Page 22 - 4749

Figure 1.11

Internal force factors can be expressed by full stress
components. Consider the elementary area dA of the cross section
A (fig.1.11). On the area dA there are elementary forces dA ,
 dA ,  dA. Multiplying each elemental force by a distance
y z
corresponding to the axis, we obtain the basic aspects of internal
forces:

dM   dA y   dA z  ,
x z y
dM   dA z  ,
y
dM   dA y  .
z

Summing the elementary forces and moments on the cross-
sectional area, we get the integral relationship between internal
force and stress factors:



N   dA ; M   z y  y  z dA ; 
x 
x 
A A 

Q   y dA ; M   zdA ;  (1.2)
y 
y 
A A 

z 
Q   z dA ; M   ydA . 
z 
A A 

1.8 Model of a deformable rod

The model of deformable rod is based on the system of
hypotheses, which validity has been confirmed experimentally.

22