Prokon Tutorials

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Concrete Design

The concrete design modules can be used for the design of reinforced

and pre-stressed concrete

Concrete Structural Systems

Typical Beam/column/slab

Columns

Columns carry all vertical loads to the foundations in compression. There may be bending moments as a result of the frame action.

Floor slabs

Transmit live loads as well as stationary dead loads to the horizontal beams, which are part of the frame. Slabs do this in bending and shear.

Beams

Transmit loads from the slabs to the vertical columns in bending and shear.

Foundations

Carry all vertical loads to the soil. Vertical

loads include all dead load and live loads.

Concrete Design using PROKON

Beam and slab design

-The Continuous Beam and Slab Design.

-Rectangular Slab Panel Design .

-Finite Element Slab Design.

-The Punching Shear Design module.

Column design

-Rectangular Column Design.

-Circular Column Design.

-General Column Design .

Substructure design

-Column Base Design

-Retaining Wall.

Section design

- Concrete Section Design.

- Section Design for Crack

Continuous Beam and Slab Design

The Continuous Beam and Slab Design module is used to design and detail reinforced concrete beams and slabs as encountered in typical building projects. The

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns without increasing the sagging moments at mid span.

Slabs

One - Direction

Slabs may be simply supported and span in one or two

directions.

Two - Direction

If Ly/Lx > 2

If Ly/Lx < 2 the slab spans in two directions as shown in the sketch the slab spans only in the shorter direction.

One-Way Continuous Slabs And

Beams

The following sketches show some one-way spanning continuous slabs and beams.

Beams and girders T-beam and slab

Rectangular Slab Panel Design

Design

scope

The program designs rectangular reinforced concrete flat slab panels. Design loads include own weight, distributed and concentrated dead and live loads. Slab edges can be made free, simply supported or continuous.

The design code symbols are used as far as possible :-

Slab geometry

dx : Effective depth for reinforcement in the longer span direction, i.e. parallel to the X-axis (mm or in).

dy : Effective depth for reinforcement in the shorter span direction, i.e. parallel to the Y-axis (mm or in).

h : Overall slab depth (mm or in).

Lshort : Length of the short side of the slab, taken parallel to the Y-axis (m or ft). Llong : Longer side length of the slab, taken parallel to the X-axis (m or ft).

Material properties

fcu : Concrete cube strength (MPa or psi). fy : Reinforcement yield strength (MPa or psi). €: Time factor for long-term deflection

n : Poisson’s ratio, typically equal to 0.2. g : Unit weight of concrete (kN/m³ or lb/ft³)

List of symbols

€ time factor Duration of load 2.0 years or more 5 1.4 months 12 1.2 months 6 1.0 months 3 0.0 Instantaneous

Applied loads

WADL : Additional distributed dead load (kN/m² or kip/ft²). WLL : Additional distributed dead load (kN/m² or kip/ft²).). PDL : Additional dead point load (kN or kip).

PLL : Additional live point load (kN or kip).

Reinforcement calculation

The finite element analysis yields values for bending stresses about the X and Y-axes and

tensional stresses. Due to the practical difficulties involved in reinforcing a slab to resist

torsion, the Wood and Armer equations are used to transform the bending and tensional

stresses to effective bending moments in the X and Y-directions.

Design output

Abotx : Bottom steel parallel to the X-axis (mm²/m or in²/ft). Atopx : Top steel parallel to the X-axis (mm²/m or in²/ft). Aboty : Bottom steel parallel to the Y-axis (mm²/m or in²/ft). Atopy : Top steel parallel to the Y-axis (mm²/m or in²/ft).

Column Design

The concrete column design modules are suitable for the design of

the following column types:

-Rectangular Column Design, RecCol: Solid rectangular columns of which the larger column dimension does not exceed four times the smaller dimension.

Circular Column Design, CirCol: Solid circular columns where the simplified design approach applicable to rectangular columns may be applied.

General Column Design, GenCol: Columns of any general shape and columns with openings.

All column design modules can design reinforced concrete columns subjected to bi-axial

bending. Bending schedules can be generated for editing and printing using the

PROKON

Conditions of columns in Prokon

S.C with axial load S.C with bi-axial bending

Braced column with bi-axial bending

Unbraced column with

bi-axial bending

with to bi-axial bending

Short Column

Slender Column

General Column Geometry Input

GenCol is used to design columns of any general shape and hence has a reasonably intricate input procedure.

Retaining Wall

Design

The Retaining Wall Design module

is used to analyze retaining walls for normal soil and

surcharge loads or seismic load conditions. Various types of walls can be considered, including

Cantilever Wall

Simply

supported

The base has no fixity, i.e. free to rotate. The wall is

supported horizontally at the bottom and at the level

defined by Hr.

Propped Cantilever Wall

A_t : Wall thickness at the top (m).

A_b : Wall thickness at the bottom (m).

B : Horizontal base dimension in front of the wall (m). C : Depth of the base (m).

