 ) /
    32
  • Expression can be simplified by defining the
    polar section modulus, Zp J / c, where c r
    D/2
  • Solid circular section, Zp p D3 / 16
  • Hollow circularsection, Zp p (Do4 - Di4 ) /
    (16Do)
  • Then, tmax T / Zp

11
Chapter Six Shear Forces and Bending Moments in
Beams
  • Sign Convention
  • Positive Moment M
  • Bends segment concave upward ? compression on
    top

12
Relationships Between Load, Shear and Moment
  • Shear Diagram
  • Application of a downward concentrated load
    causes a downward jump in the shear diagram. An
    upward load causes an upward jump.
  • The slope of the shear diagram at a point (dV/dx)
    is equal to the (negative) intensity of the
    distributed load w(x) at the point.
  • The change in shear between any two points on a
    beam equals the (negative) area under the
    distributed loading diagram between the points.

13
Relationships Between Load, Shear and Moment
  • Moment Diagram
  • Application of a clockwise concentrated moment
    causes an upward jump in the moment diagram. A
    counter-clockwise moment causes a downward jump.
  • The slope of the moment diagram at a point
    (dM/dx) is equal to the intensity of the shear at
    the point.
  • The change in moment between any two points on a
    beam equals the area under the shear diagram
    between the points.

14
Chapter Seven Centroids and Moments of Inertia
of Areas
  • Centroid of complex shapes can be calculated
    using
  • AT Y ? (Ai yi ) where
  • AT total area of composite shape
  • Y distance to centroid of composite shape
    from some reference axis
  • Ai area of one component part of shape
  • yi distance to centroid of the component part
    from the reference axis
  • Solve for Y ? (Ai yi ) / AT
  • Perform calculation in tabular form
  • See Examples 7-1 7-2

15
Moment of Inertia ofComposite Shapes
  • Perform calculation in tabular form
  • Divide the shape into component parts which are
    simple shapes
  • Locate the centroid of each component part, yi
    from some reference axis
  • Calculate the centroid of the composite section,
    Y from some reference axis
  • Compute the moment of inertia of each part with
    respect to its own centroidal axis, Ii
  • Compute the distance, di Y - yi of the
    centroid of each part from the overall centroid
  • Compute the transfer term Ai di2 for each part
  • The overall moment of inertia IT , is then
  • IT ? (Ii Ai di2)
  • See Examples 7-5 through 7-7

16
Chapter Eight Stress Due to Bending
  • Positive moment compression on top, bent
    concave upward
  • Negative moment compression on bottom, bent
    concave downward
  • Maximum Stress due to bending (Flexure Formula)
  • smax M c / I
  • Where M bending moment, I moment of inertia,
    and c distance from centroidal axis of beam to
    outermost fiber
  • For a non-symmetric section distance to the top
    fiber, ct , is different than distance to bottom
    fiber cb
  • stop M ct / I
  • sbot M cb / I

17
Section Modulus, S
  • Maximum Stress due to bending
  • smax M c / I
  • Both I and c are geometric properties of the
    section
  • Define section modulus, S I / c
  • Then smax M c / I M / S
  • Units for S in3 , mm3
  • Use consistent units
  • Example if stress, s, is to be in ksi (kips /
    in2 ), moment, M, must be in units of kip
    inches
  • For a non-symmetric section S is different for
    the top and the bottom of the section
  • Stop I / ctop
  • Sbot I / cbot

18
Chapter Nine Shear Stress in Beams
  • The shear stress, ? , at any point within a beams
    cross-section can be calculated from the General
    Shear Formula
  • ? VQ / I t, where
  • V Vertical shear force
  • I Moment of inertia of the entire cross-section
    about the centroidal axis
  • t thickness of the cross-section at the axis
    where shear stress is to be calculated
  • Q Statical moment about the neutral axis of the
    area of the cross-section between the axis where
    the shear stress is calculated and the top (or
    bottom) of the beam
  • Q is also called the first moment of the area
  • Mathematically, Q AP y , where
  • AP area of theat part of the cross-section
    between the axis where the shear stress is
    calculated and the top (or bottom) of the beam
  • y distance to the centroid of AP from the
    overall centroidal axis
  • Units of Q are length cubed in3, mm3, m3,

19
Shear Stress in Common Shapes
  • The General Shear Formula can be used to develop
    formulas for the maximum shear stress in common
    shapes.
  • Rectangular Cross-section
  • ?max 3V / 2A
  • Solid Circular Cross-section
  • ?max 4V / 3A
  • Approximate Value for Thin-Walled Tubular Section
  • ?max 2V / A
  • Approximate Value for Thin-Webbed Shape
  • ?max V / t h
  • t thickness of web, h depth of beam

20
Chapter Fifteen Pressure Vessels
  • If Rm / t 10, pressure vessel is considered
    thin-walled
  • Stress in wall of thin-walled sphere
  • s p Dm / 4 t
  • Longitudinal stress in wall of thin-walled
    cylinder
  • s p Dm / 4 t
  • Longitudinal stress is same as stress in a sphere
  • Hoop stress in wall of cylinder
  • s p Dm / 2 t
  • Hoop stress is twice the magnitude of
    longitudinal stress
  • Hoop stress in the cylinder is also twice the
    stress in a sphere of the same diameter carrying
    the same pressure
Write a Comment
User Comments (0)
About PowerShow.com