REINFORCED CONCRETE STRUCTURE COURSE STR … · REINFORCED CONCRETE STRUCTURE COURSE STR 302A ... One-Way Ribbed or Hollow-Block Slab ... Effective Span i) L e for simple or continues

PROF. Dr. MAGDY KASSEM - LECTURES OF 3RD YEAR CIVIL – 1ST TERM - 2012/2013

REINFORCED CONCRETE STRUCTURE

COURSE STR 302A

CL0SED BOOK EXAM

THIRD YEAR CIVIL FIRST

TERM YEAR 2012 – 2013

COURSE CONTENTS : DESIGN OF DIFFERENT SLABS

TYPES OF SLABS

- Solid Slab - Hollow Block Slab

- Paneled Beam Slab - Stairs

- Flat Slab

GRADES

TUTORIAL & ASSIGNMENT

20%

MED TERMEXAM

10%

FINAL EXAM 70% TOTAL 100%

ناحتمالا ىف ةیرورض( میمصتلا تادعاسم – لامحالا دوك – ةناسرخلا دوك)

ظنام حصص الشرح كام ھو عمروف

SOLVED EXAMPLES

PREPARED BY

PROF. DR. MAGDY KASSEM


3rd Year Civil 1 st Term - 2012 - 2013

No Date Lecture Tutorial

1 15-9-2012 Solid Slabs Solid Slabs

2 22-9-2012 Solid Slabs Solid Slabs

3 29-9-2012 Solid Slabs Quiz + Grading S slabs

4 6-10-2012 Paneled Beams Paneled Beams

5 13-10-2012 H.B Slabs Quiz + Grading P.B

6 20-10-2012 H.B Slabs H.B Slabs

عید اضألحى المبارك 10-2012-(26-29) 7

إمتحانن صف الفصل ادلراسى 2012- 3-11 8

9 10-11-2012 H.B Slabs H.B Slabs

10 17-11 -2012 Flat Slabs Quiz + Grading H.B

11 24-11-2012 Flat Slabs Flat Slabs

12 1-12- 2012 Flat Slabs Flat Slabs

13 8-12-2012 Stairs Quiz + Grading F.S

14 15-12-2012 Stairs Stairs

15 22-12-2012 Quiz + Grading Stairs


One-Way Ribbed or Hollow-Block Slab

System

If the ribs are arranged in one direction, loads are transferred in one direction; the slab is called one-way ribbed (joist) slab, see Figures 3 and 4. The ribs are supported on girders that rest on columns.

Structural Plan


Figure 3: One-Way hollow-block slab system

Figure 4: Isometric of one-way hollow-block slab system


Two-Way Ribbed or Hollow-Block Slab

System

If ribs are arranged in two directions, loads are transferred in two directions; the slab is called two-way ribbed (joist) slab.

Different systems can be provided of two-way ribbed slab as

follows, see Figure 5.

i. Two-way rib system with permanent fillers between ribs that

produce flat slab is called two-way hollow-block (joist) slab system, see Figure 5a1 and 5a2.

Figure 5a-1: Structural plan of two-way hollow-block slab


Figure 5a-2: Isometric of two-way hollow-block slab system

ii. Two-way rib system with voids between the ribs that obtained by using special removable forms (pans), normally square in shape, is called two-way ribbed (joist)slab system, Figure 5b.

Figure 5b: Structural plan of two-way ribbed slab


iii. Two-way rib system, with voids between the ribs, has the ribs continuing in both directions without supporting beams and

resting directly on columns through solid panels above the columns. This type is called a waffle slab system, Figure 5c.

Figure 5c: Interior panel of waffle slab system


Reinforcement details and blocks

arrangement

Figure 10 shows the reinforcement details of one-way hollow-block slab systems.

Sec. (1-1)


Sec. (2-2)

Sec. (3-3)

Figure 10: Reinforcement details of one-way hollow-block slab system on plan and in cross-sections


Reinforcement details and blocks

arrangement The arrangement of hollow-block and shape of reinforcement details of two-way slab systems are shown in Figure 12.

Figure 12: Plan of reinforcement details of two-way simply

supported hollow-block slab system


Paneled Beam Slab

Design of Edge Beams

The floor "mother" slab a × b is divided into small slabs s1, s2, s3

by a system of paneled beams. Each of the baby slabs s1, s2, s3 ….. is designed as a solid (or hollow blacks) slab.

For the designer of edge beams, consider the whole slab a × b to be carried by the four beams at the four edges: For analysis of edge beams, there are two approaches:

1. distribute load on edge beams from slab as if there is no

paneled beams inside, i.e. assuming fracture lines at 45o

from corners.

