Structural frame ( Vol A- construction and detailing )

Structural frame elements

Columns

Beams

Slabs

Staircases

Foundation

Structural frame loading

Gravity Loads

Seismic loads

Structural frame behaviour

Beams and columns

Slabs

Structural frame elements
 Columns

Floor plan with the vertical load bearing elements highlighted

The vertical load bearing elements of the structural frame are usually called with a common name: “columns”.

3D display of storey columns

Due to their varied behaviour, their different design rules and most of all, their differences in reinforcement and detailing, they are separated into three major categories namely columns, shear walls and composite elements.

Rectangular columns

As Columns are defined the rectangular elements in which the larger dimension of their cross-section is less than 4 times the smaller dimension e.g. 400/400, 400/600, 250/900, etc. (dimensions in mm).

Various column types

The columns category also comprises circular sections, for example D=500 and quadrilateral sections like 500/600 with an inside angle equal to 60˚.

Various column types

The columns category may also include elements with “L”, “T” or “Z” cross-sections, in which the dimension ratio of their orthogonal parts is lesser than 4 e.g. “Γ” cross-section 400/800/250/250, “T” cross-section 700/500/250/250, “Z”cross-section 600/700/900/250, etc.

Shear walls

As Shear walls are defined the rectangular elements with a length to thickness ratio greater or equal to 4 e.g. cross-sections 1000/250, 1500/300.

Composite elements

As Composite elements are defined the elements composed of one or more rectangular elements, at least one of which must be a shear wall. Generally speaking and due to the fact that the two ends of each shear wall are locally reinforced as columns, a wall could be characterized as a composite element. For example a wall with an ”L” cross-section 1200/1000/250/250, or an ”L” cross-section 1200/700/250/250, elevator cores with or without flanges, double elevator cores with a slope on one side etc are composite elements.

Beams

Various beam types ‹project: beams›

Beams are the horizontal or inclined bearing elements of the structural system that connect columns and support slabs

When beams support slabs, they function together with the slab thus forming a “T” section beam. Depending on the relative levels of the slabs compared to the levels of the beams T beams are called common beams, inverted beams or “Z” beams.

Various beam types

Generally, beams are supported by columns (beam to column connection)

However, in some cases one or both beam ends are supported by another beam (beam to beam connection) and in other cases only one end is supported by a column or beam while the other end has no support at all. The beam supported only in one end is called a cantilever.

 Slabs

Various slab types ‹project: slabs›

Slabs are surface plane elements that bear loads transverse to their plan

Slabs are statically indeterminate elements therefore redistributing the stresses applied to them. This ability makes them highly safe against bending and shear failure. Cantilever slabs do not dispose of this property as they are statically determinate elements and therefore need special care in their construction.

Hypothetical formwork plan, where the arrows indicate the supported sides of slabs

Depending on their support conditions, slabs are classified as follows:
One-way slabs (simply supported)
They are those supported on two out of four, opposite sides like S1 of the above example.
Two-way slabs
They are those supported on all four sides like S2, S3 of the above example
Cantilever slabs
They are those with a fixed support on only one out of four sides, like S4 of the above example.
Two-way slabs supported on three edges
They are those supported on three out of four sides, like S5 of the above example.
Two-way slabs supported on two adjacent edges
They are those supported on two adjacent sides, like S6 of the above example.

Slab behaviour

The slab with the bilateral continuity (a) behaves in the best way. Next comes the slab with the unilateral continuity (b) while last comes the slab with no continuity (c)

As regards to support, the safest slab is the two-way slab and the most vulnerable one is the cantilever slab. This happens because in a two-way slab, potential loss of one support results in a two-way three support slab, while in the case of a cantilever slab potential support loss results in collapse.

One–way ribbed slab ‹project: zoellner10›

Ribbed slabs (waffle slabs) (Zoellner, sandwich) can be used for large spans, like the one shown in the figure

A ribbed slab with total thickness of 300 mm may have a self-weight equal to 3.75kN/m², which corresponds to the self-weight of a 150 mm thick solid slab.

