How to calculate hinged support, normal thrust and shear of a three hinged circular arch

This construction video tutorial is based structural analysis. You will learn how to make calculation of reaction at the support as well as normal thrust and shear for three hinged circular arch.

This video is presented by renowned engineer Mr. Parag Pal.

Three hinged system:

a. A three hinged system comprises of two plates, attached collectively with a hinge containing two hinged supports A and B resting on the ground.
b. When the plates 1 and 2 comprises of curved bars, the system is known as a three-hinged arch.
c. The distance 1 among the centers of the hinges at the support is known as the span of arch.
d. When distance f from the center of the crown hinge to the straight line going through the former two is defined as its rise.

The reactions of a three hinged arch will be completely established with four parameters, as for example, the amounts of reaction Ha, Hb, Va, and Vb.

So, a three hinged system is always statically determinate.

Benefits:

a. The bending moments and shears operative over cross sections of three hinged arches are significantly smaller as compared to the subsequent stresses in a simple beam covering the equivalent span and bearing the same load. So, three hinged arches are inexpensive relating to ordinary beams, specifically for large span structures.

b. Calculations are very simple as compared to other type of arches.
c. No bending moments are generated at the abutments and the crown since hinges cannot withstand moments.
d. Differential settlements of the supports do not impact stresses, since the pines or hinges allow the arch to assume the slightly different shape consequent upon settlement.

e. The pin joints allow the arch to modify itself to expansions and contractions because of alterations in temperature.

In this video, solution is given to the following problem: A three-hinged circular arch hinged at the springing and crown points contain a span of 40 m and a central rise of 8 m. It bears a consistently distributed load 20 kN/m over the left-half of the span collectively along with a concentrated load of 100 kN at the right quarter span point.

Determine the supports, normal thrust and shear at a section 10 m from left support.

To get the solution, go through the following video tutorial.

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Published By
Rajib Dey
www.constructioncost.co
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Different types of beam section in RCC structures

In this construction video tutorial, you will gather information on different types of beam section in RCC structures. Usually, there are three types of beam sections which range from balanced beam section , under reinforced beam section and over reinforced beam section.

It is known that a beam comprises of two components i.e. reinforcement and concrete.

Balanced Beam Section: If the ratio of steel to concrete in a section prevails in such a manner that the strain in steel and strain in concrete attain their maximum values all at once, the section is identified as a balanced or critical section and the percentage of steel in this section is defined as critical steel percentage.

Under-Reinforced Beam Section: Under-reinforced section: A section that contains steel percentage below the critical percentage is called as under-reinforced section. As steel lacks to adjust compression in concrete, the tensile strain in steel attains yield value whereas the highest compressive strain in concrete is under its ultimate crushing value.

The section undertakes large rotational deformations from the preliminary phase of yielding of steel to the final stage of crushing of concrete, providing adequate warning of impending failure.

Given below, an extensive lists of different types of basic geometry formulas :-

Yielding of steel in under-reinforced beam section does not signify that the structure has failed, because if steel yields, extreme deflection and cracking in beam will happen prior to failure which provides sufficient time to occupants to escape ahead of the section fails.

The failure in under-reinforced beam section occurs as the concrete attains its ultimate failure strain of 0.0035 prior to steel attains its failure strain which is greater than 0.20 to 0.25.

Over-Reinforced Beam Sections: Reinforced concrete beam sections, in which the failure strain in concrete is attained sooner than the yield strain of steel is obtained, are known as over-reinforced beam sections.

If over-reinforced beam is designed and loaded to complete strength then the steel in tension zone will not yield much prior to the concrete attains its ultimate strain of 0.0035. It happens because of little yielding of steel, the deflection and cracking of beam does not happen and provide enough warning prior to failure.

Failures in over-reinforced sections happen suddenly. This type of design is not approved in practice of beam design.

To get more in-depth information, go through the following video tutorial.

Video Source: Tutorials Tips

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Published By
Rajib Dey
www.constructioncost.co
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