D : Horizontal base dimension at back of the wall (m). F : Depth of the shear key (m).

H₁ : Total wall height (m).

H₂ : Height of soil in front of the wall (m).

H₃ : Height from top of wall to soil level at back of wall (m).

H_r : Height of the support point from the top of the wall for a simply supported or propped cantilevered wall (m).

H_w : Height of water table, measured from the top of wall (m). X : Inclination of the wall (m).

X_f : Position of the shear key, measured from the front of the base (m). X_L : Position of the line load, measured from the front edge of the wall (m). X_P : Position of the point load, measured from the front edge of the wall (m). ß : Angle of soil behind wall (°).

Where possible, the same symbols are used as in the design codes.

Wall geometry

f_cu : Concrete cube compressive strength (MPa). f_y : Reinforcement yield strength (MPa).

δ : Angle of friction between wall and soil (°). Must be zero if Rankine theory is specified.

Ф: Angle of internal friction (°).

ν: Poisson’s ration for the soil. The plane strain value should be used rather than the triaxial value – see geometry and loads input.

k_h.( : Horizontal acceleration for seismic analysis (g k _v.(: Vertical acceleration for seismic analysis (g .(L : Line load on or behind the wall (kN/m

L_h.( : Horizontal line load at top of wall (kN/m .(P : Point load on or behind the wall (kN

.(W : Uniform distributed load behind the wall (kN/m2

Material properties

DL_fact : Ultimate limit state dead load factor. LL_fact : Ultimate limit state live load factor.

P_max : Design bearing pressure at serviceability limit state (kPa)

SF_Ovt : Allowable safety factor for overturning at serviceability limit state. SF_Slip : Allowable safety factor for slip at serviceability limit state.

A_s1 : Flexural reinforcement in the wall (mm2).

A_s2 : Flexural reinforcement in the back part of the base (mm2). A_s3 : Flexural reinforcement in the front part of the base (mm2). A_c1 : Compression reinforcement in the wall (mm2).

A_c2 : Compression reinforcement in the back part of the base (mm2). A_c3 : Compression reinforcement in the front part of the base (mm2). D_s : Density of soil (kN/m3).

K : Active pressure coefficient, including seismic effects. K_a : Active pressure coefficient.

K_p : Passive pressure coefficient.

K_ps : Passive pressure coefficient including seismic effects. M₁ : Maximum ultimate moment in the wall (kNm).

M₂ : Maximum ultimate moment in back part of the base (kNm). M₃ : Maximum ultimate moment in front part of the base (kNm).

P_fac : Pressure factor used for Terzaghi-Peck pressure distribution diagram. V : Shear force in wall at base-wall junction (kN).

v : Shear stress in wall at base-wall junction (MPa).

v_c : Allowable shear stress in wall at base-wall junction (MPa). μ: Friction coefficient between base and soil.

Design parameters

 A unit width of the wall is considered.

 Predominantly active soil pressures are assumed to act on the right-

hand side of the wall.

 Predominantly passive pressures are present on the left-hand side of

the wall.

 Soil pressure, soil weight and wall self-weight are taken as dead loads.

 Applied distributed loads, line loads and point loads are considered to be

live loads.

 If a water table is specified behind the wall, a linear pressure distribution

is used along its depth. The pressure applied on the bottom of the base is

varied linearly from maximum at the back, to zero at the front.

 Point loads are distributed along the depth of the soil. In contrast, line

loads are taken constant in the transverse direction of the wall.

General assumptions

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The equation for determine Ka is deferent for all types of walls

Ka = tan 2(45 – (Ф/2)) …………for Cantilever & simple support wall

- Overturning: F.S > 2.0 …………. Ok

- Sliding: F.S > 1.5 ……….………..Ok

Base pressure

ــــص ضوع دمحم روتكدلا باتك نم ةحفصلا هذه حرش متي

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Determine

:-Section Design for Crack width

The Section Design for Crack width can be used to design reinforced

concrete sections to meet specific crack requirements. Both beam and slab sections can be designed for the combined effects of axial tension, bending moment and temperature.

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Section dimensions

bt : Width of the section (mm or in).

h : Overall height of the section (mm or in). he : Effective surface zone depth (mm or in).

Material properties

fcu : Concrete cube strength (MPa or psi).

fy : Main reinforcement yield strength (MPa or psi).

Design scope

Codes of practice

List of symbols

R : Restraint factor.

T1 : Hydration temperature difference (°C). T2 : Seasonal temperature variation (°C).

a : Thermal expansion coefficient of concrete (m/m per °C or in/in per °C).

T_SLS : The tensile force on the full section at serviceability limit state (kN or kip).

T_ULS : The tensile force on the full section at ultimate limit state. (kN or kip).

M_SLS : Serviceability limit state moment (kNm or kipft). M_ULS : Ultimate limit state moment (kNm or kipft).

Ro critical : The minimum percentage of reinforcement to be supplied.

