University of Florida/Egm3520/s13.team1.r6

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TEAM 1: REPORT


R6.1: Problem 4.101[edit]

Figure P4.101.
Contents taken from Page 274 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Contents taken from Page 274 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664


Knowing that the magnitude of the horizontal force P is 8 kN, determine the stress at (a) point A, (b) point B.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R6.1 Solution[edit]

  • We must first analyze the cross sectional area.
  • Next calculate the moment of inertia of the rectangular cross section.
  • Next calculate the centroid of the rectangle
  • Next we show a free body diagram of the forces present on the bracket

FBD6.1.jpg

  • Find the eccentricity
  • Calculate the bending couple using P = 8kN and e = 0.033m
  • Now we can calculate the stresses
  • Stress induced at point A:
  • Stress induced at point B:


R6.2: Problem 4.103[edit]

Figure P4.102.
Contents taken from Page 274 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Contents taken from Page 274 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

The vertical portion of the press of the press shown consists of a rectangular tube of wall thickness t = 8 mm. Knowing that the press has been tightened on wooden planks being glued together until P = 20 kN, determine the stress at (a) point A, (b) point B.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R6.2 Solution[edit]

Given(s):

  • Rectangular cutout is 64 mm x 44 mm
  • Stress induced at point A:
  • Stress induced at point B:


R6.3: Problem 4.112[edit]

Figure P4.112.
Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

* Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664. (*) = Reference to listed textbook

An offset h must be introduced into a metal tube of 0.75 in outer diameter and 0.08 in wall thickness. Knowing the maximum stress after the offset is introduced must not exceed 4 times the stress in the tube when it is straight, determine the largest offset that can be used.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R6.3 Solution[edit]

GIVEN
Term Desig Value
Outer Diameter
Thickness
Inner Diameter
Area
Stress


  • The internal forces in the cross section are equivalent to a centric force P and a bending curve M. (*) Ex:4.07 on pg 272
  • EQ 4.49 on page 270(*) states:
(Where F = Force at centroid, P = Line of action load, M = Moment, and d = offset distance.)
  • EQ 4.5 on page 271(*) states:
(Distance from centroid)
  • The Moment of Inertia of a Hollowed Cylindrical Cross-Section:
  • To ensure the the max stress does not exceed 4 times the stress in the tube and making an assumption that P = 1, we can derive the following solution:




R6.4: Problem 4.114[edit]

Figure P4.114 and P4.115.
Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664. (*) = Reference to listed textbook

A vertical rod is attached at point A to the cast iron hanger shown. Knowing that the allowable stress in the hanger are and , determine the largest downward force and the largest upward force that can be exerted by the rod.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.

R6.4 Solution[edit]

  • Max allowable stresses on the hanger:
  • Find centroid:
  • Take as a distance measured from left end of shape.
  • Due to same parameters,
  • Due to same parameters,


  • Must incorporate the parallel axis theorem to find moment of inertia:
b = base, h = height, A = area, and d = perpendicular distance between centroidal axis and parallel axis
  • Due to same parameters,
Total moment of inertia is:
  • The normal stress at point A is due to bending:
  • "The internal forces in the cross section are equivalent to a centric force P and a bending couple M " (Example Problem 4.07 page 272(*)):
distance of the force from the centroid of the cross section. (EQ 4.49 page 270 (*))
Normal stress due to centric load:
  • Combine:
(EQ4.50, p.221(*))
Total normal stress acting at point A.


  • Largest downward force:
  • Assuming conventions: = distance of acting force from the centroid
  • Largest upward force:
  • The limiting factor is at 7.86 kips force upward.
  • Apply negative sign throughout equation:
  • The Downward force becomes:
  • The Upward Force becomes:


Limit is at



R6.5: Problem 4.115[edit]

Figure P4.114 and P4.115.
Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664.

Contents taken from Page 276 in the Mechanics of Materials: 6th Edition textbook. Authors: F.P BEER, E.R. JOHNSTON, J.T. DEWOLF AND D.F. MAZUREK ISBN:9780077565664

A vertical rod is attached at point B to the cast iron hanger shown. Knowing that the allowable stress in the hanger are and , determine the largest downward force and the largest upward force that can be exerted by the rod.

Honor Pledge: On my honor, I have neither given nor received unauthorized aid in doing this assignment.


R6.5 Solution[edit]



Figure P4.114 and P4.115.
3D Representation of Figure 4.115
  • Max allowable stresses on the hanger:
  • Find centroid:
  • Take as a distance measured from left end of shape.
  • Due to same parameters,
  • Due to same parameters,



  • Must incorporate the parallel axis theorem to find moment of inertia:
b = base, h = height, A = area, and d = perpendicular distance between centroidal axis and parallel axis
  • Due to same parameters,
Total moment of inertia is:
  • The normal stress at point A is due to bending:
  • "The internal forces in the cross section are equivalent to a centric force P and a bending couple M " (Example Problem 4.07 page 272(*)):
distance of the force from the centroid of the cross section. (EQ 4.49 page 270 (*))
Normal stress due to centric load:
  • Combine:
(EQ4.50, p.221(*))
Total normal stress acting at point A.


  • Largest downward force:
  • Assuming conventions: = distance of acting force from the centroid
  • Largest upward force:
  • Apply negative sign throughout equation:


Egm3520.s13.Jeandona (discusscontribs) 12:47, 10 April 2013 (UTC)