• this approach becomes more appropriate as the number of paneled beams not supported directly on columns increases.


2. Transfer reactions of panelled beams to edge beams and solve the edge beam subjected to:

1. reaction of panelled beams

2. slab loads of slabs adjacent to the edge beam.

• this approach becomes more appropriate than the former

one as the number of panelled beams supported directly on

column increases.



Flat Slabs

Introduction

Flat slabs are beamless slabs resting directly on columns. They may have drop panels and/ or columns may have column capitals

as shown in Figure (1). They may be solid or ribbed in two

directions with or without hollow blocks. Generally speaking, flat slabs behave like two continuous

orthogonal frame system. Accordingly, the bigger moments occur in the direction of bigger spans. This behavior is different than two- way solid slabs supported on all four sides.

Flat slabs Roofs

Solid Slabs Flat Slabs


Flat Slabs without drop Panel ( L.L 500 kg/cm2)

B

A A

B

ts

Section A - A

Flat slabs with drop Panel ( L.L 1000 kg/cm2)

A A

ts (drop panel) ts

Section A - A



Flat Slabs



o Stairs Slab and Beam Type

Slab Type Cantilever Type

Cantilever Type


Solid Slabs

O ne Way Slabs

Effective Span

Loads

Minimum Thickness

Bending Moments

Reinforcement

Supports

Two Way Slabs

General

Effective Spans

Minimum Thickness

Simplified Method for Calculating

B.M. in Two Way Slabs

Reinforcement

Calculations

Practical Cases

Concluding Remarks


Waffled slabs (ribbed slabs without hollow

blocks , spacing about 1 m each direction)

• Solid Slabs

• Hollow Block Slabs

• Flat Slabs

• Waffle Slabs

• Paneled Beams Slabs

•Loads

•Spans

•Design Requirements

Structural system must be chosen

Ly to satisfy economic requirements

according to these factors

Lx


One-way slabs

Thickness t = b / 30

= b / 35

= b / 40

= b / 10

Two-way slabs


= b / 40

= b / 45



One Way Slabs

* Slabs supported on two opposite sides only

* Slabs supported on four sides with effective length (be) greater than twice the effective

length (ae)

* One way slabs are to be calculated based on strips of unit length in the short

direction


Effective Span

i) Le for simple or continues slab is the larger of :

c s

or 1.05 Lc

or Le < L

ii) Le for cantilever slabs is the smaller of :

L

or Lc + ts

iii) Continuous or simply supported slabs supported on beams with b > 0.2 Lc can

be

designed as fixed at support, and every span can be calculated separately


Loads

* Total load on slab: W = WD + WL

* Dead loads:

WD = slab self weight + flooring = ts (mm) × 2.5 + (1.5 → 3.5)

kN/m2

* Live loads:

WL: depends on the function of the building.

* If designing using Limit State Design Method,

use Wu = 1.4 WD + 1.6 WL

L.L IS TO BE TAKEN FROM FROM CODE ACCORDING TO THE

FUNCTION OF THE BUILDING

Supports

The width of the support for slab is the larger of :

ts or 150 mm …..for brick walls

100 mm …………for R.C. beams


Minimum Thickness

1. Slab thickness shall not be less than the absolute minimum of:

tmin = Le/30 simply supported at both ends tmin = Le/35 continuous at one end

tmin = Le/40 continuous at both ends Where Le is the effective span as defined above

2. For ordinary buildings and cast-in-situ slabs:

ts > 80 mm under static loads ts > 120 mm under dynamic loads

3. Smaller thicknesses can be used in pre-cast slabs.

4. Minimum thickness to satisfy the deflection limits in ordinary buildings (i.e. no need to

check deflection if the slab thickness is not less than the values indicated) is as follows:

Table (4-10) – ECCS 203-2001

Span / depth ratio; L/d

* Table (4-10) applies only if the following conditions are satisfied:

1. ordinary buildings

2. spans ≤ 10 m

3. uniform, but not heavy, live load, (live load ≤ twice dead load)


Bending Moments

N.B.

* In designing with Ultimate Limit States Design Method: w = w ultimate

* In designing with Working Stress Design Method: w = wworking





Bending moment of slab

According to ECCS 203-2001, the bending moment of equal span ribs or

with maximum difference not greater than 20% of the larger span is as follows:

M = wL2/k, where k is as follows:

- Simple span

- Two spans

- More than two spans

Reinforcement

The main reinforcement of a slab shall satisfy the requirements of equilibrium:

C = T Mu = C . yct = T. yct

cover = 15 – 25 mm

The reinforcement shall also be arranged along the direction of short span.Normal

to the main reinforcement, shrinkage and temperature (distributes) reinforcement

are provided.


