BIBLIOGRAFIA
• Bernard J. Hamrock, Elementos de máquinas.
Ed. Mc Graw Hill.
• Robert L. Norton, Diseño de máquinas. Ed.
Prentice Hall.
• Shigley, Diseño en Ingeniería Mecánica, Ed.
Mc Graw-Hill
Load, Stress and Strain
When I am working on a problem, I never think
about beauty. I only think of how to solve the
problem. But when I have finished, if the solution
is not beautiful, I know it is wrong.
Richard Buckminster Fuller
Image: A dragline lifts a large load in a
mining operation.
A Simple Crane
Figure 2.1 A simple crane and
forces acting on it. (a) Assembly
drawing; (b) free-body diagram
of forces acting on the beam.
text reference: Figure 2.1, page 30
Supports and Reactions
Table 2.1: Four types of support with their
corresponding reactions.
text reference: Table 2.1, page 35
Ladder Free Body Diagram
Figure 2.5: Ladder having contact with the house
and the ground while having a painter on the ladder.
Used in Example 2.4. The ladder length is l.
text reference: Figure 2.5, page 36
Load Classification
Figure 2.2 Load classified as to location and method of application. (a) Normal,
tensile (b) normal, compressive; (c) shear; (d) bending; (e) torsion; (f) combined
text reference: Figure 2.2, page 31
Sign Convention
Figure 2.3 Sign convention used
in bending. (a) y coordinate
upward; (b) y coordinate
downward.
text reference: Figure 2.3, page 32
Lever Assembly
Figure 2.4 Lever assembly and results.
(a) Lever assembly; (b) results showning
(1) normal, tensile, (2) shear, (3)
bending, (4) torsion on section B of lever
assembly.
text reference: Figure 2.4, page 33
Beam Supports
Figure 2.8 Three types of beam support. (a) Simply supported; (b) cantilevered; (c)
overhanging.
text reference: Figure 2.8, page 39
Simply Supported Bar
Figure 2.9 Simply supported bar with (a) midlength load and reactions; (b) free-body
diagram for 0<x<l/2; (c) free body diagram for l/2<x<l; (d) shear and bending moment
diagrams.
text reference: Figure 2.9, page 40
Singularity Functions (Part 1)
Table 2.2 Six singularity and load intensity functions with corresponding graphs and
expressions.
text reference: Table 2.2, page 43
Singularity Functions (Part 2)
Table 2.2 Six singularity and load intensity functions with corresponding graphs and
expressions.
text reference: Table 2.2, page 43
Shear and Moment Diagrams
Figure 2.10 (a) Shear and (b) moment diagrams for Example 2.8.
text reference: Figure 2.10, page 44
Example 2.10
Ø6mm
□25mm
Ø10mm
Figure 2.12 Figures used in Example 2.10. (a) Load assembly drawing; (b) free-body
diagram.
text reference: Figure 2.12, page 48
Example
Se desea transmitir una potencia de 40 CV a través de un eje que gira a 1500 rpm
mediante una chaveta de profundidad máxima= 6 mmy L= 12 mm.
Datos: eje macizo de Øext=45.
Example
40 CV a 1500 rpm H/2= 6 mmy L= 12
mm.Datos: eje macizo de Øext=45.
Mt 
71720 CV

71720  40
n
Mt  Ft  r  Ft  Mt
Ft
d 

Ac
Ft
 1912 , 5 kg  cm
1500
Ft
W L

Ft
r

850
1, 2  1, 2
1912 , 5
2 , 25
 590 , 3
850
 850 kg
kg
cm
 1180 , 5
kg
S S Y  0 , 577 S Y  0 ,577  3800  2196 , 2
kg
d 

Ap
n cd 
n pd 
h
2
S SY
d
Sy
d

L

0 , 6  1, 2
2196 , 2
 3,7
590 , 3

2196 , 2
1180 ,5
 1,86
Determinación de cargas
2
Determinación de esfuerzos
cm
2
Aplicación Criterio de Fallo
cm
2
Determinación del coeficiente de
seguridad para un material, en este
caso AISI1040 615/380
General State of Stress
Figure 2.13 Stress element showing general state of three-dimensional stress with
origin placed in center of element.
text reference: Figure 2.13, page 49
2-D State of Stress
Figure 2.14 Stress element showing two-dimensional state of stress. (a) Three
dimensional view; (b) plane view.
text reference: Figure 2.14, page 51
Equivalent Stresses
Figure 2.15 Illustration of equivalent stresss states; (a) Stress element oriented in the
direction of applied stress. (b) stress element oriented in different (arbitrary)
direction.
text reference: Figure 2.15, page 52
Stresses in Oblique Plane
Figure 2.16 Stresses in oblique plane at angle .
text reference: Figure 2.16, page 52
Stresses in Oblique Plane
 
x  y

2
 
2
 x  y
2




 x  y
cos 2   xy sen 2
sen 2   xy cos 2
 0  tan 2 
2 xy
 x  y
 x 
 0  tan 2  
y
2 xy
text reference: Shigley pag 28,29
 
 x  y
2
sen 2   xy cos 2
Mohr’s Circle
Figure 2.17 Mohr’s circle
diagram of Eqs. (2.13) and
(2.14).
text reference: Figure 2.17, page 55
Mohr’s Circle Example
Un elemento con el siguiente estado tensional. Se desea: a) hallar los esfuerzos y
las direcciones principales e indicar en el elemento su orientación correcta, con
respecto al sistema xy. Se trazará otro elemento en que se muestren T1 y T2,
determinando los esfuerzos normales correspondientes y marcando los signos
letras.
 80



