ENGINEERING ARCH THEORY - The fundamental feature of arched structures is that horizontal reactions appear even if the structure is subjected to vertical loads only. This phenomenon is known as arch action. As the height or rise of the arch decreases, the outward thrust increases and as a result, maintaining the arch action and preventing the arch from collapsing, internal ties or external bracing must be employed. The efficiency of an arch can be demonstrated by comparing it with a beam of the same span under the same loading conditions.

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Engineering Arch Theory

What is engineering arch theory?

StructX

Engineering Arch Theory

Arches employ the principal that when weight is uniformly applied to them the forces resolve into axial compressive stresses and thrust at the base or bearing points instead of into bending moments.

The fundamental feature of arched structures is that horizontal reactions appear even if the structure is subjected to vertical loads only.

This phenomenon is known as arch action.

As the height or rise of the arch decreases, the outward thrust increases and as a result, maintaining the arch action and preventing the arch from collapsing, internal ties or external bracing must be employed.

The efficiency of an arch can be demonstrated by comparing it with a beam of the same span under the same loading conditions.

Fixed arch: statically indeterminate structures to the third degree, the end points require solid restraints. These types of arches are the most ridged but are sensitive to relative settlement at the supports as well as any additional forces created by changes in temperature.

Two-hinged arch: statically indeterminate to the first degree and although are not as rigid as fixed arches, they are somewhat insensitive to relative settlement at the supports.

Three-hinged arch: statically determinate and are not affected by settlement or the additional forces created by temperature changes.

Tied-arch: provides an internal member or tie to resist the outward thrust caused by arch action. A strong tension member connected between the arch springing points reduces the amount of any external bracing requirements.

Parabolic arch: because both the shape of the arch and the shape of the bending moment diagram are parabolic, when the arch is subjected to a uniform load, the bending moment at every section of the arch is theoretically zero. The arch will be under pure axial compression.

Assumptions and Limitations

·  The cross-section of the arch is considered small compared to its length (beam is long and thin)

·  Loads act transverse to the longitudinal axis and pass through the shear centre (any torsion/twist is eliminated).

·  Self weight of the arch has been ignored (this may have to be added).

·  The material of the arch is homogenous and isotropic and has a constant Young's modulus in all directions.

·  The young's modulus is considered to be constant in both compression and tension.

·  The resultant moment of the bending stress is equal to the external moment along the entire length of the beam.

·  The centroidal plane (Neutral surface) is subjected to zero axial stress and does not undergo any change in length.

·  Deflections are assumed to be very small compared to the overall length of the arch.

·  The cross-section remains planar and perpendicular to the longitudinal axis during bending.

·  Any deflection of the arch follows a circular arc with the radius of curvature considered to remain large compared to the dimension of the cross section.

"Good engineers don't need to remember every formula; they just need to know where they can find them."

StructX was created in an effort to provide a comprehensive and freely accessible resource for the structural engineering community - "Good engineers don't need to remember every formula; they just need to know where they can find them". Fundamentally, StructX is an ever adapting source of formulas, data, properties and techniques commonly adopted by structural engineers worldwide.

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BRIDGES AND GEOMETRY - Geometric design is important in bridge design. roperly used, geometric figures can create extremely strong bridges. Though some bridges may use more geometric concepts than others, all bridge designs evenly distribute weight for proper bearing. Truss bridges rely heavily on triangles. Used properly, triangles evenly distribute weight throughout the bridge. Instead of pushing straight down, the weight of an arch bridge is carried outward along the curve of the arch to the supports at each end. Connector plates are used to help strengthen connecting points on bridges. Symmetry is important in bridge design because the entire length of the bridge must be able to bear weight. An asymmetrical bridge can cause the bridge to collapse.

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Bridges And Geometry

Geometric Concepts Found in Bridges

By Jennifer Elrod

Different bridge designs can be found throughout the world. You can find truss, arch, cable, beam, suspension and cantilever bridges in different areas.

The type of bridge used largely depends on the distance it must cover and the amount of load it must bear.

Geometric design is important in bridge design. Properly used, geometric figures can create extremely strong bridges.

Though some bridges may use more geometric concepts than others, all bridge designs evenly distribute weight for proper bearing.

Triangles

Truss bridges rely heavily on triangles. Used properly, triangles evenly distribute weight throughout the bridge.

Triangles are used on the sides and sometimes even the top of the bridge.

The top of a truss bridge may have an "x" design, where four triangles create enough support to bear a great deal of weight.

Students can use simple wooden craft sticks to create a truss bridge strong enough for the teacher to stand on.

A well-designed bridge is less about the materials and more about the design.

Arches

Arches are used to create arch bridges.

According to PBS.org, "Arch bridges are one of the oldest types of bridges and have great natural strength. Instead of pushing straight down, the weight of an arch bridge is carried outward along the curve of the arch to the supports at each end."

It may be a one-arch bridge, or there may be several arches side by side to create the support needed.

Connector Plates

Connector plates are used to help strengthen connecting points on bridges.

A connector plate is most commonly shaped as either a square or a triangle. They are made of steel and bolted onto intersecting points on a bridge.

The shape of the plate adds strength to these areas of the bridge. When pressure is added to the point of intersecting, the connector plate distributes the pressure.

There are different-sized plates and most have a galvanized coating to help prevent rust corrosion.

Symmetry

Symmetry is a geometric concept that is used in bridge design. Symmetry is where one half of a figure is the mirror image of its other half.

Symmetry is important in bridge design because the entire length of the bridge must be able to bear weight. An asymmetrical bridge can cause the bridge to collapse.

Each arch on an arch bridge must be symmetrical. The triangles on a truss bridge must be symmetrical. Even the spacing on cable and suspension bridges must be even and symmetrical.

About the Author

I'm an experienced teacher with a degree in Multidisciplinary Studies-Human Learning. I've worked with various grade levels at different educational facilities. My expertise includes: lesson planning, curriculum development, child development, educational practices and parent involvement.

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