Two–way ribbed (waffle) slab ‹project: zoellner20 ›

Usually two-way slabs have square voids between the ribs because the demand for adequate bending strength is equal in both directions

The square voids are being shaped either using lightweight fillings like polystyrene or using plastic moulds. The latter have significant constructive advantages (qualitative, fast construction) thus providing economical solutions.

Stairs

3D display of a staircase

Although stairs are not part of the structural load bearing frame, they affect and they are affected by its behavior especially when horizontal loading is applied, mainly due to seismic actions

If the staircases are both properly placed in the structure’s plan and properly constructed they may even enhance the structure’s antiseismic behavior.

Foundation

Foundation consisting of flexible and rigid spread footings (no connecting beams)

<project: Foundation10>
Foundations are meant to carry the structural frame loads to the underlying soil imposing a light compressive stress

Foundation generally includes the footings and the pedestals. The simplest type of foundation is the spread foundation (pad foundation) i.e. isolated column footings. As a rule, spread footings consist only of a box and they are usually called flexible. Sometimes they may have a relatively large height and a sloped end, and they are called rigid.

Spread footing section

Footing dimensions depend on the soil quality and the loads transferred by the columns (column loads are determined by the distance between the columns along with the number and loads of the structure’s storeys). The usual footing dimensions range from 1.0x1.0 m to 3.0x3.0 m although sometimes they may be larger and their height varies between 0.5 and 1.0 m for flexible spread footings and between 0.7 and 2.0 m for rigid spread footings.

Foundation consisting of flexible spread footings and connecting beams

<project: Foundation20>

In order to ensure the proper behavior of the foundation, the use of foundation beams (connecting beams) is mandatory. These beams tie together the column’s bases thus making the footings behave in a even way especially during seismic incidents. Usually their cross section width ranges from 300 and 500 mm and their cross section height from 500 to 1500 mm.

Side view and plan of flexible spread footing

Footings are constructed symmetrically to their mass centre, except in those cases when due to building restrictions they are eccentrically constructed e.g. like boundaries of the building line or edge of the building land as shown below.

Foundation consisting of spread footings eccentrically constructed

<project: Foundation30>

The higher the footing’s construction eccentricity is, the strongest must the connecting beam in that direction should be.
Spread foundation (pad foundation) is used in a good quality soil. In case of low soil capacity strip foundation is used.

Strip foundation with connecting beams

<project: Foundation040>
For a more effective behavior it is advisable to use grid foundation

Section and plan of a footing beam

Strip foundation as an inverted T beam consists of the web and the flange (the footing). The usual dimensions of the footing vary between 400 to 600 mm for its thickness and between 1000 to 2500 mm for its width. The typical web cross sections range from 300x800 to 500x1500.

Raft Foundation with connecting beams

<project: Foundation50>

In poor soil conditions a slab which extends over the entire loaded area, the so called raft foundation, is usually preferable. Frequently it is used in other soil conditions for practical reasons basically because of its fast and easy construction.
Raft foundation may have normal foundation beams as ribs, as shown in the above figure, or beams embedded into the foundation as hidden beams.
The usual thickness of a raft foundation, ranges from 400 to 1000 mm, while the dimension of the raft foundation beams vary from 300x800 to 500x2000 mm.

Two level foundation

<project: Foundation60>

Generally foundation should be preferably placed at one single level. However, in certain cases such as for example building on a sloped plot, foundation is placed on more than one level.

 

Structural frame loading

Gravity Loadings

Building loads

In every building like the one shown in the above figure, permanent (dead) and imposed (live) loads are applied. The latter are much lower than the former, for example 3 persons and the living-room furniture weight as much as a single m2 of slab surface while a car weights as much as a sole beam. Structure loads can be classified into three categories gravity loads, seismic loads and wind loads.

Permanent and imposed loads

The structural frame is designed to continuously withstand the vertical gravitational loads (self-weight, masonry walls, floor coverings, cars, furniture, people etc) and, not in a continuous but in a periodical basis, the wind and snow actions. Moreover it must always bear the “self-induced” loadings caused by temperature changes etc.

