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3.1-1 Continuous beams

Every building, whether it is large or small, must have a structural system capable of

carrying all kinds of loads - vertical, horizontal, temperature, etc. In principle, the entire

resisting system of the building should be equally active under all types of loading. In other

words, the structure resisting horizontal loads should be able to resist vertical loads as well, and

many individual elements should be common to both types of systems.

A beam may be determinate or indeterminate

Statically determinate beams are those beams in which the reactions of the supports

may be determined by the use of the equations of static equilibrium.

If the number of reactions exerted upon a beam exceeds the number of equations in static

equilibrium, the beam is said to be statically indeterminate. In order to solve the reactions of

the beam, the static equations must be supplemented by equations based upon the elastic

deformations of the beam.

The degree of indeterminacy is taken as the difference between the number of reactions to the

number of equations in static equilibrium that can be applied.

The degree of indeterminacy is taken as the difference between the number of reactions

to the number of equations in static equilibrium that can be applied.

Continuous beams are those that rest over three or more supports, thereby having one

or more redundant support reactions. According to figure 3.1.1-1, we determine the reactions

and sketch the shear diagrams. Then we compute the values of maximum vertical shear V and

maximum positive bending moment M.

Sufficient reinforcement should be provided at all sections to resist the envelope of the

acting tensile force, including the effect of inclined cracks in webs and flanges.

The area of steel provided over supports with little or no end fixity assumed in design, should

be at least 25% of the area of steel provided in the span.

Where a beam is supported by a beam instead of a wall or column, reinforcement

should be provided and designed to resist the mutual reaction. This reinforcement is in

addition to that required for other reasons. This rule also applies to a slab not supported at the

top of a beam.

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Figure 3.1.1-1

A continuous beam carries a uniform load over two equal spans as shown in figure 3.1.1-1.

A beam carrying the loads shown in figure 3.1.1-2 is composed of four spans. It is supported

by five vertical reactions. We determine the values of the bending moments over supports as

follows.

Figure 3.1.1-2

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A uniform load is carried over three equal spans as shown in figure 3.1.1-3.

Figure 3.1.1-3: equal spans of continuous beam

A uniform load is carried over the more than 3 equal spans with different shapes of cross-

section as shown in figure 3.1.1-4, figure 3.1.1-5.

Figure 3.1.1-4: four spans continuous beam

Figure 3.1.1-5

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Figure 3.1.1-6: Floor T-Beam Reinforcing Elevation

According to figure 3.1.1-7 a simple beam shown of length L that carries a uniform load

of gd (kN/m) throughout its length and is held in equilibrium by reactions Ra and Rb. Assume

that the beam is cut at a distance of Sm from the left support and the portion of the beam to the

right of Sm be removed. The portion removed must then be replaced by vertical shearing force

V together with a couple M to hold the left portion of the bar in equilibrium under the action of

Ra and gd Sm.

Figure 3.1.1-7: Simple supported rectangular reinforced concrete beam

In T-beam construction, the flange and web shall be built integrally or otherwise

effectively bonded together. The effectively flange width to be used in the design of

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symmetrical T-beams shall not exceed 0.40 of the span length of a simply supported beam or

0.25 of the span length of a continuous beam, and its overhanging width on either side of the

web shall not exceed 12 times the slab thickness, nor one-half of the clear distance of the next

web.

Figure 3.1.1-8

Figure 3.1.1-9: cross-section of T-beam

Without shear reinforcement the beam would have a catastrophic failure due to shear-

web and flexure-shear cracks. These cracks would form due to the shear forces in the beam and

cause equivalent tension stresses that would cause failure in the beam since concrete is very

weak in tension. There-fore stirrups at a determined spacing are used to provide a source of

tensile strength against these shear forces (and equivalent tensile stresses). figure 3.1.1-8 shows

a sample factored shear diagram for the floor load of reinforced concrete beam.

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Figure 3.1.1-10: The shear diagram of reinforced concrete beam

Concrete frame structures are very common – or perhaps the most common – type of

modern building. This type of building consists of a frame or skeleton of concrete. Horizontal

members of this frame are called beams and slabs, and vertical members are called columns.

The column is the most important, as it is the primary load-carrying element of the building.

The structural system of a building is a complex three-dimensional assembly of

interconnected discrete or continuous structural elements. The primary function of the structural

system is to carry all the loads acting on the building effectively and safely to the foundation.

The structural system is therefore expected to:

1. Carry dynamic and static vertical loads.

2. Carry horizontal loads due to wind and earthquake effects.

3. Resist stresses caused by temperature and shrinkage effects.

4. Resist external or internal blast and impact loads.

5. Resist, and help damp vibrations and fatigue effects.

The design principle of Strong Beam-Column Joints is essential for building structure to

resist horizontal load such as wind or earthquakes figure 3.1.1-11.

So the structure is actually a connected frame of members, each of which are firmly

connected to each other. These connections are called moment connections, which means that

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the two members are firmly connected to each other. In concrete frame structures have moment

connections in perfect fixed. This frame becomes very strong, and must resist the various loads

that act on a structure during service load figure 3.1.1-11 and figure 3.1.1-12.

Figure 3.1.1-11: Internal column beam multi-storey frame

Figure 3.1.1-12: corner column – beam connection

Figure 3.1.1-13

Figure 3.1.1-14 Redistribution procedures for frames

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Structural floor systems are, of course, influenced by the material used, but in all cases

they are a combination of slabs and joists or secondary beams (floor beams in the case of larger

spacing). The characteristic element, for the whole floor structure, is the floor slab whose

thickness and reinforcement is dependent upon the span, the loading and the support conditions.

Figure 3.1.1-15: Diagram of reinforcement in RC frame

They are structural elements with a small thickness comparable to their dimensions in

the other two directions. Used for floor, roofs and bridge decks. Maybe supported by edge

beams or walls, or they may be supported directly by columns, flat slab. When two-way slab

systems are supported directly on columns, shear around the columns is critically important,

especially at exterior slab-column connections where the total exterior slab moment must be

transferred directly to the column.

For a typical continuous RC slab as shown in figure 3.1.1-16, is a flexural member that

requires flexural reinforcement in addition to the concrete strength. Concrete, reinforcement,

and formwork are the three primary expenses in cast-in-place concrete floor construction to

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consider throughout the design process, but especially during the initial planning stages. In

general, span lengths, floor loads, and geometry of a floor panel all play a key role in the

selection process The section fails if the design moment exceeds the resistance moment

Figure 3.1.1-16: Continuous reinforced concrete slabs

Additional parameters must be considered when selecting an economical floor system.

The corners of the slab lift, if they are not loaded by vertical forces of constructions above,

resulting in torsional moments.

Figure 3.1.1-17

The most efficient floor plan is rectangular, not square, in which main beams span the

shorter distance between columns and closely spaced floor beams span the longer distance

between main beams. The spacing of the floor beams is controlled by the spanning capability

of the concrete floor construction.

The structure rests on foundations, which transfer the forces – from the building and on the

building – to the ground.

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There are other types of connections, including hinged connections, respectively fixed

connections, which are used in steel structures figure 3.1.1-18 and figure 3.1.1-19.

.

Figure 3.1.1-18

Figure 3.1.1-19