Shear stresses in beams p

rectanular section , triangular section, symmetric I section , unsymmetrical I section, T section, circular section

1. Shear stresses in beams
Venkata Sushma Chinta
Assistant Professor, MED

2. Shear stress in Beams:
The bending stress act longitudinally and its intensity is directly proportional to
its distance from neutralaxis.
Atypicalbeam
sectionissubjectedtoshear
forceinadditiontobending
moment.Thevariationof
shearingstress,whichisdue
tothepresenceofshear
force,isstudiedinthis
chapter.

6. Note:The above expression is for horizontal shear
stress. From The principle of complementary
shear, this horizontal shear stress Is accompanied
by a vertical shear stress of the sameintensity.

7. The integral represents the moment of the area
A’ about the neutral axis. We will denote this by
symbol Q. Since the location of the centroid A’ is
determined from ??????̅’.

11. Q1.Awoodenbeam100mmwideand150mmdeepissimply
supportedoveraspanof4meters.Ifshearforceatasectionof
thebeamis4500N,i)findtheshearstressatadistanceof25mm
abovetheN.A.ii)Shearstressatneutralaxisiii)meanshearstress

13. Q2.Atimberbeamofrectangularsectionissimplysupportedat
theendsandcarriesapointloadatthecenterofthebeam.The
maximumbendingstressis12N/mm
2
andmaximumshearing
stressis1N/mm
2
,findtheratioofthespantothedepth.

14. Q3.Asimplysupportedwoodenbeamofspan1.3mhavingacross-
section150mmwideby250mmdeepcarriesapointloadWatthe
center.Thepermissiblestressare7N/mm
2
inbendingand1N/mm
2
inshearing.CalculatethesafeloadW.

24. A100mmX40mmI-beamissubjectedtoashearforceof15kN.Findthe
transverseshearstressattheneutralaxisandatthetopoftheweb.Compare
itwiththemeanstressontheassumptionofuniformdistributionoverthe
web.Whatisthepercentageofshearforcecarriedbytheweb?Momentof
inertiaofthesectionis1.1X10
6
mm
4
,webthicknessis3mmandflange
thicknessis4mm.

25. A100mmX40mmI-beamissubjectedtoashearforceof15kN.Findthe
transverseshearstressattheneutralaxisandatthetopoftheweb.Compare
itwiththemeanstressontheassumptionofuniformdistributionoverthe
web.Whatisthepercentageofshearforcecarriedbytheweb?Momentof
inertiaofthesectionis1.1X10
6
mm
4
,webthicknessis3mmandflange
thicknessis4mm.

29. Asimplysupportedbeamof2-mspancarriesauniformlydistributedloadof
140kNpermoverthewholespan.Thecross-sectionofthebeamisaT-section
withaflangewidthof120mm,webandflangethicknessof20mmandoverall
depthof160mm.Determinethemaximumshearstressinthebeamanddraw
theshearstressdistributionforthesection.