Reinforced Concrete II
CHAPTER 10
10.1
Dr. Nasr Abboushi
STAIRS
INTRODUCTION
Stairs must be provided in almost all buildings, either low-rise or high-rise, even if adequate numbers of elevators are provided. Stairs consist of rises, runs (or treads), and landings. The total steps and landings are called a staircase. The rise is defined as the vertical distance between two steps, and the run is the depth of the step. The landing is the horizontal part of the staircase without rises.
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10.2
Dr. Nasr Abboushi
TYPES OF STAIRS
There are different types of stairs, which depend mainly on the type and function of the building and on the architectural architectural requirements. The most common types are as follows. 1. Single-flight stairs: The structural behavior of a flight of stairs is similar to that of a one-way slab supported at both ends. The thickness of the slab is referred to as the
waist. When the flight of stairs contains landings, it may be more economical to provide beams at
and between landings (see next figure). If such supports are
not provided, which is quite common, the span of the staircase will increase by the width of two landings and will extend between landing width is in the range of is about 6 m.
and
, and the total distance between
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. In residential buildings, the and
Reinforced Concrete II
Dr. Nasr Abboushi
An alternative method of supporting a single flight of stairs is to use stringers, or edge beams, at the two sides of the stairs; the steps are then supported between the beams. 2. Double-flight
stairs:
It
is
more
convenient in most buildings to build the staircase in double flights between floors. The types commonly used are quarter-turn and closed-or open-well
stairs, as shown in figure. For the structural analysis of the stairs, each flight is treated as a single flight and is considered supported on two or more beams, as shown in the previous figure (page 318). The landing extends in the transverse direction between two supports and is designed as a oneway slab. In the case of open-well stairs, the middle part of the landing carries a full load, whereas the two end parts carry half-loading only, as shown in figure (d). The other halfloading is carried in the longitudinal direction by the stair flights, sections A-A and B-B. 3. Three or more flights of stairs: In some cases, where the overall dimensions of the staircase are limited, three or four flights may be adopted. Each flight will be treated separately, as in the case of double-flight staircases. 319
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4. Cantilever stairs: Cantilever stairs are used mostly in fire-escape stairs, and they are supported by concrete walls or beams. The stairsteps may be of the full-flight type, projecting from one side of the wall, the half-flight type, projecting from both sides of the supporting wall, or of the semispiral type. In this type of stairs, each step acts as a cantilever, and the main reinforcement is placed in the tension side of the run and the bars are anchored within the concrete wall. Shrinkage and temperature reinforcement is provided in the transverse direction.
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Another form of a cantilever stair is that using open-riser steps supported by a central beam, as shown below. The beam has a slope similar to the flight of stairs and receives the steps on its horizontally prepared portions. In most cases, precast concrete steps are used, with special provisions for anchor bolts that fix the steps into the beam. 5. Precast flights of stairs: The speed of construction in some projects requires the use of precast flights of stairs. The flights may be cast separately and then fixed to castin-place landings. In other cases, the flights, including the landings, are cast and then placed in position on their supporting walls or beams. They are designed as simply supported one-way slabs with the main reinforcement at the bottom of the stair waist. Adequate reinforcement must be provided at the joints.
Provisions must be made for lifting and handling the precast stair units by providing lifting holes or inserting special lifting hooks into the concrete. Special reinforcement must be provided at critical locations to account for tensile stresses that will occur in the stairs from the lifting and handling process.
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6. Free-standing staircase: In this type of stairs, the landing projects into the air without any support at its end. The stairs behave in a springboard manner, causing torsional stresses in the slab.
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Three systems of loading must be considered in the design of this type of stairs, taking into consideration that torsional moments will develop in the slab in all cases: a. When the live load acts on the upper flight and half the landing only (Case 1), the upper flight slab will be subjected to tensile forces in addition to bending moments, whereas the lower flight will be subjected to compression forces, which may cause buckling of the slab. b. When the live load acts on the lower flight and half the landing only (Case 2), the upper flight slab will be subjected to tensile forces, whereas the lower flight will be subjected to bending moment and compression forces. c. When the live load acts on both upper and lower flights, the loading of one flight will cause the twisting of the other. The torsional stresses developed in the stairs require adequate reinforcement in both faces of the stair slabs and the landing. Transverse reinforcement in the slab and the landing must be provided in both faces of the concrete in the shape of closed U-bars lapping at midwidth of the stairs. Typical reinforcement details are shown in the figure below.
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This type of stairs is favored by architects and sometimes called a pliers-shaped staircase or jackknife staircase.