Apart from the usual loads, in earthquake prone regions, the structural frame must have enough strength surplus distributed in such a way so that in the critical moment of an earthquake, to be able to respond successfully, retaining the building intact.

Dead loads – self-weight

The density and the related unit weight of the materials used in construction are:
Reinforced concrete ρ=2.50 t/m3 (ε=25.0 kN/m3)
Light- weight concrete for ground leveling ρ=0.80 t/m3 (ε=8.0 kN/m3)
Sand mortar ρ=2.00 t/m3 (ε=20.0 kN/m3)
Marble ρ=2.70 t/m3 (ε=27.0 kN/m3)
The dead mass of one m2 of the above slab is,
g = 0.15*2.50 + 0.04*0.8 + 0.02*2.0 + 0.02*2.7 = 0.5 t,
i.e. the self mass of one square meter of a usual slab is 0.5 t (weight 5.0 kN)

Dead loads – water

ρ = 1.00 t/ m3 (ε = 10.0 kN/m3)
The dead mass of one m2 of a pool slab, when the pool is filled with just 1.0 m of water is,
1.4 t (weight 14.0 kN)

Dead loads – garden soil

ρ = 2.50 t/m3 (ε = 25.0 kN/m3)
The dead mass of one m2 of a slab, with 1.0 m of soil on top is 2.5 t (weight 25.0 kN)

Dead loads – masonry

Masonry stretcher bond ρ = 0.21 t/m² (ε = 2.1 kN/m²)
Masonry Flemish bond ρ = 0.36 t/m² (ε = 3.6 kN/m²)

A wall of 1.00 m length, 2.85 m height and 100 mm thickness has a mass equal to 0.6 t. (weight 6.0 kN).

Live loads – normal human loading

ρ = 0.20 t/m² (ε = 2.0 kN/m²)
The live mass of one m2 residential building is 0.2 t (weight 2.0 kN)

Live loads - humans concentration

ρ = 0.50 t/m² (ε = 5.0 kN/m²)
The live mass of one m² commercial area is 0.5 t (weight 5.0 kN)

As a rule, snow loading is lower than the live load generated by the use of people and its value ranges between 0.60 and 1.50 kN/m².

Vehicle live loads

ρ = 0.25 t/m² (ε = 2.5 kN/m²)
The live distributed load of 1 m² of a parking space is 0.25 t (weight 2.5 kN)

Dead-live loads comparison

In a residential building, the maximum live loads are about 20% of the dead loads

Live loads during an earthquake

In random cases like earthquakes, the extensive live loads may reach 6% of the dead loads

 

Seismic loads

The effect that a seismic action will have in a structure is determined by regarding an earthquake with horizontal design ground seismic acceleration equal to A=α*g

In the duration of an earthquake, a horizontal seismic force H is applied in every mass M that has gravity load W. The H force is equal to a percentage ε of the W force. ε value usually varies between 0.00 and 0.50 while in a very intense seismic action it may rise above 1.00.

Seismic acceleration distribution

In general terms, the distribution of seismic accelerations has the form of a triangle.

The structure shown above belongs to the Seismic Zone Z1 (seismic ground acceleration equal to 0.16), the mean value of the design seismic acceleration is around 0.12g (ε0=0.12) and the resultant seismic force Fs is around 1400 kN. The theoretical height that this force is applied to, is around the 2/3 of the structure’s total height.

Comparison of wind forces F_w and seismic forces F_s

Comparing the wind and the seismic forces applied to that structure we realize that the wind effect upon the structure is at least four times smaller than the seismic effect

In the same structure, when placed in a geographical region with intense winds, the mean value of the wind pressure is around 1.50 kN/m² and the resultant force around 400 kN. The total service load applied is 12.000 kN. Therefore the wind force is equal to 0.03% of the vertical loads and its theoretical application area is in the middle of the structure’s height.

