Civil Engineering Reference
In-Depth Information
The horizontal retaining wall movements for the 20-ft bay frame with a column
to beam stiffness ratio of 4 are substantially smaller than their counterparts of the
smaller stiffness frame shown in Fig. 8.8. The range of movements with
temperature cycles is also larger when compared to the results found for the three
rigid frames presented earlier. According to table 7.2, the lateral stiffness of the
frame presented in this section is approximately 2.5 times larger than the first rigid
frame presented (F1), and 40% smaller than the second frame (F7), and 4.5 larger
than the third frame (F13). This indicates that the frame possesses a relatively
large lateral stiffness that is responsible for smaller horizontal movements found
from the analysis. Additionally, length of the rigid frame is twice as long as the
10-ft bay frames thus resulting in larger horizontal thermal strains due to
temperature changes, which explains the larger range of movements for retaining
wall shown in Fig. 8.13.
The magnitude of the bending moment in the wall is similar to its counterpart
shown in Fig. 8.8. In this case, however, the moment developed in the wall during
the expansion cycles is nearly 50% larger than the moments found during
contraction cycles and at the initial backfill stage. The bending moment
distribution indicates the retaining wall assumed a double curvature shape.
The lateral earth pressure developed behind the structure, shown in Fig. 8.14, is
nearly equal at the initial backfill stage and during the contraction cycles, but
slightly larger during the expansion cycles. The longer expansion length of the 20-
ft bay frame combined with the larger column to beam stiffness ratio resulted in
the largest increase in lateral earth pressure during the expansion cycles of all
single-story single bay frames presented thus far.
10
1 bay, L
b
= 20 ft
φ
σ
'
a
σ
8
= 30
o
'
ec1
σ
'
cc1
σ
'
ec2
σ
S
c
/S
b
= 4
6
'
cc2
4
'
ec3
σ
2
0
0
0.2
0.4
0.6
0.8
1
1.2
'
h
, kips/ft
2
σ
Fig. 8.14
Retaining Wall Earth Pressure (Single Bay, L
b
= 20 ft, S
c
/S
b
= 4)
The horizontal movements of the end column, shown in Fig. 8.15, indicate a
large increase in horizontal displacement away from the soil mass during the
expansion cycles compared with the initial backfill stage. The shear force and
bending moment in the end column corresponding to the last expansion cycle are
nearly 32% larger than their counterpart developed at the backfill stage. The
difference in displacement, shear and bending moment in the end column between
