# Reactions of Simply Supported Bems Sample Essay

A beam with a changeless tallness and breadth is said to be prismatic. When a beam’s breadth or tallness ( more common ) varies. the member is said to be non-prismatic. Horizontal applications of beams are typically at resists the rotary motion.

TYPES OF LOADS AND BEAMS
Radio beams can be catalogued into types based on how they are loaded and how they are supported. Tonss that are applied to a little subdivision of the beam are simplified by sing the burden to be individual force placed at a specific point on the beam. These tonss are referred to as concentrated tonss. Distributed tonss ( w. normally in units of force per direct length of the beam ) occur over a mensurable distance of a beam. For the interest of finding reactions. a distributed burden can be simplified in to an equivalent concentrated burden by using the country of the distributed burden at the centroid of the distributed burden. The weight of the beam can be described as unvarying burden. A minute is a twosome as a consequence of two equal and opposite forces applied at certain subdivision of the beam. A minute induced on any point can be mathematically described as a force multiplied by at one terminal and merely supported at the other ( see figure 2d ) . A uninterrupted beam has more than two simple supports. and a constitutional beam ( see figure 2f ) is fixed at both terminals.

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The balance of this study deals merely with simple and over-hanging beams loaded with concentrated and uniformly distributed tonss.

STATICS-RIGID BODY MECHANICS
were speed uping in some way the amount of the forces would be the mass multiplied by the acceleration. Radio beams are described as either statically determinate or statically undetermined. A beam is considered to be statically determinate when the support reactions can be solved for with lone statics equations. The status that the warps due to tonss are little plenty that the geometry of the ab initio unloaded beam remains basically unchanged is implied by the look “statically indeterminate” . Three equilibrium equations exist for finding the support statically determinate. merely two reaction constituents can be. The two staying equilibrium equations become ?FY = 0?MZA = 0

Merely supported. overhanging. and cantilever beams are statically determinate. The other types of beams described above are statically undetermined. Statically undetermined beams besides require load distortion belongingss to find support reactions. When a construction is statically undetermined at least one member or support is said to be excess. because after taking all redundancies the construction will go statically determinate. Forces and minutes are the internal forces transferred by a transverse cross subdivision ( subdivision a. figure 3c ) necessary to defy the external forces and remain in equilibrium. Stresss. strains. inclines. and warps are a consequence of and a map of the internal forces. The merely supported individual span beam in figure 3a is introduced to a unvarying burden ( tungsten ) and two concentrated tonss ( P1 ) and ( P2 ) . Using the equilibrium equations and a free organic structure diagram the support reactions for the beam in figure 3a will be determined. This illustration will besides demo how internal forces ( shear and minute ) can be found at any point along the beam. This same method is applicable to any statically determinate beam.

Finding the support reactions requires a free organic structure diagram that notes all external forces that act on the beam and all possible reactions that can happen

Procedure
The steel beam was hung on the maulers at the bottom terminal of the spring balances. A burden hanger was placed at the mid-point of the beam of given span. and the spring balances read. The 2kg weight was placed on the hanger and the warp in the spring balances read. The burden was increased in stairss of 2kg up to 16kg and the balances read in each instance ( i. e. at each incremental burden. All weights were so removed.

Next. the burden hanger weight was placed straight under the spring balance A and the two spring balances read. A 8kg weight was put on the burden – hanger and the spring balances read. It was so ( i. e. the burden ) was so put ( transferred ) to the following 100mm.

The experiment was carried out utilizing steel beam of span 1000mm with a center if 500mm. The burden used for the first portion was 2kg. 4kg and at intervals of 2kg up to 16kg. For the 2nd portion of the experiment. a changeless burden of 8kg was used.

DISCUSSION AND CONCLUSION

From the consequences. for the first portion of it the experiment. a relation between RA and RB is observed. As both reactions are at equidistance from the burden applied. they both portion the weight of the burden. Thus the magnitude of the reactions are half that of the burden and are equal to each other i. vitamin E.

RA = RB = ? ( Weight of Load )

For the 2nd portion of the experiment. the place of the burden on the beam varies therefore the two reactions vary every bit good. as the burden is borne as a map of the distance of it. from that reaction.

When the burden is at A. RA = weight of the burden while the reaction RB = 0. As the burden is at this point. the reaction RA is maximal ( equal to burden ) . As the burden is shifted off from RA. the reaction RA reduces while RB additions. until the burden is at point B. in which instance RB has the maximal reaction equal to the burden. and RA is void or nothing. Here an inversely relative relation is observed.

Comparing the experimental values and those of the theoretical for this portion of the experiment. a divergence is seen to happen in values. However. this can be as a consequence ( for the experimental portion ) of zero mistake on the meter regulation of the spring balance as some estimates were made.

Precaution

Zero mistake of the meter regulation in mensurating the length of the beam was avoided.

It was made certain that the beam was absolutely horizontal

It is therefore proven that for every action. there is an equal and opposite reaction

Mentions

1 ) Strength of Materials by G. H. Ryder

2 ) Strength of Material by Beer & A ; Johnson