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Example 3

(project <Β_422-3>)

Region of three-edge- supported slabs


Figure 4.2.3-21: Shear force envelopes
Figure 4.2.3-21: Shear force envelopes

The most unfavourable shear forces are equal to:


Figure 4.2.3-22: Front view of the 3D shear force diagrams, corresponding to the envelope of [Vx]
Figure 4.2.3-22: Front view of the 3D shear force diagrams, corresponding to the envelope of [Vx]


Figure 4.2.3-23: Side view of the 3D shear force diagrams, corresponding to the envelope of [Vy]
Figure 4.2.3-23: Side view of the 3D shear force diagrams, corresponding to the envelope of [Vy]

Note that although the live load has a relatively high value, the differences between the shear forces do not exceed 9%.


Figure 4.2.3-24: Bending moment envelopes
Figure 4.2.3-24: Bending moment envelopes

The most unfavourable bending moments are equal to:


Figure 4.2.3-25: Front view of the 3D bending moment diagrams, corresponding to the envelope of [Mx]
Figure 4.2.3-25: Front view of the 3D bending moment diagrams, corresponding to the envelope of [Mx]


(Fig. 4.2.3_26) Side view of the 3D bending moment diagrams, corresponding to the envelope of [My]
(Fig. 4.2.3_26) Side view of the 3D bending moment diagrams, corresponding to the envelope of [My]

Notice that although the live load has a relatively high value, the differences between the bending moments are small.


Figure 4.2.3-27: Deflection envelopes
Figure 4.2.3-27: Deflection envelopes

Maximum deflections of y=-1.58 (-1.14 ) [*]NoteNoteThe respective results corresponding to global loading are shown in brackets. mm occur at the free edges of the three-edge-supported slabs. At the same edges opposite sign deformation of y=0.23 mm is also developed.

In the middle cross-section of the slabs the extreme deflections are y=-1.30(- 0.94) mm and y=0.18 mm respectively.


Figure 4.2.3-28: Front view of the 3D deflection diagrams
Figure 4.2.3-28: Front view of the 3D deflection diagrams


Figure 4.2.3-29: Side view of the 3D deflection diagrams
Figure 4.2.3-29: Side view of the 3D deflection diagrams

Note that the deflections are quite higher reaching up to 40% and, at the same time, opposite sign deformations also arise (blue lines).

Cantilever region


Figure 4.2.3-30: Shear force envelopes
Figure 4.2.3-30: Shear force envelopes

The most unfavourable shear forces are equal to:


Figure 4.2.3-31: Front view of the 3D shear force diagrams, corresponding to the envelope of [Vx]
Figure 4.2.3-31: Front view of the 3D shear force diagrams, corresponding to the envelope of [Vx]


Figure 4.2.3-32: Side view of the 3D shear force diagrams, corresponding to the envelope of [Vy]
Figure 4.2.3-32: Side view of the 3D shear force diagrams, corresponding to the envelope of [Vy]

Notice that although the live load has a relatively high value, the differences between the shear forces do not exceed 6% except for the peak of the cantilever middle support reaching 15%.


Figure 4.2.3-33: Bending moment envelopes
Figure 4.2.3-33: Bending moment envelopes

The most unfavourable bending moments are equal to:


Figure 4.2.3-34: Front view of the 3D bending moment diagrams, corresponding to the envelope of [Mx]
Figure 4.2.3-34: Front view of the 3D bending moment diagrams, corresponding to the envelope of [Mx]


Figure 4.2.3-35: Side view of the 3D bending moment diagrams, corresponding to the envelope of [My]
Figure 4.2.3-35: Side view of the 3D bending moment diagrams, corresponding to the envelope of [My]

The differences between the unfavourable bending moments and the bending moments due to global loading, range from 15 to 50%.


Figure 4.2.3-36: Deflection envelopes
Figure 4.2.3-36: Deflection envelopes

Maximum deflection of y=-0.96 (-0.64) [*]NoteNoteThe respective results corresponding to global loading are shown in brackets. mm and opposite sign deflection of y=0.31 (0.09) mm occur in two-way slabs.

In cantilever slab the maximum deflection is y=-3.11 (-2.81) mm.


Figure 4.2.3-37: Front view of the 3D deflection diagrams
Figure 4.2.3-37: Front view of the 3D deflection diagrams


Figure 4.2.3-38: Side view of the 3D deflection diagrams
Figure 4.2.3-38: Side view of the 3D deflection diagrams

The slightly fluctuating deformations of the cantilever longitudinal free edge, are due to the fluctuations of the two-way slabs deformations behind the cantilever.

 


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