Applied loads

Ast : Area of suggested reinforcement layout. (mm² or in²). fst : Tensile stress in reinforcement (MPa or psi).

Mu : Ultimate moment capacity of section (kNm or kipft). TU : Ultimate tensile capacity of surface zone (kN or kip).

Design output

The following checks are considered for each load case at serviceability limit state:

· The combined effect of bending moment, tensile force and the seasonal temperature

variation, i.e. M_SLS + T_SLS + T2.

· Early thermal movement, T1 only.

· Early thermal movement and seasonal variation combined, i.e. T1 + T2. · The section is also evaluated at ultimate limit state by considering the combined effect of

bending moment and tensile force, i.e. M_ULS + T_ULS.

Desgin Scope

Concrete

Section

module is a simple utility for designing concrete sections for combined

bending, shear and torsion. Rectangular and T-sections are accommodated.

The Concrete Section Design

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Section dimensions

B : Width of the web (mm). Bf : Width of the flange (mm).

Dct, Dcb : Distance from the top or bottom face to the centre of the steel (mm).

H : Overall height of the section (mm). Hf : Depth of the flange (mm).

Material properties

fcu : Concrete cube strength (MPa).

fy : Main reinforcement yield strength (MPa). fy : Shear reinforcement yield strength (MPa).

Design scope

List of symbols

As : Bottom steel required for bending (mm2). A’s : Top steel required for bending (mm2). Anom : Nominal flexural reinforcement (mm2). Asv : Required shear reinforcement (mm2/mm). Asvn : Nominal shear reinforcement (mm2/mm).

Mu : Ultimate moment capacity for bottom reinforcement only (kNm).

v : Shear stress (MPa)

vc : Allowable shear stress (MPa). vt : Torsional shear stress (MPa).

د باتك يف دوجوم هباشم لاثم حرش

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Design output

Some Reinforcement Configurations Are Also Suggested:

-· Number and diameters of reinforcement bars to resist bending only. · Links to resist shear only in the web.

· Links to resist torsion only in the web and flange.

· Longitudinal reinforcement bars to resist combined bending and torsion in the web. The bottom and top bar configurations are chosen to exceed the required flexural reinforcement at that position plus half the total longitudinal torsion reinforcement.

Punching

Shear

The Punching Shear Design

module designs flat slabs for punching shear at edge, corner or internal columns. Only reinforced concrete slabs are designed – to

design pre-stressed concrete slabs for punching shear, use the Pre-stressed Beam/Slab Design module, Captain, instead.

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Slab geometry

A : Horizontal column dimension, as shown on the screen, or diameter of circular column .((mm or in

.(B : Vertical column dimension, as shown on the screen (mm or in .(Deff : Average effective depth of the slab (mm or in

X : Horizontal distance, as shown on the screen, from the column centre to the slab .(edge (mm or in

.(Y : Vertical distance from the column centre to the slab edge (mm or in

Material properties

fcu : Concrete cube compressive strength (MPa of .(psi

fy : Yield strength of flexural reinforcement (MPa or (psi

fyv : Yield strength of shear reinforcement (MPa or .(psi

Design scope

List of symbols

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A_sx1-4 : Average area of main steel parallel to the X-axis crossing each of the four perimeters (mm² or in²). The first perimeter denotes the innermost perimeter. A_sy1-4 : Average area of main steel parallel to the Y-axis crossing each of the four perimeters (mm² or in²).

Slab reinforcement

A_sv : The total area of stirrups to be provided within 1.5Deff inside a perimeter (mm² or in²). U_crit : Length of critical perimeter (mm or in).

v_c : Allowable punching shear stress (MPa or kip). V_c : Shear force capacity at a stress of vc (MPa of psi).

V_eff : The effective shear force as a function of Vt, Mtx and Mty (kN or kip).

Design output

M_tx : Ultimate bending moment about the X-axis (kNm or kipft). M_ty : Ultimate bending moment about the Y-axis (kNm or kipft). V_t : Ultimate vertical load on column (kN or kip).

The design procedure includes the following steps:

- The effective shear force, Veff, is calculated.

- The program chooses four shear perimeters. The first perimeter is taken a distance 1.5 · Deff away from the column face. Subsequent perimeters are spaced at 0.75 · Deff. The perimeters are chosen to be as short as possible, extending to the slab edge when necessary.

د لاثم ةيؤر . ةحفص يف ريمس 345 باسح متي فيكو Punching Shear يف Flat Slab يف :

Interior Columns

Edge Columns

Corner Columns.

Pre-stressed Beam and

Slab Design

Captain

)

C

omputer

A

ided

P

ost

T

ensioning

Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design and detail most types of continuous pre-stressed beam and slab systems encountered in typical building projects. The design incorporates automated pattern loading and moment redistribution.

Both unbounded systems, e.g. flat slabs, and bonded systems, e.g. bridge decks, can be

designed. Estimates for quantities are calculated and tendon profile schedules can be generated for use with Padds.

Finite Element Slab Analysis

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