The compaction factor is the ratio of the weight of concrete in the cylinder to the weight of an equivalent volume of fully compacted concrete. Where δ = deviation of the individual test strength from the average or mean strength of n samples. Normally, the width of the beam b is governed by: (i) proper encapsulation of rebar and (ii) architectural considerations.
The effective depth plays the main role in meeting the requirements of (i) bending moment strength and shear strength, and (ii) beam deflection. Providing more depth also helps in the amount of steel being less than that required for M. V in the above expression can be increased by 30% when the ends of the reinforcement are constrained by a compressive reaction.
MODULE-2
Selection of preliminary depth of slab
Design loads, bending moments and shear forces
Determination/checking of the effective and total depths of slabs
Depth of the slab for shear force
The depth of the slab must be assumed from the ratio of span to effective depth. The value of c must be changed after knowing the multiplication factor k from the depth provisionally chosen for the plate in step 3.
Determination of areas of steel
Determination of effective and total depths of slab From Eq. M
Depth of slab for shear force
Selection of diameter and spacing of reinforcing bars
However, as in the one-way slab, the depth of the two-way slabs must also be checked for the shear stresses to avoid any reinforcement for shear. The shear forces per unit width of the strips aa and bb are highest at the ends of the strips. Furthermore, the length of half of the strip bb is equal to the length of the strip aa.
Tied slabs are considered to be divided into two types of strips in each direction: (i) one center strip of width equal to three-quarters of the respective span in either direction, and (ii) two edge strips, each of equal width up to one-eighth of the relevant span in both directions. The maximum positive and negative moments per unit width of the plate, calculated using Eqs. Under-stress reinforcing bars having a mid-span in the middle strip shall extend in the lower part of the slab to within 0.25 l of a continuous edge, or 0.15 l of a discontinuous edge (cf. D-1.4 of IS 456).
To resist the negative moment at a discontinuous edge, depending on the degree of fit at the edge of the slab, top tension reinforcing bars equal to fifty percent of that provided at midspan 0.1l in the span span (cl. Clause D) - 2.1 states that fifty percent of the tension reinforcement provided at the center of the span must extend to the supports. First, we can increase the depth of the beam, which may not be feasible in many situations.
Doubly reinforced beams therefore have moments of resistance more than the single reinforced beams of the same depth for specific grades of steel and concrete. In many practical situations, architectural or functional requirements may limit the overall depth of the beams.
To determine M
In the design type of problems, the given data are b, d, D, grades of concrete and steel.
To determine M
To check if the beam is under-reinforced or over-reinforced
To determine A
To determine M
In such situations, part of the plate acts integrally with the beam and bends in the longitudinal direction of the beam. The part of the beam below the flange is often called the web, although technically the web is the full rectangular part of the beam apart from the overhanging parts of the flange. The "effective width of flange" can be defined as the width of a hypothetical flange that resists in-plane compressive stresses of uniform magnitude equal to the peak stress in the original wide flange, such that the value of the resulting longitudinal compressive force is the same (Fig. 2.8).
In the case of a continuous flange beam, the negative moment at the front of the support generally exceeds the maximum positive moment (at or near the midspan) and therefore determines the proportionality of the cross-section of the beam. However, towards the center of the beam the beam behaves like a true flange beam (where the flange is under bending compression). The determination of the actual reinforcement in a flanged beam depends on the location of the neutral axis x.
The horizontal upper part of a step (where the foot rests) is called the tread, and the vertical projection of the step (ie the vertical distance between two neighboring steps) is called the riser [Fig. The slab component of the stair (whether comprising an insulated tread slab, a tread unit, or a riser slab) is supported on its side(s) or cantilevered laterally from a central support. The slab supports gravity loads by bending substantially in a transverse vertical plane with the span along the width of the stairs.
In the case of the cantilever slabs, it is economical to provide insulated treads (without risers). Assume that the stairs are supported on 230 mm thick masonry walls at the outer edges of the landing, parallel to the risers [Fig.
MODULE-3
To check if the column is short or slender
Area of steel Fro Eq.10.4, we have
Lateral ties
IS 456 recommends the following simplified method based on Bresler's formulation for design of biaxially loaded columns.
