TITLE OF EXPERIMENT:
REACTIONS OF SIMPLY SUPPORTED BEAMS
13TH OF AUGUST 2008.
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
• Two spring balances.
• A steel beam of hollow section.
• Load hanger.
• Load / weights ranging from 2kg to 10kg.
• Meter rule.
• Inextensible cord.
A beam with a constant height and width is said to be prismatic. When a beam’s width or height (more common) varies, the member is said to be non-prismatic. Horizontal applications of beams are typically
at resists the rotation.
TYPES OF LOADS AND BEAMS
Beams can be catalogued into types based on how they are loaded and how they are supported. 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. These loads are referred to as concentrated loads. Distributed loads (w, usually in units of force per lineal length of the beam) occur over a measurable distance of a beam. For the sake of determining reactions, a 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. The weight of the beam can be described as uniform load. A moment is a couple as a result of two equal and opposite forces applied at certain section of the beam. 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). A continuous beam has more than two simple supports, and a built-in beam (see figure 2f) is fixed at both ends. [pic]
The remainder of this report deals only with simple and over-hanging beams loaded with concentrated and uniformly distributed loads.
STATICS-RIGID BODY MECHANICS
were accelerating in some direction the sum of the forces would equal the mass multiplied by the acceleration. Beams are described as either statically determinate or statically indeterminate. A beam is considered to be statically determinate when the support reactions can be solved for with only statics equations. 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”. Three equilibrium equations exist for determining the support statically determinate, only two reaction components can exist. The two remaining equilibrium equations become ∑FY = 0
∑MZA = 0
Simply supported, overhanging, and cantilever beams are statically determinate. The other types of beams described above are statically indeterminate. Statically indeterminate beams also require load deformation properties to determine support reactions. When a structure is statically indeterminate at least one member or support is said to be redundant, because after removing all redundancies the structure will become 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. Stresses, strains, slopes, and deflections are a result of and a function of the internal forces. The simply supported single span beam in figure 3a is introduced to a uniform load (w) and two concentrated loads (P1) and (P2). Using the equilibrium equations and a free body diagram the support reactions for the beam in figure 3a will be determined. This example will also show how internal forces (shear and moment) can be found at any point along...
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