 

Structural frame behaviour 

 

Non-earthquake resistant structural frame

The frame of the figure comprises two columns and one beam and it bears only gravity loads i.e. no seismic loading is applied

Deformations of a non-earthquake resistant structural frame

The figure shows the concrete deformations and cracks. They are presented in a very large scale to provide a thorough understanding of the way the members behave. In reality they are so small that they are not visible to the human eye.
The tensile stresses generated in some areas of concrete cause the formation of cracks; therefore in those areas the necessary reinforcement is placed. When the cracks are perpendicular to the axis of the member, longitudinal reinforcement is placed i.e. rebars that prevent the expansion of the hairline cracking.
When the cracks are diagonal, transverse reinforcement i.e. stirrups is placed to control them.

One-bay earthquake resistant structural frame

<project: frame1>

An earthquake ground motion causes horizontal displacements that in their turn cause horizontal inertia forces, forces created by the sudden change in the kinetic state of the body.
During the seismic action the applied horizontal forces constantly shift direction. This fact results in a continuous change in the frame’s behavior and consequently the tensile stresses and thus the diagonal cracks appear in different positions and directions. This position- direction alteration is the reason why earthquake design and reinforcement detailing are so critical in areas with high seismic activity.

Behaviour of a one-bay frame during an earthquake

No matter how well designed a structure is, one or possibly more structural members will exceed their design strength, either because seismic forces might exceed the design assumptions or because of local conditions during the construction.

1^st Defense mechanism: In case of an earthquake greater than the design earthquake we don’t want failure (fracture) of any member even if it remains permanently deformed, this means that we need ductile structural members.
2^nd Defense mechanism: in the case of an extremely intense earthquake, where failure of some members is unavoidable, the elements that must not fail are the columns; this means that the columns must have sufficient capacity-overstrength.
In the second defense mechanism all failures must be flexural because of their ductile nature as opposed to shear failures that have a brittle behavior (i.e. sudden fracture

Structural frame ductility

This figure illustrates a column with cross-section 500x500 and three stirrups on every layer, required by the Seismic Code to ensure ductility

Ductility is the ability of a reinforced concrete member to sustain deformation after the loss of its strength, without fracture.
Ductility i.e. the element’s deformation capability beyond its yielding point concerns flexure and presumes adequate shear strength. For this reason shear design is based on the elements capacity-overstrength so as to avoid potential shear failure.

Beam with ductility requirements

Basic rules for beam reinforcement:
(a) Rebars placed in the beams lower part must be equally well anchored as those placed in the upper part since tension and therefore the resulting transverse cracking, continuously change place during a seismic action and as a consequence in critical earthquakes, tensile stresses appear at the lower fibers of the supports.
(b) There must be plenty of strong transverse reinforcement consisting of dense and well-anchored stirrups because the high intensity of the diagonal stresses and thus the large inclined diagonal cracking, shift direction during an earthquake.
Columns and beams usually fail in the joint area i.e. the area where the beam intersects with the column. Therefore columns and beams must be ductile in the joint area.

Beam with high ductility requirements

If all members of the structure system have enough ductility the structure’s strength capacity will depend upon the strength capacity of all the structural members, otherwise it will be depended upon the strength capacity of the most vulnerable structural member.

 

Slabs

 

Steel reinforcement

Reinforced concrete is made of two materials, concrete and reinforcement. The reinforcement is usually made out of steel and, rarely, at least for the time being, it is made out of composite materials, composites.
The reinforcement is divided into two basic categories: (a) the longitudinal reinforcement in the form of rebars and (b) the transverse reinforcement mainly in the form of stirrups.

Behaviour and reinforcement of an one-way slab

Under loading (such as self weight, marble floor coverings, human activities etc) and due to their elastic behaviour, slabs are deformed as shown at the following figure. The real deformation is in the order of millimeters and although it is not visible to the human eye it always has this form. Concrete has a high compressive strength; therefore in the compression zone where there are only compressive stresses, no longitudinal reinforcement is placed. On the contrary, concrete has a very low tensile strength therefore in the slab’s tensile zone where there are only tensile stresses, longitudinal reinforcement is placed.

 Credit 

http://www.buildinghow.com/en-us/Products/Books/Volume-A/The-structural-frame/Structural-frame-behaviour/Slabs 

 

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