DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

Lecture

When a bar is stretched and compressed, its longitudinal and transverse dimensions change (Fig.2.4).

DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

Fig. 2.4

When stretching:

The length of the bar changes to DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

(elongation),

The width of the beam changes to DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

(narrowing).

When compressed:

(shortening)

(increase

Hooke's law expresses a directly proportional relationship between normal stress and relative deformation:

or, if presented in another form:

where E is the modulus of longitudinal elasticity.

This is a physical constant matter, characterizing its ability to resist elastic deformation.

EF is the stiffness of the cross-section of the timber at eastsion-compression.

absolute deformation (cm, m)	dimensionless relative deformation	lateral strain coefficient, Poisson’s ratio
l longitudinal	dredging
b transverse	transverse

The deformation of the timber (tension or compression) causes the displacement of cross sections.

Consider three cases of loading under tension.

In the first case, when a bar is stretched, the section nn moves to the position n ₁ -n ₁ by the value DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

. Here: the movement of the cross section is equal to the deformation (elongation) of the beam DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

l. (Fig.2.5).

Fig. 2.5

In the second case of stretching (Fig. 2.6)

Fig. 2.6

The l-th section of the beam is deformed (lengthened) by DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

l ₁ , the cross section nn moves to the position n ₁ -n ₁ by the value DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

lion =

l ₁ .

The llth section of the beam is not deformed, since there is no longitudinal force N, the section mm moves to the position m ₁ -m ₁ by the value

In the third case, we consider the bar deformations under the loading scheme shown in the figure (Fig. 2.7).

Fig. 2.7

In this example: moving the section nn ( DEFORMATION AND MOVEMENT DURING STRETCHING - COMPRESSION

lion) is equal to the elongation of the 1st section of the beam:

The mm section will move to the position m ₁ -m ₁ due to the deformation of the 1st section of the beam, and to the position m ₂ -m ₂ due to its own elongation (Fig. 2.8):