This limit state is also called as strength limit state as it corresponds to the maximum load carrying capacity i.e., the safety requirements of the structure. The limit state of collapse is assessed from collapse of the whole or part of the structure. As per this limit state, the resistance to bending, shear, torsion and axial loads at every section shall not be less than that produced by the most unfavorable combination of loads on that structure.
INTRODUCTION
Limit state of collapse shear and bond :
A beam loaded with transverse loads is subjected to shear force and bending moment. The shear force at any section is equal to the rate of change of bending moment. The shear force results into shear stresses across the cross-section is given by the following equations.
\[q=\frac{V(A.\bar{y})}{I.b}\]
where, q = Shear stress
I = Moment of inertia of the beam section
b = Width of section
V = Shear force at the section
(A.ȳ) = First moment of the area above the section about neutral axis
On the basis of above equation the shear stress distribution across a rectangular cross-section is shown in Fig. 5.1(b).
LIMIT STATE OF COLLAPSE SHEAR AND BOND
It is parabolic with zero at top and bottom and the maximum shear stress, occurs at neutral axis is equal to\[ \frac{3V}{2bd}\].
Types of shear reinforcement : Vertical stirrups, Bent up bars along with stirrups, Inclined stirrups, contribution of bent up bars TYPES OF SHEAR REINFORCEMENT The following three types of shear reinforcement are used : Vertical stirrups. Bent up bars along with stirrups. Inclined stirrups. Vertical Stirrups These are the steel bars vertically placed around the tensile reinforcement at suitable spacing along the length of the beam. Their diameter varies from 6 mm to 16 mm. The free ends of the stirrups are anchored in the compression zone of the beam to the anchor bars (hanger bar) or the compressive reinforcement. Depending upon the magnitude of the shear force to be resisted the vertical stirrups may be one legged, two legged, four legged and so on as shown in Fig. 5.5. It is desirable to use closely spaced stirrups for better prevention of the diagonal cracks. The spacing of stirrups near the supports is less…
Learn : Effects of Shear Diagonal Tension, maximum bending tensile stress, tensile stress (σ) as well as shear stress (τ),crack pattern for a simply supported beam, The maximum bending moment in this beam will be at midspan and the maximum shear force, at the supports. EFFECTS OF SHEAR DIAGONAL TENSION Consider a beam AB subjected to transvers loads as shown in Fig. 5.3(a). The maximum bending moment in this beam will be at midspan and the maximum shear force, at the supports. The beam is subjected to bending and shear stresses across the cross-section. Let us consider a small element (1) from the tensile zone of the beam. It is subjected to bending tensile stress (σ) as well as shear stress (τ) as shown in Fig. 5.3. (b). At the midspan, the bending moment is maximum and the shear force is zero. So the element 2 is subjected to maximum…
Shear Stresses in R.C.C. beam (Reinforced cement concrete beam), Stress Based Approach (Elastic Theory), IS Code Approach SHEAR STRESSES IN R.C.C. BEAMS Stress Based Approach (Elastic Theory) R.C.C. is a composite materials so the exact shear distribution as per elastic theory is very complex. It is shown in Fig. 5.2(b) by the hatched portion of the curve.It is parabolic in the compression zone with zero at the top and maximum at the neutral axis. The value of shear-stress is constant in the tensile zone and is equal to the maximum shear-stress (q) because the concrete, below the neutral axis (tensile zone) is assumed to be cracked and neglected. The maximum value of shear stress (q) as per elastic theory is given by \[q=\frac{V}{bjd}\] where V = shear force at the section b and d = dimensions of the section j = Lever arm depth factor IS Code Approach As per IS code…
