# Reactions of Simply Supported Bems

Topics: Force, Beam, Statics Pages: 7 (1254 words) Published: February 11, 2013

NAME

MATRIC

060403009

DEPARTMENT

ELECTRICAL/ELECTRONICS

COURSE

CEG 202

GROUP NO

4

TITLE OF EXPERIMENT:

REACTIONS OF SIMPLY SUPPORTED BEAMS

DATE PERFORMED:

13TH OF AUGUST 2008.

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.
• A steel beam of hollow section.
• Load / weights ranging from 2kg to 10kg.
• Meter rule.
• Inextensible cord.

THEORY
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.
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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...