internal forces in beamsjhjugyug.docx lab

7/24/2019 Internal Forces in Beamsjhjugyug.docx Lab

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Internal Forces in Beams

Beam is one of the most common structure member used in structure for supportingvertical loads which are perpendicular to the axis of the beam. Usually the axial forces

of internal forces along the axis of the beam can be ignored as there is either nohorizontal load acting on the beam or the horizontal loads can be neglected. Therefore,the internal forces in beam are shear and bending memont only. However, when theapplied forces to the beam is not perpendicularl to the the axis of the beam, the internalaxial forces should also be considered.

Shear and Bending Moment

Consider there is only vertical loading acting on a long straight prismatic bar withuniform crosssectional area throughout the beam length, the e!uilibrium e!uations are


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"ince there is no axial force in the beam, the internal forces in a beam is shear andbending moment.

Consider the member section #C of length $#C, the internal forces at point C are


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Conventions of Internal Forces

%n general, the length, measured from point # on the left to point C on the right, isconsidered as a positive length, the external applied force , pointing upward is alsoconsidered as a force in positive sense and the produced moment due to the externalforce about point C is in negative sense. The direction of internal forces at point C ofbeam section #C can then be defined by assuming the beam section #C is fixed at pontC. Therefore the positive signed shear ' of negative sense in downward direction andthe positive signed bending moment ( of positive sense in anticloc)wise direction aredirected at point C of the beam section #C. #nd the internal forces at point C of thebeam section CB can then be defined as internal force of e!ual in magnitude andopposite in sense using the e!uilibrium e!uations at point C of an beam #B ine!uilibrium or by direct calculation thruough setting up e!uilibrium e!uations of beamsection CB. #ccording to the convention of the internal forces used in the free bodydiagrams, the calculated values from the two free body beam sections are the same for

the internal forces, since the senses of the internal forces are represented by thestandard conventions used in the free body diagrams, i.e. a positive calculated valuesimplies correct sign conventions used in both free body diagrams and a negativecalculated value implies incorrect sign conventions used in both free body diagrams, butinternal forces in both force diagrams are still e!ual in magnitude but opposite in sense.%mply


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Types of Beam Supports

There are several common types of support used in beam design for engineeringstructure design. The beam supports are

Hinged Support

# hinged support is a simple end support at an end of a beam at which there may beslope, but no displacement is allowed.

Roller Support


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# roller support is a simple end support at an end of a beam at which there may be

slope, but no displacement is allowed.Fixed Support

# fixed support is an fixed end support at an end of a beam at which no slope and nodisplacement is allowed.

Free End


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# free end does not have any support or constraint at an end of a beam at which both

slope and displacement is allowed.Interior Support

or

#n interior support can be a hinged or roller support located between ends of a beam atwhich slope is continuous from one side of the support to the other, but no displacementis allowed.

Intenal Hinge


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#n intenal hinge is a hinge lin)age located between ends of two separate beams at

which there may be discontinuous slope from one side of the hinge lin)age to the other,and the allowed displacement on both sides of the hinge lin)age separating the twobeams is continuous.

Types of Beams

Beam can be named according to how the beam is supported. The distance $ betweentwo supports is the span of the beam for supporting loads. The common types of beamsare

Simply Supported Beam

# simply supported beam is supported by a hinged support at one end of the beam anda roller support at another end of the beam.

Overhanging Beam


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# overhanging beam is supported by a hinged support *or roller support+ at one end of

the beam and a roller support *or hinged support+ at the another side of the beam whichis located away from the another end of the beam.

Cantilever Beam

# cantilever beam is supported by a single fixed support at one end of the beam onlyand the another end of the beam there is a free end without any support or constraint.

Continuous Beam


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# continuous beam is supported by more than two supports along the length of a beam.

%n general, a continuous beam is supported by a hinged support at one end of thebeam, a roller support at another end of the beam, and one or more roller supports areused between the two end supports.

Fixed Beam

# fixed beam is supported by two fixed supports at both ends of the beam.

Cantilever with simply supported Beam


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# cantilever with simply supported beam is supported by a fixed supports at one end of

the beam and a roller support at another end of the beam.Hinge Connected Beams

Hinge connected beams is a single continuous structure by connecting two or moredifferent )inds of supported beams end to end together by hinges.

&or example, a hinge connected beam with simply support beams connected by internalhinge

r, a hinge connected beam with fixed beam and simply support beam connected byinternal hinge


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Loads and Reactions

$oads are applied along the span of a beam. %n general, the loads considered in staticare the concentrated load - and distributed load . Concentrated load is the one whichcan be considered as acting at a point although the load is distributed over a smalllength of the beam in practice. /istributed load is the one which can not be consideredas acting at a point because the load is spread over a considerable length of the beam.The distributed load is usually expressed as load w per unit length. The distributed loadis called uniformly distributed load when the load w per unit length is a constant oruniform from point to point over the lengh of load distributed. #nd those distributed loadswith varying loading from point to point over the lengh of load distributed are groupedas varying distributed load, e.g linear varying distributed load.


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"upports commonly used for the support and connection of beams are the hingedsupport, roller support, fixed support, and the internal hinge connection. %f the totalun)nown reactions involved in all supports are three un)nowns only, the reactions willbe statically determinate. Therefore, simply supported beam, overhanging beam andcantilever beam are statically determinate beams. %f the total un)nown reactionsinvolved in all supports are more than three un)nowns, the reactions will be statically

inderterminate. "ince only three un)nowns can be determined by static methods,methods of statics is not sufficient to determine the reactions. Therefore, continuousbeam, fixed beam and cantilever with simply supported beam are statically indeterminebeams.

%n order to determine the reactions for statically indetermine beams, additionale!uations can be ta)en from the relationships based on the properties of the beam andthe resistance to bending under the applied loads. %f there are totally only two un)nownreactions involved in all supports, the beam is not stable for any applied loads and thebeam is partially constrained only. Therefore beam supported by two rollers is partitallyconstrained. The beam is stable when the applied loads is vertical and the beam will

move when the horizotal components of the applied loads is not e!ual to zero.Therefore in practice, a horizontal restraint is usually used in one support to restrain thebeam from rotating or moving horizontal

internal forces in beamsjhjugyug.docx lab

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