50
0
0

0 MPa

0 
text reference: Shigley, page 31-32
Results from Example
Figure 2.18 Results from Example
2.13 (a) Mohr’s circle diagram;
(b) stress element for principal normal
stresses shown in x-y coordinates;
(c) stress element for principal stresses
shown in x-y coordinates.
text reference: Figure 2.18, page 57
Mohr’s Circle for Triaxial Stress State
Figure 2.19 Mohr’s circle for triaxial stress state. (a) Mohr’s circle representation;
(b) principal stresses on two planes.
text reference: Figure 2.19, page 59
Example 3.5
Figure 2.20 Mohr’s circle diagram for
Example 3.5. (a) Triaxial stress state when
1=23.43 ksi, 2=4.57 ksi, and 3=0; (b)
biaxial stress state when 1=30.76 ksi and
2=-2.760 ksi; (c) triaxial stress state when
1=30.76 ksi, 2=0, and 3=-2.76 ksi.
text reference: Figure 2.20, page 60
Stresses on Octahedral Planes
Figure 2.21 Stresses acting on octahedral planes. (a) General state of stress. (b)
normal stress; (c) octahedral shear stress.
text reference: Figure 2.21, page 61
Normal Strain
Figure 2.22 Normal strain of cubic element subjected to uniform tension in x
direction. (a) Three dimensional view; (b) two-dimensional (or plane) view.
text reference: Figure 2.21, page 64
Shear Strain
Figure 2.23 Shear strain of cubic element subjected to shear stress. (a) Three
dimensional view; (b) two-dimensional (or plane) view.
text reference: Figure 2.23, page 65
Plain Strain
Figure 2.24 Graphical depiction of plane strain element. (a) Normal strain x; (b) normal
strain y; and (c) shear strain xy.
text reference: Figure 2.24, page 66
Circular Bar with
Tensile Load
Figure 4.10 Circular bar with
tensile load applied.
text reference: Figure 4.10, page 149
Example
text reference: Figure 2.12, page 48
Twisting due to Applied Torque
Figure 4.11 Twisting of member due to
applied torque.
 
r
l
Hipotesis de Coulomb: secciones
transversales circulares, permanecen planas.
Principio de Saint Venant: secciones
transversales no circulares.
text reference: Figure 4.11, page 152
Bending of a Bar
Figure 4.12 Bar made of
elastomeric material to illustrate
effect of bending. (a)
Undeformed bar; (b) deformed
bar.
text reference: Figure 4.12, page 156
Elements in Bending
Figure 4.14 Undeformed and deformed
elements in bending.
text reference: Figure 4.14, page 157
Bending Stress Distribution
Figure 4.15 Profile view of bending stress variation.
text reference: Figure 4.15, page 158
Las secciones más económicas, serán aquellas que tengan el
mayor módulo resistente wz, con el menor gasto de material.
¿Calcular b´ tal que tengan el mismo valor de Wx?
Example 4.10
Figure 4.16 U-shaped cross section experiencing bending moment,
used in Example 4.10.
text reference: Figure 4.16, page 159
Curved Member in Bending
 
( r  rn ) d 
r
text reference: Figure 4.17, page 161
Curved Member in Bending
 
( r  rn ) d 
  E 
r
Condición: sumatorio de esfuerzos en el rn=0
  dA 
Ed 

A
A  rn 
A
dA
r

A
( r  rn )
dA  0
r
A
 0  rn 

A
dA
r
E ( r  rn ) d 
r
Curved Member in Bending
  E 
M 
 (r  r
n
)(  dA ) 
A
Ed 

E ( r  rn ) d 
r

A
( r  rn )
2
dA 
r
Ed  
dA  Ed 
2

  rdA  rn A  rn A  rn 

  A
r 

A
rn 

A
M 
r  EAe
r  rn
 
Mc
Aer
dA
r
Ed 

2
( r  2 rr n  rn )
2

dA 
r
A

 Ed 
Ae
  rdA  rn A  

 A

_
r 
1
A
 r dA
A
_
e  ( r  rn )
Cross Section of Curved Member
Figure 4.18 Rectangular cross
section of curved member.
text reference: Figure 4.18, page 162
Example: Cross Section of Curved Member
Una sección transversal rectangular
de un elemento curvo, tiene las
dimensiones:
b= 1´ y h=r0-ri=3´, sometida a
un momento de flexión puro de
20000lbf-pulg.
Hallar:
a)
Elemento recto.
b)
Elemento curvo. r=15´.
c)
Elemento curvo. r=3´.
text reference: Figure 4.18, page 162
Tabla de Ganchos
Example: Cross Section of Curved Member
Una sección trapezoidal de un
elemento curvo, tiene las
dimensiones:
ri=10 cm
F= 125 kg
Tadm=1380 Kg/cm2
Hallar: valor de a.
rn  ri 
h b1  2 b 0
3 b1  b 0
text reference: Figure 4.18, page 162
Development of Transverse Shear
Figure 4.19 How transverse shear is developed.
text reference: Figure 4.19, page 165
Maximum Shear Stress
Table 4.3 Maximum shear
stress for different beam cross
sections.
text reference: Table 4.3, page 168
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