1. Minimum main reinforcement:

* For mild steel :

* For high strength steel :

The main reinforcement should be arranged to cover all the tension zones and

extend beyond the end of these zones enough to develop the necessary

anchorage.


One way slab reinforcement details.

3. Maximum spacing between bars of main steel is 2 ts and < 200 mm.

For ts < 100 mm, spacing of 200 mm may be used. 4. A minimum of 1/3 of the main steel must be extended to the supports.

5. Distributors with minimum of 4 bars/m. 6. Minimum diameter for straight bars is 6 mm.

Minimum diameter for bent bars is 8 mm.

Bars of smaller diameters may be used for welded wire mesh and pre-cast concrete.

7. When using steel mesh, all conditions above must be satisfied.


8. For slabs with thicknesses ≥ 160 mm, top mesh must be provided. The top mesh must

be taken ≥ 20% of the bottom reinforcement, but not less than 5Ø8 /m' for mild steel

or 5Ø6 /m' for high strength steel.

Choice of Slab Reinforcement

1. Chosen bars diameters:

- mild steel (24/35) 8, 10, 13mm

- high grade steel(36/52) 8, 10, 12mm

2. Half of the steel is straight bars & the other half is bent bars

3. Min. number of bars (in 1.0 m) is 5 and max. number is 10, the

common number is 6 – 8 ( 6 10/m )

4. We can use bars of the same diameters or two successive diameters

( 310+ 38/m ) and the big diam is the bent bar

5. The number of bars should be the same in the same direction

6. Steel in long direction (secondary) 0.25 steel in short direction

(main)

7. Rules of bent bars in beams ( L / 7, L / 5, L / 4) are applied for slabs


Practical Cases

1- In one way slab, difference between adjacent spans is greater than

20%: - Solve continuous strip (1.0 m width)

2- One way slab adjacent to two way slab:

- Design for the larger – ve moment at the common support

3- Washrooms: - Drop slab of the washrooms by (100-150) mm.

Hence slabs become not continuous with adjacent slab of the floor.

4- Slab with openings:

- For small openings less than spacing between bars; do nothing.

- For small openings greater than spacing between bars; use additional reinforcement.


* For large openings, use more accurate analysis.


Two Way Slabs

Two-way slabs


= b / 40

= b / 45


Two Way Slabs

- A small element of medium – thick plate is shown in figure:


The following equation gives the basic equilibrium requirement for a medium thick plate:

Unlike one way slabs which deform under load into nearly a cylindrical surface, two way slabs bend into a dished surface. This means that at any point, the slab is curved in both directions. The applied distributed load “W” on the element is carried partly by bending as a beam strip in the x- direction producing “Mx”, partly by bending of the strip in the y-direction

producing “My”, and the remainder by interaction between the x and y

strips, i.e. by torsion producing Mxy .

General

1. Rectangular slabs supported on all four sides can be considered as two way slabs if the

rectangularity ratio “r” is smaller than 2, or large than 0.5.

2. Slabs can be solved according to the elastic theories on condition that

the reinforcement resisting –ve moments is placed in the right position during casting..

3. The following method of design is valid only for ordinary buildings with

small uniformly

distributed live load up to 5 kN/m2.


Loads

* Total load on slab: W = WD + WL

* Dead loads:

WD = slab self weight + flooring = ts (mm) × 2.5 + (1.5 → 3.5)

kN/m2

* Live loads:

WL: depends on the function of the building.

* If designing using Limit State Design Method,

use Wu = 1.4 WD + 1.6 WL

L.L IS TO BE TAKEN FROM FROM CODE

ACCORDING TO THE FUNCTION OF THE BUILDING

Supports

The width of the support for slab is the larger of :

ts or 150 mm …..for brick walls

100 mm …………for R.C. beams

Effective Spans

- Refer to one way slabs.


Minimum Thickness

1. Slab thickness shall not be less than the absolute minimum of:

tmin = Le/35 for freely supported slab

tmin = Le/40 for slab continuous at one end

tmin = Le/45 for continuous or fixed slab

Where Le = the smaller effective span of the slab as indicated in one way

slabs.


Simplified Method for Calculating B.M. in Two Way

Slabs

Rectangular slabs, monolithically cast with beams and supported on all four sides, with rectangularity ratio “r” less than 2 and greater than 0.5 subjected to uniform loads can be calculated according to the following simplified method:

where: mb = ratio of length between points of inflection for a loaded strip in

direction

of span “b” to the effective span “b”. ma = same but for span “a”

a = the effective span in direction a.

b = the effective span in direction b.

