Shear and Diagonal Tension in Beamsteacher.buet.ac.bd/tahsin/ce315/chapter4.pdf · •Shear...
Transcript of Shear and Diagonal Tension in Beamsteacher.buet.ac.bd/tahsin/ce315/chapter4.pdf · •Shear...
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Shear and Diagonal Tension
in Beams
Chapter 4
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Introduction
• Chapter 3 deals with flexure
• Beams must have adequate safety margin
against other types of failure
• They may be more dangerous-more
uncertain and more catastrophic
• Shear failure is one such failure
• It is not fully understood and sudden
without warning
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• Special shear reinforcement are provided to
ensure flexural failure would occur before
shear failure if overloading happens.
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DIAGONAL TENSION
• Shear analysis and design are not really
concerned about shear as such.
• The real concern is DIAGONAL TENSION
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DIAGONAL TENSION: video
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Diagonal Tension in
homogeneous beams
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Principal Stresses
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RC BEAMS WITHOUT SHEAR
REINFORCEMENTS
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RC Beams without shear
reinforcements
• No flexural failure unlike plain concrete
beam
• Diagonal tension failure occurs elsewhere
• Caused by shear alone or combined action
of shear and flexure
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Web-shear crack
• when flexure small
•Near neutral axis
•Shear stress equals tensile strength
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Flexure shear cracking
• Both moment and shear significant
• Fails at a lower stress due to preexisting
cracks due to flexure
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• The shear at which diagonal cracks develop
depends on the ratio of shear force to
bending moment
• more precisely on the v to f near the top of
flexural crack
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Behaviour of diagonally cracked beam
• Flexural cracks are harmless as longitudinal
steel is present
• If shear reinforcement is not present,
diagonal cracks is critical and determines
the strength
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•Two types of behaviour as diagonal cracks
formed:
• The diagonal cracks spread immediately
from tension face to compression, splitting
it in to two and failing- for shallow beams
(span to depth 8 or more)
• For deeper beams, the crack spreads
partially in to compression zone. Failure
load is significantly higher
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Once crack is formed
Dowel V is small and can
cause splitting
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Formation of diagonal crack produce
following redistribution of stress
• Shear stress increases on the uncracked area
• Compression force increases
• Tension in steel increases
• Failure occurs in various ways-yielding,
crushing, splitting, pull out
• Relatively deep beam can take significant
load after formation of diagonal crack, but
this reserve strength is erratic and is ignored
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RC BEAM WITH WEB
REINFORCEMENT
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Types of web reinforcement
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Behaviour of web reinforced concrete beams
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Beams with vertical stirrups
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Beams with inclined bars
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ACI CODE PROVISIONS
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Vc
•Conservative where shear-moment ratio is high
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Minimum web reinforcement
Read from book
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Design of web reinforcement
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Graphically
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More rigorous formula
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Provide stirrups even if not required