University of Mississippi Department of Civil Engineering
CE407: Civil Engineering Laboratory II
Experiment S1: Horizontal Thrust Reaction on a Three-Hinged Arch Bridge
Dr. Chris L. Mullen
Last Updated: 10-15-01
1.0 INTRODUCTION
1.1 The HST.3/5 setup for the Hi-Plan 2 Structures Apparatus is to
be used to determine the horizontal thrust reaction for a three-hinged
arch bridge under a variety of loading and geometry patterns.
1.2 The objective is to observe how the horizontal thrust reaction may
be measured at the right hand bearing position and to compare the measured
predictions with theoretical estimates obtained by elementary structural
analysis such as influence lines.
2.0 THEORY
2.1 Definitions.
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Three hinged arch bridge- curved structure of length, L0= LA + LB,
loaded in transverse direction, pin-supported at both ends, points A and
B, and pin-connected at the crest of the arch, C. All reactions and internal
forces are statically determinate.
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Horizontal thrust reaction- reactions, HA and HB, acting at the
springing points of the arch that prevent lateral spreading of the supports
under vertical loading of the arch.
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Influence line- plot of response, e.g. HB, due to a unit load placed
at variable positions, x, on the arch, measured horizontally from point
A.
2.2 Analysis
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Compute the influence line for the reaction, HB(x), for a single load,
P=1, for x / L0 ={0, ..., 1}.
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Use a unit load analysis and the principle of superposition to estimate
HB for the two-axle (tandem) loading case which is intended to characterize
a typical highway truck. Use the relative position and intensity of the
axle loads described below.
3.0 EQUIPMENT
The HST.3/5 setup is shown in the figure below. The right hand bearing
assembly runs on a horizontal track plate with marker and hanging weights
that provide the only variable readout in the experiment.
4.0 EXPERIMENTAL PROCEDURE
Consider both symmetrical and unsymmetrical arch configurations. For
the symmetrical configuration, consider all three load cases described
below, and for the unsymmetrical configuration, consider only the first
load case. Compare the theoretical and experimental values in a table.
Create the table using a spreadsheet which calculates the theoretical values
and enter the experimental values. Clearly identify the measured
raw data and values processed from those values.
Use measured values of lengths in all instances.
Note that in order to measure a reaction, it is not necessary to implant
something into or cut any member. It is however, necessary to release one
of the restraints, in this case the horizontal restraint at the right support.
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Load Case 1. A single 50 N weight is placed at ten positions from
x / L0= 0.1 to x / L0 = 1.0, in increments of 0.1 .
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Load Case 2. One 25 N leader (front axle) weight twinned with one
50 N follower (rear axle) weight. Consider the following three positions
of the leader weight: x / L0= {0 .25 , 0 .55, and 0.85 }. The positions
of the follower weight are: x / L0= {0.15 , 0.45, 0.75}, respectively.
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Load Case 3. A uniform design lane load is simulated using 4 bars
having weight/length, w= {25, 50, 75, 100} N/m.
5.0 RESULTS AND CALCULATIONS
Summarize the recorded data , calculated predictions, and relative
error (express as a percentage of the theoretical value), in a table.
(Format to be discussed in lab.).
6.0 DISCUSSION
Comment on sources of error and random variation in the recorded data.
Comment on possible explanation of differences between recorded data
and theoretical predictions.
7.0 CONCLUSIONS
State what you accomplished through the experiment. Were your measurements
reasonable? Was the apparatus well suited for this measurement? Do you
have any suggestions to improve the procedure?
APPENDIX
Draw appropriate sketches and give formulation for theoretical prediction
for both symmetrical and unsymmetrical configurations. Plot predicted
influence lines.