NAMEADETAYO OLUWAKAYODE MATRIC 060403009 DEPARTMENT ELECTRICAL/ELECTRONICS COURSE CEG 202 GROUP NO 4 TITLE OF EXPERIMENT: REACTIONS OF SIMPLY SUPPORTED BEAMS • A steel beam of hollow section. AIM: (I) TO DETERMINE THE REACTIONS RA AND RB FOR A BEAM SIMPLY SUPPORTED AT ITS ENDS (II) TO DETERMINE THE VALUES OF RA AND RB AS A GIVEN LOAD MOVES FROM ONE END OF A SIMPLY SUPPORTED BEAM TO THE OTHER APPARATUS: • Two spring balances.DATE PERFORMED: 13TH OF AUGUST 2008. . • Inextensible cord. • Load / weights ranging from 2kg to 10kg. • Meter rule. THEORY A beam with a constant height and width is said to be prismatic. When a beam’s .• Load hanger. Horizontal applications of beams are typically at resists the rotation. Loads that are applied to a small section of the beam are simplified by considering the load to be single force placed at a specific point on the beam. For the sake of determining reactions. These loads are referred to as concentrated loads. a . the member is said to be non-prismatic. Distributed loads (w. TYPES OF LOADS AND BEAMS Beams can be catalogued into types based on how they are loaded and how they are supported. usually in units of force per lineal length of the beam) occur over a measurable distance of a beam.width or height (more common) varies. . A moment induced on any point can be mathematically described as a force multiplied by at one end and simply supported at the other (see figure 2d). The weight of the beam can be described as uniform load. A continuous beam has more than two simple supports.distributed load can be simplified in to an equivalent concentrated load by applying the area of the distributed load at the centroid of the distributed load. A moment is a couple as a result of two equal and opposite forces applied at certain section of the beam. and a built-in beam (see figure 2f) is fixed at both ends. Beams are described as either statically determinate or statically indeterminate. The condition that the deflections due to loads are small enough that the geometry of the initially unloaded beam remains essentially unchanged is implied by the expression “statically indeterminate”.The remainder of this report deals only with simple and over-hanging beams loaded with concentrated and uniformly distributed loads. A beam is considered to be statically determinate when the support reactions can be solved for with only statics equations. STATICS-RIGID BODY MECHANICS were accelerating in some direction the sum of the forces would equal the mass multiplied by the acceleration. Three equilibrium equations exist for determining the support . only two reaction components can exist. and cantilever beams are statically determinate. Statically indeterminate beams also require load deformation properties to determine support reactions. . because after removing all redundancies the structure will become statically determinate. Stresses. When a structure is statically indeterminate at least one member or support is said to be redundant. strains. The two remaining equilibrium equations become ∑FY = 0 ∑MZA = 0 Simply supported.statically determinate. Forces and moments are the internal forces transferred by a transverse cross section (section a. figure 3c) necessary to resist the external forces and remain in equilibrium. overhanging. The other types of beams described above are statically indeterminate. slopes. Using the equilibrium equations and a free body diagram the support reactions for the beam in figure 3a will be determined. and deflections are a result of and a function of the internal forces. This same method is applicable to any statically determinate beam. The simply supported single span beam in figure 3a is introduced to a uniform load (w) and two concentrated loads (P1) and (P2). This example will also show how internal forces (shear and moment) can be found at any point along the beam. Finding the support reactions requires a free body diagram that notes all external forces that act on the beam and all possible reactions that can occur . The 2kg weight was placed on the hanger and the deflection in the spring balances read. and the spring balances read.e. at . A load hanger was placed at the mid-point of the beam of given span.PROCEDURE The steel beam was hung on the hooks at the bottom end of the spring balances. The load was increased in steps of 2kg up to 16kg and the balances read in each case (i. TABLE OF RESULTS WEIGHT (KG) 0 2 4 6 8 10 12 (N) 0 20 40 60 80 100 120 REACTION A RA (KG) (N) 0 0 1 10 2 20 3 30 4 40 5 50 6 60 REACTION B RB (KG) (N) 0 0 1 10 2 20 3 30 4 40 5 50 6 60 . All weights were then removed. Next.each incremental loading. the load hanger weight was placed directly under the spring balance A and the two spring balances read. It was then (i. A 8kg weight was put on the load – hanger and the spring balances read.e. the load) was then put (transferred) to the next 100mm. For the second part of the experiment. a constant load of 8kg was used.LOAD (KG) 8 8 8 8 8 8 8 8 POSITI ON OF LOAD (CM) 0 10 20 30 40 50 60 70 REACTION A RA (KG) 8 7 7 6 5 4 3 2 (N) 80 70 70 60 50 40 30 20 REACTION B RB (KG) 0 1 1 2 3 4 5 6 (N) 0 10 10 20 30 40 50 60 REPORT The experiment was carried out using steel beam of span 1000mm with a midpoint if 500mm. 4kg and at intervals of 2kg up to 16kg. The load used for the first part was 2kg. . DISCUSSION AND CONCLUSION From the results. RA = RB = ½ (Weight of Load) . Thus the magnitude of the reactions are half that of the loading and are equal to each other i. a relation between RA and RB is observed. As both reactions are at equidistance from the load applied. they both share the weight of the load.e. for the first part of it the experiment. from that reaction. until the load is at point B. RA = weight of the load while the reaction RB = 0. As the load is shifted away from RA. Nevertheless. the reaction RA reduces while RB increases. When the load is at A. Comparing the experimental values and those of the theoretical for this part of the experiment. as the load is borne as a function of the distance of it. and RA is null or zero. As the load is at this point. in which case RB has the maximum reaction equal to the load. Here an inversely proportional relation is observed. the reaction RA is maximum (equal to load). a deviation is seen to occur in values.For the second part of the experiment. this can be as a result (for the experimental part) of zero error on the metre rule of . the position of the load on the beam varies therefore the two reactions vary as well. there is an equal and opposite reaction . PRECAUTIONS Zero error of the metre rule in measuring the length of the beam was avoided. It was made sure that the beam was perfectly horizontal It is thus proven that for every action.the spring balance as some approximations were made. Ryder 2) Strength of Material by Beer & Johnson .REFERENCES 1) Strength of Materials by G.H.