The values of ma & mb are to be determined from theory of elasticity. For slabs, the following values may be adopted.

Knowing the value of “r”, the load carried in each of the two perpendicular directions can be calculated using the values of α and β of Table (6-1) (ECCS

203-2001)

Table (6-1) EC 2001

For slabs monolithically cast with beams

α = 0.5r – 0.15 β = 0.35/r2


The bending moment in continuous slabs can be calculated as follows:

where: k = 10 for slabs continuous at one end. = 12 for slabs continuous at both ends.

N.B.: negative moment of at exterior support must be considered. For slabs resting on masonry walls, the load distribution factors, α and β are determined according to Table (6-2) ECCS 203-2001.

Table (6-2) (ECCS 203-2001) For slabs resting on masonry walls

* If live load ≥ 500 kg/m2, use Table (6-3) instead of Tables (6-1) and (6-2).

Table (6-3) (ECCS 203-2001)

For solid slabs resting with L.L. ≥ 500 kg/m2


Two-way slabs


= b / 40

= b / 45


1. Loadings :

* Dead Load (wD) - concrete weight : 0.12 x 2500 kg/m2

- flooring 150 – 200 kg/m2

* Live Load (wL) = according to building type

* Total slab load :

ws = wD + wL

2. Load distribution according to Code :

* distribution factor “ 1 r 2 ”

* continuity factor “ m ”

m1 * L1 m = 1.00 r =

m2 * L2 m = 0.87

m = 0.76

The loads in each direction are as:

For two way slabs

w = w s ---- short direction

w = w s ---- long direction

Using “ r “ ---- Get , from

Code table (6-1)…………..page(5)

in the curves

For one way slabs

w = w s

w = 0.0


3. bending moments in slabs

w L2

M = 8

w L2

M = 10

w L2

M = 12

w L2

M = 2

4. Design of sections

dshort = ts – 1.5 cm

dlong = ts – 2.5 cm

dlong

dshort t


Reinforcement

The main reinforcement of a slab shall satisfy the requirements of equilibrium

C = T

Mu = C . yct = T. yct

cover = 15 – 25 mm

The reinforcement shall also be arranged along the direction of short span.Normal

to the main reinforcement, shrinkage and temperature (distributes) reinforcement

are provided.

1. Minimum main reinforcement:

* For mild steel :

* For high strength steel :

2. The main reinforcement should be arranged to cover all the tension zones a nd

extend beyond the end of these zones enough to develop the necessary

anchorage.

:


EACH DIRECTIN OF X AND Y

One way slab reinforcement details. 3. Maximum spacing between bars of main steel is 2 ts and < 200 mm.

For ts < 100 mm, spacing of 200 mm may be used. 4. A minimum of 1/3 of the main steel must be extended to the supports.

5. Minimum diameter for straight bars is 6 mm.

Minimum diameter for bent bars is 8 mm.

Bars of smaller diameters may be used for welded wire mesh and pre-cast concrete.

6. When using steel mesh, all conditions above must be satisfied.

7. For slabs with thicknesses ≥ 160 mm, top mesh must be provided. The top mesh must be taken ≥ 20% of the bottom reinforcement, but not less than 5Ø8

/m' for mild steel or 5Ø6 /m' for high strength steel.


Reinforcement

1. Maximum spacing of main reinforcement in the middle zone of the span

is 2ts but not more than 200 mm. However, For ts < 100 mm , 5 bars/m may be

used.

2. Reinforcement in the secondary direction should not be less than 0.25 of

the main reinforcement with minimum of 5 bars/m'.

3. Positive reinforcement adjacent and parallel to a continuous edge may be reduced

by 25% for a width of not more than ¼ the shorter span of the panel.

4. For other details, refer to one way slabs.




- mild steel (24/35) 8, 10, 13mm









(main)


ANALYSIS AND DESIGN APPROACHE:

- TAKING STRIPS IN BOTH DIRECTION X & Y

- USING DESIGN TABLES


Calculations

Calculations may be carried out in a table form as follows:

1. Load distribution

2. Bending moment and reinforcement For each direction (i.e. main and secondary directions) a table in the

following form may be used.

i) For short direction


10-

300

(31

0/m

) 1

0-30

0 (31

0/m

)

Slab Reinforcement

L / 4

10-400 (2.5 10/m)

10-400 (2.5 10/m)

L / 7 L / 5

L

Slab Reinforcement

1.5 L

10 – 100 ( 10 10 / m )

• • •

• • •

• • • • • •

• • • • • • • • •

• •• • •

Main reinforcement

(10 – 100 )

Secondary reinforcement

( 8 – 200 T & B )

Cantilever Slab


Practical Cases

1- In one way slab, difference between adjacent spans is greater than

20%: - Solve continuous strip (1.0 m width)

2- One way slab adjacent to two way slab:

- Design for the larger – ve moment at the common support

3- Washrooms:

- Drop slab of the washrooms by (100-150) mm. Hence slabs become not continuous with adjacent slab of the floor.