For practical design, the parameters may be chosen as follows: flight width between and
, horizontal span
between
, and slab thickness between
and
and
, total (light height between
.
and
The above information is a guide to help the designer to choose the right parameters for an economical design. 7. Run-riser stairs: Run-riser stairs are stepped underside stairs that consist of a number of runs and risers rigidly connected without the provision of the normal waist slab. This type of stairs has an elegant appearance and is sometimes favored by architects.
The structural analysis of run-riser stairs can be simplified by assuming that the effect of axial forces is negligible and that the load on each run is concentrated at the end of the run 324
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(see next figure). For the analysis of a simply supported flight of stairs, consider a simple flight of two runs,
, subjected to a concentrated load
are rigid, the moment at joint
where
. Because joints
and
, is constant and is equal to
.
is equal to the moment at
is the width of the run. The moment in rise,
When the rise is absent, the stairs,
at
, or
, act as a simply supported beam, and the maximum
bending moment occurs at midspan with value
For a flight of stairs that consists of a number of runs and risers, the same approach can be used; the bending moment diagram is shown below. The moment in
equal to the moment at joint
, or
. Similarly,
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is constant and is
, and
Reinforced Concrete II
Dr. Nasr Abboushi
8. Helical stairs (open-spiral stairs): A helical staircase is a three-dimensional structure, which usually has a circular shape in plan. It is a distinctive type of stairs used mainly in entrance halls, theater foyers, and special low-rise office buildings. The cost of a helical stair is much higher than that of a normal staircase.
The stairs may be supported at some edges within adjacent walls or may be designed as a free-standing helical staircase, which is most popular. The structural analysis of helical staircases is complicated. Design charts for helical stairs are also prepared. Under load, the flight slab will be subjected to torsional stresses throughout. The upper landing will be subjected to tensile stresses, whereas compressive stresses occur at the bottom of the flight. The forces acting at any section may consist of vertical moment, lateral moment, torsional moment, axial force, shearing force across the waist of the stairs, and radial horizontal shearing force. The main longitudinal reinforcement consists of helical bars placed in the concrete waist of the stairs and runs from the top landing to the bottom support. The transverse reinforcement must be in a closed stirrup form to resist torsional stresses or in a U-shape lapped at about the midwidth of the stairs.
Based on many studies, the possible practical dimensions may be chosen as follows: Total subtended arc between thickness between
and
and
, stair width between
and stair height between and
and
, stairs slab
.
The above information can be used as a guide to achieve a proper and economical design of helical staircase. 326
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An alternative method of providing a helical stair is to use a central helical girder located at the midwidth of the stairs and have the steps project equally on both sides of the girder. Each step is analyzed as a cantilever, and the reinforcement bars extend all along the top of the run. Precast concrete steps may be used and can be fixed to specially prepared horizontal faces at the top surfaces of the girder. 10.3
SLAB TYPE STAIRS. STRUCTURAL SYSTEM.
In the second and third types (slab type stairs), the main supporting element could be the slab itself. The flight could be supported on the landing, which is in turn supported on the supporting beams. From the structural point of view, it is better that the main supporting element is spanning in the short direction. However, this depends on the surrounding beams. If the beams exist around the perimeter of the stair well or at least along the long sides, solution A in the figure below is more economical. If the supporting beams are only at the short side, solution B is the only valid structural system.
Since the landing and the stairs are not straight, internal forces are generated in these
sloped elements. The two tensile forces outward force
and
generated at the kink, producing a third
as shown in the next figure. This force tends to cause splitting cracks if the
produced stresses exceed concrete tensile strength. Thus, tension reinforcement should be extended from each side so that no outward force is generated. 327
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Example
Design the staircase shown below, which carries a uniform live load of rise of
and a run of
. Use
and
. Assume a
.
Solution
1. Structural system: If no stringer beam is used, one of the four possible solutions shown in figure (page 318) may be adopted. When no intermediate supports are used, the flight of stairs will be supported at the ends of the upper and lower landings. This structural system will be adopted in this example.
2. Minimum slab thickness for deflection is (for a simply supported one-way solid slab)
In the case presented here, where the slab ends are cast with the supporting beams and additional negative reinforcement is provided, minimum thickness can be assumed to be
Take
.
3. Loads: The applied live loads are based on the plan area (horizontal projection), while the dead load is based on the sloped length. To transform the dead load into horizontal projection the figure below explains how. Flight Dead Load computation:
() ()
∙∙ ∙ cos
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Reinforced Concrete II
Material
Tiles
mortar
Stair steps
Dr. Nasr Abboushi
( ) ( ) ( ) cos cos ∙∙ ∙∙ ∙ ∙
Reinforced Concrete solid slab Plaster Total Dead Load,
Quality Density
Landing Dead Load computation:
Material
Tiles mortar
Quality Density
Reinforced Concrete solid slab Plaster
Total Dead Load
8.01
Live Load:
Total factored Load:
Because the load on the landing is carried into two directions, only half the load will be considered in each direction
.
