Equations of Equilibrium.
F  0
M O  0
Fx  0
Fy  0
Fz  0
M x  0
M y  0
M z  0
Fx  0
Fy  0
M O  0
Example
Determine the resultant internal loadings acting on the
cross section at C of the machine shaft. The shaft is
supported by bearings at A and B, which exert only
vertical force on the shaft.
ESFUERZO
DISTRIBUCIÓN DEL ESFUERZO NORMAL PROMEDIO
+↑ FRz =  Fz;
 dF   dA
A
P  A
P

A
EJEMPLO
La lámpara de 800 N está sostenida por dos barras AB y
BC. Si AB tiene un diámetro de 10 mm y BC tiene un
diámetro de 8 mm, determine el esfuerzo normal medio en
cada barra.
ESFUERZO CORTANTE PROMEDIO
 prom
V

A
Cortante simple
Cortante doble
EJEMPLO
The wooden strut is suspended froma10mm diameter steel
rod, which is fastened to the wall. If the strut supports a vertical
load of 5kN, compute the average shear stress in the rod at the
wall and along the two shaded planes of the strut, one of which
is indicated as abcd.
SOLUCIÓN
Esfuerzo cortante promedio
V
5000 N
 
 63.7 MPa
2
A   0.005m 
Para la barra,
 prom
Para el puntal,
 prom 
V
2500 N

 3.12 MPa
A  0.04m  0.02m 
Ans....
Ans....
The average-shear-stress distribution on the sectioned rod and
strut segment as shown in figs. (d) and (e), respectively. Also
shown with these figures is a typical volume element of the
material taken at a point located on the surface of each section.
Note carefully how the shear stress must act on each shaded
face of these elements and then on the adjacent faces of the
elements.