4- Slab with openings:

- For small openings less than spacing between bars; do nothing.

- For small openings greater than spacing between bars; use additional reinforcement.


* For large openings, use more accurate analysis.


• Solid Slabs

• Hollow Block Slabs

• Flat Slabs

• Waffle Slabs

• Paneled Beams Slabs

•Loads

•Spans

•Design Requirements

Structural system must be chosen

Ly to satisfy economic requirements

according to these factors

Lx


One-way slabs


= b / 35

= b / 40

= b / 10

Two-way slabs


= b / 40

= b / 45


1. Loadings :

* Dead Load (wD) - concrete weight : 0.12 x 2500 kg/m2

- flooring 150 – 200 kg/m2

* Live Load (wL) = according to building type

* Total slab load :

ws = wD + wL

2. Load distribution according to Code :

* distribution factor “ 1 r 2 ”

* continuity factor “ m ”

m1 * L1 m = 1.00 r =

m2 * L2 m = 0.87

m = 0.76

The loads in each direction are as:

For two way slabs

w = w s ---- short direction

w = w s ---- long direction

Using “ r “ ---- Get , from

Code table (6-1)…………..page(5)

in the curves

For one way slabs

w = w s

w = 0.0


3. bending moments in slabs

w L2

M = 8

w L2

M = 10

w L2

M = 12

w L2

M = 2

4. Design of sections

dshort = ts – 1.5 cm

dlong = ts – 2.5 cm

dlong

dshort t


S1

9.00

0.00

0.00

--

--

--

cm2/m

--

5 8/m

S2 4.50 0.39 0.745 10.50 0.027 0.032 3.60 3 8/m+3 10/m

S3

2.25

0.975

0.365

10.50

0.0132

0.024

2.63 6 8/m

S4

2.25

0.975

0.438

10.50

0.0159

0.024

2.63 6 8/m

S5 3.50 0.712 1.011 10.50 0.0367 0.041 4.6 6 10/m

S6

5.50

0.312

0.94

09.50

0.04

0.05

4.95 3 10/m+3 13/m

S7

2.00

0.975

2.25

10.50

0.082

0.105

11.48 6 13/m

S8

5.50

0.224

0.81

09.50

0.036

0.04

4.10 6 10/m

Slab leffx wx t/m Mx d cm R as As chosen/m

x- direc.

Slab leffx

wx

t/m My

d (cm) R As

cm2/m

As chosen

/m

S1 1.50 0.975 1.322 10.5 0.048 0.058 6.35 6 10/m

S2 5.00 0.283 0.642 9.5 0.029 0.032 3.42 3 8/m++3 10/m

y- direc. S3 5.00 0.00 -- 9.5 -- -- -- 5 8/m

S4 5.00 0.00 -- 9.5 -- -- -- 5 8/m

S5 6.00 0.117 0.504 9.5 0.023 0.024 2.40 6 8/m

S6 6.00 0.366 1.051 10.5 0.0381 0.042 4.65 6 10/m

S7 6.00 0.00 -- 9.5 -- -- -- 5 8/m

S8 5.00 0.463 1.10 10.5 0.04 0.05 4.95 3 10/m+3 13/m




- mild steel (24/35) 8, 10, 13mm









(main)



1

0-3

00 (3

10/

m)

1

0-3

00 (

3

10/m

)

Slab Reinforcement

L / 4

10-400 (2.5 10/m)

10-400 (2.5 10/m)

L / 7 L / 5

L


Slab Reinforcement

1.5 L

10 – 100 ( 10 10 / m )

• • •

• • •

• • • • • •

• • • • • •

• • •• •

• • •

Main reinforcement

(10 – 100 )

Secondary reinforcement

( 8 – 200 T & B )

Cantilever Slab



Final Reinforcement

of Slab


Documents

REINFORCED CONCRETE STRUCTURE COURSE STR … · REINFORCED CONCRETE STRUCTURE COURSE STR 302A ... One-Way Ribbed or Hollow-Block Slab ... Effective Span i) L e for simple or continues