Civil Engineering Reference
In-Depth Information
8
Shear and Diagonal Tension
8.1
INTRODUCTION
As repeatedly mentioned earlier in this topic, the objective of today's reinforced concrete
designer is to produce ductile members that provide warning of impending failure. To
achieve this goal, the Code provides design shear values that have larger safety factors
against shear failures than do those provided for bending failures. The failures of rein-
forced concrete beams in shear are quite different from their failures in bending. Shear
failures occur suddenly with little or no advance warning. Therefore beams are designed
to fail in bending under loads that are appreciably smaller than those that would cause
shear failures. As a result, those members will fail ductilely. They may crack and sag a
great deal if overloaded, but they will not fall apart as they might if shear failures were
possible.
8.2
SHEAR STRESSES IN CONCRETE BEAMS
Although no one has ever been able to accurately determine the resistance of concrete to
pure shearing stress, the matter is not very important because pure shearing stress is proba-
bly never encountered in concrete structures. Furthermore, according to engineering me-
chanics, if pure shear is produced in a member, a principal tensile stress of equal magnitude
will be produced on another plane. Because the tensile strength of concrete is less than its
shearing strength, the concrete will fail in tension before its shearing strength is reached.
You have previously learned that in elastic homogeneous beams, where stresses are
proportional to strains, two kinds of stresses occur (bending and shear) and they can be
calculated with the following expressions.
Mc
I
f
VQ
Ib
v
An element of a beam not located at an extreme fiber or at the neutral axis is subject
to both bending and shear stresses. These stresses combine into inclined compressive
and tensile stresses, called
principal stresses
, which can be determined from the follow-
ing expression:
f
f
2
2
v
2
f
p
2
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