Verification of the eccentricities
Assuming a trial section including the reinforcement
Determination of M
Determination of P
Design of transverse reinforcement
The design of slender compression members should be based on the forces and moments determined from an analysis of the structure, including the effect of deflections on moments and forces. Where the effect of deflections is not taken into account in the analysis, the additional moment specified in cl No. 39.7.1 of IS 456:2000 shall be taken into account in appropriate direction. D = depth of the section perpendicular to the major axis, and b = width of the element.
Determine the required reinforcement for a braced column against the side with the following data: dimensions of the column = 350 x 450 mm (Fig. concrete and steel qualities.
Modification factors
Determination of P
Uniaxial moment capacities
Checking of column for safety
- Deep foundations
- Two-way or punching shear (cls.31.6 and 34.4)
However, the bending moment in each section will be determined by taking all the forces acting on the entire area on one side of the base section, which is obtained by passing a vertical plane through that section that extends along the base (cl.34.2. 3.1 of IS 456). Two-way or punching shear shall be checked around the column at a perimeter of one-half the effective depth of the base plate, away from the face of the column or pedestal. Therefore, the necessary slab thickness must be provided to avoid shear reinforcement.
In the case of unidirectionally reinforced foundation slabs, such as wall footings, the reinforcement must be evenly distributed over the entire width of the foundation, i.e. perpendicular to the direction of the wall. In two-way reinforced square foundation slabs, the reinforcement extending in each direction must be evenly distributed over the entire width/length of the foundation. iii). In the case of two-way reinforced rectangular base plates, the reinforcement in the longitudinal direction must be evenly distributed over the entire width of the base plate.
In the short direction, a central band corresponding to the width of the footing must be marked along the length of the footing, where the part of the reinforcement must be determined as indicated in the equation below. Reinforcement in the middle band = {2/(β+1)} (Total reinforcement in the short direction) Where β is the ratio between the longer dimension and the shorter dimension of the base plate (Fig.3.10). Each of the two end bands shall be provided with half of the remaining reinforcement, distributed uniformly over the respective end band.
The stud shall extend into the column, a distance equal to the development length of the column strip and into the footing, a distance equal to the development length of the stud, as defined in cl.34.4.4 of IS 456. For a cut of way, the critical section is located at a distance ‗d' from the face of the column where the shear force V is given by.
MODULE-4
Lateral loads acting on the facade of the building are transferred through the floor (which act as horizontal beams) to the transverse walls which act as horizontal beams) to the transverse walls which act as shear walls. Due to lateral loading, there will be an increase in compressive stress on the windward side and a decrease in compressive stress on the windward side in the transverse walls. The so-called "transverse wall" construction may not have much lateral resistance in the longitudinal direction.
If openings in longitudinal walls are located in such a way that sections of these walls act as flanges for transverse walls, the strength of the transverse walls is significantly increased and the structure becomes much more stable. vii) Usually a load bearing masonry structure is designed for allowable compressive and shear stresses (without tension) as a vertical cantilever according to accepted principles of engineering mechanics. No moment transfer is allowed, at floor-to-wall connections and lateral forces are assumed to be resisted by diaphragm action of floor, roof slabs, acting as horizontal beams, transfer lateral forces to cross walls in proportion to their relative stiffness (moment of inertia). Since we will consider combined stresses due to vertical loads and wind load, we will work out all loads at the top of foundation footing, which are.
It is clear that wind load perpendicular to the long walls will be critical, and therefore we will calculate bending stresses in both long and transverse walls due to wind load perpendicular to the long walls. Total wind load for the building (5 bays) = 31.20 X 5 = 156 kN Moments due to wind load on long wall. It can be assumed that this lateral support will be sufficient as a horizontal girder to transfer the wind force to the transverse walls.
Since the cross walls are identical except for a small door opening in the middle in one wall, for practical purposes it can be assumed that the wind loads are shared equally by the 2 walls. If bricks of this strength are not available locally, it would be necessary to insert posts under the beams in order to increase the bearing area while reducing the stress on the masonry. ii) Masonry for cross walls.
