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5.3Shear& Moment Diagrams 99

+

• 
  

+ve Shear

+ve Load

+ Axial Force

+ve Moment

Figure5.9:ShearandMoment SignConventionsforDesign

Load Positive alongthebeam'slocaly axis(assuminga right handsideconvention),

thatis positive upward.

Axial:tensionpositive.

FlexureA positive moment is onewhich causestensionin thelower bers,andcompres-

sionin theupper ones.For framemembers,a positive moment is onewhich causes

tensionalongtheinnerside.

Shear A positive shearforceis onewhich is \up"ona negative face, or\down"on

a positive one. Alternatively, a pair of positive shearforceswillcause clockwise

rotation.

TorsionCounterclockwisepositive

3D: Usedouble arrow vectors (andNOTcurvedarrows). Forcesandmoments (including

torsions)arede nedwithrespectto a right handsidecoordinatesystem,Fig.5.10.

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Figure5.10:SignConventionsfor3DFrameElements

5.3.1.2 Load,Shear,Moment Relations

50 Letus(re)derive thebasicrelationsbetweenload,shearandmoment. Consideringanin-

nitesimallengthdxof a beamsubjectedto a positive load

6

w(x), Fig.5.11. Theinnitesimal

sectionmustalsobe in equilibrium.

51 Therearenoaxialforces,thus we onlyhave two equationsof equilibriumto satisfyFy= 0

andMz= 0.

52 Sincedxis in nitesimallysmall,thesmallvariationin loadalongit canbe neglected,therefore

we assumew(x) to be constant alongdx.

6

In thisderivation,as in allotheroneswe shouldassumeallquantitiesto be positive.