Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 41

The previous analysis can be used to determine the stress and strain state in beams subject to four-point bending. The analysis will apply near the mid-plane between the planes normal to the beam axis that contain the contact points of the inner rollers used in the experiments. For this case σA=σT=σt=MT=ΔT=0 and the relations (2.235), (2.236), (2.240) and (2.241) reduce to the form

(2.242)

(2.243)

(2.244)

(2.245)

It is clear from (2.242), (2.243) and (2.245) that

(2.246)

From (2.215)₁, (2.244) and (2.246)

(2.247)

(2.248)

It is noted from (2.211) that the quantities ε¯A+12ε^Ah and ε¯T+12ε^Th appearing in (2.242), (2.243) and (2.246) are the in-plane strains on the mid-plane x3=12h (i.e. the neutral plane) which are zero for the loading case under consideration.