Civil Engineering Reference
In-Depth Information
The shear force and bending moment diagrams developed in the end column
during the various analysis cycles and corresponding to the horizontal end column
movements presented in Fig. A.20 are shown in Fig. A.21.
The bending moment is found to have a large variation in magnitude. At the lat-
ter expansion cycles, for instance, the maximum moment at the top of the end col-
umn is found nearly 233% larger than its counterpart developed at the end of the
backfill stage. Given that no external transverse load is applied onto the end col-
umn, the shear force developed in the end column of the rigid frame is equal to the
maximum moment divided by the total length of the end column. Therefore, the
variation in the magnitude of shear force is identical to the variation of the maxi-
mum bending moment.
Consequently, the shear force diagram will not be presented for the end column
for the subsequent rigid frames.
A.1.1.6 Six-Bay Frame (Bay Length, L
b
, 10 Feet, Column to Beam Stiffness
Ratio, S
c
/S
b
, of 4)
The analysis results for a six-bay frame with a bay length of 10-ft and a column to
beam stiffness ratio of 4 are presented herein. This frame has the largest lateral
stiffness of all frames presented thus far as indicated in Table 7.2. In fact, the lat-
eral stiffness of the said frame is nearly twice its counterpart for the stiffest frame
presented thus far in this Appendix.
The horizontal retaining wall movements, shown in Fig. A.22, indicate a rela-
tively small wall displacement at the initial backfill stage, followed by a relatively
large wall movement into the retained soil. This movement into the soil mass and
through the original position of the wall is the largest found hitherto.
Associated with the wall movements is a large variation in bending moment
developed during the various stages of analysis, where the retaining wall assumes
a double curvature during expansion and single curvature during contraction. The
retaining wall's largest maximum moment occurs at the last expansion cycle at top
of the wall with a magnitude nearly 8 times its counterpart found during the initial
backfill stage. The shear force developed in the retaining wall was also found to
have a large variation with temperature cycles. The maximum shear force corre-
sponds to the maximum moment developed during the last expansion cycle, and is
nearly 4.5 times larger than its counterpart found during the initial backfill stage.
The lateral earth pressure developed in the backfill soil during the analysis cy-
cles is shown in Fig. A.23. The pressure at the initial backfill stage is found simi-
lar to that developed during contraction cycles, while the earth pressure developed
during thermal expansion of the RFERS was found substantially larger, particular-
ly for the top half of the wall height. For instance, the magnitude of the lateral
earth pressure at mid-height of the retaining wall is nearly 3 times larger during
expansion, and approximately 8 times larger at about four-fifth the wall height.
The end column horizontal movements are similar in magnitude to the wall
movements at the other end of the frame, as shown in Fig. A.24. This is attributed
to the relatively large lateral stiffness of the rigid frame coupled with a relatively
long length capable of overcoming the retained soil restraint, thus leading to nearly
