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I. OBJECTIVES
1.1 To explore the relationship between the loads and the horizontal reaction force in a Two-Pinned Arch.
1.2 To determine the horizontal thrust force and reaction influence lines for a point load moving across a Two-Pinned Arch.
1.2 To determine the horizontal thrust force for a uniformly distributed load on a Two-Pinned Arch.
Figure 1
St. Louis Arch
II. INTRODUCTION AND BACKGROUND
The main advantage an arch has over a beam, is that it can carry a much larger load. Historically arches were important because they could be constructed using small, easily carried blocks of brick or stone rather than using a massive, monolithic stone beam or lentil. Romans used the semicircular arch in bridges, aqueducts, and in large-scale architecture. In most cases they did not use mortar, relying simply on the precision of their stone finish. When an arch is loaded by gravity forces, the pressure acts downward on the arch and has the effect of compressing it together instead of pulling it apart. A free body diagram of the arch supports shows the arch requires both horizontal and vertical reaction forces (Figure 2). This
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horizontal reaction force, called thrust, can cause the arch to collapse if it is not properly restrained.
Figure 2 Free Body Diagram of Two Hinged Arch.
One of the disadvantages of the arch resisting loads in compression is the possibility that the arch may buckle. Any practical arch design would include analysis involving stress, deflection and buckling. To perform such analysis, reaction forces, shear and moment diagrams are needed for a given load case. Since the arch is indeterminate, having more unknown reactions forces than equilibrium equations, methods such as the flexibility method are required to determine the reaction forces.
III. EQUIPMENT LIST
- Structures test frame
- Digital force display
- Load cell and power supply
- Aluminum arch, hangers and weights
- Scale
H A HB
V B
V A
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- Carefully zero the force meter using the dial on the right-hand side support. Gently apply a small load with a finger to the crown of the arch and release. Zero the meter again if necessary.
NEVER apply excessive loads to any part of the equipment or strike the Load Cell.
PART A
The first experiment is to measure the horizontal thrust force HB for a single load that is placed at increasing distances from the left support. A theoretical equation for the horizontal thrust force for a given load W at location x, is given below:
Where:
HB = The horizontal thrust reaction at B (N) W = Load (N)
L = Span of the arch (m)
x = Load location, distance from the left-hand side support (m)
r = Rise of the arch (m)
4.1A Measure the necessary dimensions of the two-pinned arch and record the data.
4.2A Adjust the “set zero” control on the right support so that the digital force reads zero.
4.3A Apply a 100 gm load to the left most hanger and record the thrust force. Moving the 100 gm load to the remaining hangers and record the thrust force for each location. Repeat the process for a 500 gm load. The horizontal thrust shown on the digital force display has units of Newtons
(L x 2 Lx ) 8 rL
5 Wx HB ==== 3 3 ++++^3 −−−−^2
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PART B
The second part of the experiment involves determining the horizontal thrust force for a uniform or distributed load w. The equation for the thrust force is given in Equation 9.2.
Where:
HB = The horizontal thrust reaction at B (N)
w = Uniform distributed load (N/m)
L = Span of the arch (m)
r = Rise of the arch (m)
4.1B Adjust the “set zero” control on the right support so that the digital force reads zero.
4.2B Apply 70 gm on each of the nine hangers (total of 630 gm) and record the thrust force. Repeat the procedure with 140 gm on each hanger (1260 gm total).
V. REPORT
5.1 Plot the experimental and theoretical thrust force determined in Part A of the experiment.
5.2 Compare the theoretical and experimental thrust force for the uniformly loaded arch.
VI. SELECTED REFERENCES
6.1 Megson, T.H.G., “Structural and Stress Analysis,” Butterworth Heinmann, 1996
6.2 Timoshenko, S.P., Young, D.H., “Theory of Structures”, McGraw Hill Co., New York., 1965
8 r
wL H
2 B ====
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TOTAL MASS (gm)
TOTAL MASS OF HANGERS (gm)
UNIFORM DISTRIBUTED LOAD (N/M)
MEASURED THRUST FORCE (N)
CALCULATED THRUST FORCE (N)
% ERROR
TABLE 4
DATA FOR A UNIFORMLY DISTRIBUTED LOAD
