STATICALLY UNCERTAIN TASKS

Lecture

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

Fig. 2.4

When stretching:

The length of the bar changes to STATICALLY UNCERTAIN TASKS

(elongation),

The width of the beam changes to STATICALLY UNCERTAIN TASKS

(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 STATICALLY UNCERTAIN TASKS

. Here: the movement of the cross section is equal to the deformation (elongation) of the beam STATICALLY UNCERTAIN TASKS

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 STATICALLY UNCERTAIN TASKS

l ₁ , the cross section nn moves to the position n ₁ -n ₁ by the value STATICALLY UNCERTAIN TASKS

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 ( STATICALLY UNCERTAIN TASKS

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):