Civil Engineering Reference
In-Depth Information
The horizontal movements of the frame extremities are not equal given the
varying lateral stiffness of the structural members. The lateral stiffness of the
retaining wall is substantially larger than the end column, and the rest of the frame
columns, thus creating more restraint against temperature movement at the wall
side. The horizontal wall displacement from its initial position with a 50ºF
increase in temperature is nearly 0.018 ft (0.21 in), while with 90ºF temperature
change the wall movement is approximately 0.033 ft (0.4 in). The end column, on
the other hand, is displaced nearly 0.04 ft (0.5 in) with a 50ºF rise in temperature,
and approximately 0.072 ft (0.86 in) with a 90ºF temperature change. The total
range of movement during the 90ºF expansion and contraction cycle is 0.066 ft
(0.8 in) for the retaining wall and 0.144 ft (1.7 in) for the end column.
The bending moments in the retaining wall and end column are shown in Fig.
6.4. The magnitude of the flexural stresses developed in the retaining wall is
substantially larger than those found in the end column. This is due to the larger
lateral restraint exhibited by the retaining wall due to its larger lateral stiffness.
The end column moments in all except the first level are nearly equal, with the
maximum moment occurring at the top of the first level with a magnitude of 11
kip-ft. The maximum retaining wall moment occurs at the same location and is
equal nearly 50 kip-ft.
The temperature movements and bending moments in the extreme frame
members will be further discussed in the succeeding sections and compared with
those obtained from the numerical analysis that includes the effect of the backfill
and with the results of the monitoring data obtained on site.
6.3.2 Thermal Analysis of Rigid Frame with Mohr-Coulomb
Backfill (Part 2)
6.3.2.1 Description of Analysis Procedure
The frame shown in Fig. 6.1 is analyzed with the Mohr-Coulomb backfill soil.
The Mohr-Coulomb constitutive law is a well-known soil model and is used
herein as a first approximation of the soil-structure behavior, particularly as a
qualitative study of the effect of backfill soil on the behavior of the structure under
thermal loading. The model is defined using the parameters listed in table 6.2.
The numerical analysis is performed starting with the unloaded frame as an
initial phase, followed by the addition of the backfill soil as a staged construction
phase, then by temperature loading cycles similar to those presented in Part 1.
6.3.2.2 Numerical Analysis Results (Part 2)
The results of the numerical analysis for the rigid frame with backfill soil are
discussed herein. The retaining wall and end column movements and bending
moments are presented for the initial backfill stage as well as for each temperature
