# THEORY OF STEUCTURE II LAB 1

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.

OBJECTIVES

1.1 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.

Theory:- The two hinged arch is a statically indeterminate structure of the first

degree. The horizontal thrust is the redundant reaction and is obtained y the use of

strain energy methods. Two hinged arch is made determinate by treating it as a

simply supported curved beam and horizontal thrust as a redundant reaction. The

arch spreads out under external load. Horizontal thrust is the redundant reaction is

obtained by the use of strain energy method.

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 1).

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.

EQUIPMENT LIST

1. Structures test frame

2. Digital force display

3. Load cell and power supply

4. Aluminum arch, hangers and weights

5. Scale

Procedure

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

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 50 gm on each of the nine hangers (total of 450gm) and record

the thrust force. Repeat the procedure with 60 gm on each hanger

(540) gm total).

OBSERVATION & CALCULATION