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∙ ∙√ ∙∙∙ ∙ 4. Check for shear strenght: Assume bar diameter
for main reinforcement.
Assume beam width
- for shear.
The thickness of the slab is adequate enough.
5. Calculate the maximum bending moment and steel reinforcement:
() ∙ ∙ ( )∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙∙ ∙∙ ∙ ∙ Assume bar diameter
Use
for main reinforcement.
then
Take Step
is the smallest of:
1. 2.
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.
Reinforced Concrete II
Dr. Nasr Abboushi
( ) ∙ ( ) s s – ∙ ∙ s s – 6. Temperature and shrinkage reinforcement.
Take
Step
.
is the smallest of:
1. 2.
If the slab will be cast monolithically with its supporting beams, additional reinforcement must be provided at the top of the upper and lower landings. Details of stair reinforcement are shown in the figure (page 333).
7. Design of landings: Considering a 1-m length of the landing, the load on the landing is shown in the next figure. The middle
will carry a full load, whereas the two
1.5-m lengths on each side will carry half the ultimate load.
() ∙ ∙ ( )∙ ∙ ∙ ∙ 332
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Dr. Nasr Abboushi
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Assume bar diameter
for main reinforcement. Because the bars in the landing will be
∙ ∙ ∙ ∙∙ ∙∙ ∙ ∙ ( ) ∙ ( ) s s – placed on top of the main stair reinforcement
then provide
Use
then
Take Step
.
is the smallest of:
1. 2.
8. The transverse beams at the landing levels must be designed to carry loads from stairs ( above.
) in addition to their own weight and the weight of the wall
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Example
Design the staircase shown below, which carries a uniform live load of rise of
and a run of
. Use
and
. Assume a
.
Solution
1. Minimum slab thickness for deflection is (for a simply supported one-way solid slab)
Take
.
2. Loads: Flight Dead Load computation:
Material
Tiles
mortar
Stair steps
() () ( ) ( ) ( ) cos cos Quality Density
Reinforced Concrete solid slab Plaster Total Dead Load,
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Landing Dead Load computation:
Quality Density
Material Tiles mortar Reinforced Concrete solid slab Plaster Total Dead Load
∙∙ 8.01
∙∙ ∙∙ ∙∙
Live Load:
Total factored Load:
3. Design of slab S1:
Slab S1 is supported at the centerline of slabs S2 and S3.
∙ ∙√ ∙∙∙ ∙ The reaction at each end
Check for shear strenght:
Assume bar diameter
for main reinforcement.
Take the maximum shear as the support reaction
- for shear.
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Reinforced Concrete II
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The thickness of the slab is adequate enough.
Calculate the maximum bending moment and steel reinforcement:
∙ ∙ ∙ ∙ ∙ ∙∙ ∙∙ ∙ ∙ ( ) ∙ ( ) s s – Assume bar diameter
Use
for main reinforcement.
then
Take Step
is the smallest of:
1. 2.
∙∙ Temperature and shrinkage reinforcement.
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.
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Dr. Nasr Abboushi
s s –
Take
Step
.
is the smallest of:
1. 2.
4. Design of slab S2:
Slab S2 is supported on the beams located on axis 1,2 at the floor level. The reaction of the slab S1 is applied at the centerline of the slab S2. Since the width of S2 is will be distributed along this width. Thus the load per meter
or
of the slab S1 is applied at the middle of the slab.
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equals
, the reaction
Reinforced Concrete II
Dr. Nasr Abboushi
∙√ ∙∙∙ ∙ The reaction at each end
Check for shear strenght:
Assume bar diameter
for main reinforcement.
Take the maximum shear as the support reaction
- for shear.
The thickness of the slab is adequate enough.
Calculate the maximum bending moment at midspan and the steel
reinforcement:
( ) ∙ ∙ ∙ ∙ ∙ ∙∙ ∙∙ ∙ ∙ Assume bar diameter
Use
for main reinforcement.
then
Take Step
is the smallest of:
1.
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.
Reinforced Concrete II
Dr. Nasr Abboushi
( ) ∙ ( ) s s – ∙ ∙ s s – 2.
Temperature and shrinkage reinforcement.
Take
Step
.
is the smallest of:
1. 2.
5. Design of slab S3: Slab S3 is supported on the beams, the reaction of the slab S1 is applied at the middle of the slab:
Design the slab S3 for flexure and shear as for slabs S1 and S2. 340
