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Exercise 4.9.6


Figure 4.9.6-1
Figure 4.9.6-1

Given : Covering load gεπ=1.0 kN/m2, live load q= 10.0 kN/m2, slab thickness h=140 mm.

Question: Determine bending moments of the slabs in the figure having three spans in x direction and practically infinite number of spans in y direction.

Solution:

The total dead load is equal to: gd=0.14x25.0+1.0=4.50 kN/m2 .

Due to high live load, static analysis will be performed using unfavourable loadings.

The design loads to be used for loading the slabs are gd and pd=1.35g+1.50q= g+(0.35g+1.50q) which is analyzed to:


Static analysis

Moments are determined by means of the technique described in §4.6.4. According to that, the response of the slabs is determined by the particular loadings applied. Thus, while there are actually two slab types, one with four fixed edges and one with three fixed and one free edge, two extra slab types are created: one with four free edges and one with three free and one fixed edge (as illustrated in the figures analyzing the loadings). For ε=ly/lx=4.0/4.5=0.89:


Figure 4.9.6-2
Figure 4.9.6-2

For type '1' slab from table b5.1 for

ε=ly/lx=4.5/4.0=1.125

kx,1=0.615, ky,1=0.385, vx,1=vy,1=0.595

p2x=0.615x8.29=5.10 kN/m, p2y=0.385x8.29=3.19 kN/m


Figure 4.9.6-3
Figure 4.9.6-3

For type '2' slab from table b5.2 for

ε=ly/lx=4.5/4.0=1.125

kx,1=0.391, ky,1=0.609, vx,1=0.744, vy,1=0.639

p2x=0.391x8.29=3.24 kN/m, p2y=0.609x8.29=5.05 kN/m


Figure 4.9.6-4
Figure 4.9.6-4

For type '2' slab from table b5.2 for

ε=ly/lx=4.0/4.5=0.89

kx,1=0.799, ky,1=0.201, vx,1=0.703, vy,1=0.789

p2x=0.799x8.29=6.62 kN/m, p2y=0.201x8.29=1.67 kN/m


Figure 4.9.6-5
Figure 4.9.6-5

For type '5' slab from table b5.5 for

ε=ly/lx=4.5/4.0=1.125

kx,1=0.445, ky,1=0.555, vx,1= 0.835, vy,1=0.805

p1x=0.445x12.79=5.69 kN/m, p1y=0.555x12.79=7.10 kN/m


Figure 4.9.6-6
Figure 4.9.6-6

For type '6' slab from table b5.6 for

ε=ly/lx=4.5/4.0=1.125

kx,1=0.615, ky,1=0.385, vx,1=vy,1=0.865

p1x=0.385x12.79=4.92 kN/m, p1y=0.615x12.79=7.87 kN/m


minMs1-s2

+



Figure 4.9.6-7
Figure 4.9.6-7

-



minMs1-s1


Figure 4.9.6-8
Figure 4.9.6-8


minMs2-s2


Figure 4.9.6-9
Figure 4.9.6-9


maxMs1


Figure 4.9.6-10
Figure 4.9.6-10


maxMs2


Figure 4.9.6-11
Figure 4.9.6-11


 


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