Deformation

1
Deformation
Let me tell you the secret that has led me to my
goal. My strength lies in my tenacity. Louis
Pateur
Image High speed photographs of a club striking
a golf ball. Note the large deformations in the
golf ball.
2
Normal Stress
Figure 5.6 Element subjected to normal stress
text reference Figure 5.6, page 195
3
Shear Stress
Figure 5.7 Element subjected to shear stress.
text reference Figure 5.7, page 197
4
Twisting due to Applied Torque
Figure 4.11 Twisting of member due to applied
torque.
Hipotesis de Coulomb secciones transversales
circulares, permanecen planas. Principio de
Saint Venant secciones transversales no
circulares.
text reference Figure 4.11, page 152
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Example 5.1
Figure 5.1 Cantilevered beam with concentrated
force applied at free end. Used in Example 5.1.
text reference Figure 5.1, page 184
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Examen septiembre 2006
1/ Un resorte de una puerta tiene sección
rectangular 50x6 (mm) y longitud 800 mm. Uno de
sus extremos se haya empotrado y en el otro se
producen deflexiones entre 75 y 150 mm
cíclicamente. Determinar el coeficiente de
seguridad en la sección más peligrosa en a)
caso citado b) si a L/2 se le practica un taladro
de O 12,5mm. Condiciones de carga de (a) Material
estirado en frio, E210Gpa, Su1034MPa y ? 0,3
Fiabilidad 90 aT20ºC3 puntos
text reference Figure 5.1, page 184
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Cantilever with Moment and Concentrated Force
Figure 5.5 Bar fixed at one end and free at
other with moment applied to free end and
concentrated force at any distance from free end.
(a) Complete assembly (b) free-body diagram
showing effect of concentrated force (c)
free-body diagram showing effect of moment.
text reference Figure 5.5, page 194
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Example 5.8
Figure 5.8 Cantilevered bar with concentrated
force acting at distance b from free end. (a)
Coordinate system and important points shown
(b) fictitious force shown along with
concentrated force.
text reference Figure 5.8, page 203
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Free Body Diagram of Simply Supported Beam
Figure 5.2 Free-body diagram of force anywhere
between simply supported ends. (a) Complete bar
(b) portion of bar.
text reference Figure 5.2, page 187
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Cantilevered Bar with Partial Distributed Load
Figure 5.3 Cantilevered bar with unit step
distribution over part of bar. (a) Loads and
deflection acting on cantilevered bar (b)
free-body diagram of forces and moments acting on
entire bar (c) free-body diagram of forces and
moments acting on portion of bar.
text reference Figure 5.3, page 189
11
Cantilever with Simply Supported End
Figure 5.4 Cantilevered bar with other end
simply supported and with concentrated force
acting anywhere along bar. (a) Sketch of
assembly (b) free-body diagram of entire bar
(c) free-body diagram of part of bar.
text reference Figure 5.4, page 191
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Deflection of Beams
Table 5.1 Deflection for three different
situations when one end is fixed and one end is
free and two different situations of simply
supported beams.
text reference Table 5.1, page 193
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Deflection of Beams (cont.)
Table 5.1 Deflection for three different
situations when one end is fixed and one end is
free and two different situations of simply
supported beams.
text reference Table 5.1, page 193
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Método del momento de área
La distancia vertical entre un punto cualquiera A
en la curva de flexión y la tangente a la curva
en otro punto B es igual al momento estático con
respecto a A del área del diagrama del momento
flexionante entre A y B, dividido entre la
rigidez.
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Strain EnergyAplicación Método de Castigliano
Table 5.2 Strain energy for four types of
loading.
text reference Table 5.2, page 200
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Example 5.9
Figure 5.9 Cable system arrangement. (a) Entire
assembly (b) free-body diagram of forces acting
at point A.
text reference Figure 5.9, page 204
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Example 5.10
Figure 5.10 Cantilevered bar with 90 bend acted
upon by horizontal force at free end.
text reference Figure 5.10, page 205
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Design of FOPS
Figure 5.11 Figures used in case study. (a)
Forklift truck (b) FOPS details (not to scale)
(c) idealized FOPS for analysis.
text reference Figure 5.11, page 207
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FOPS Cross Brace Analysis
Figure 5.12 (a) Free-body (b) shear and (c)
bending moment diagrams for FOPS cross brace.
text reference Figure 5.12, page 208