CENTER OF GRAVITY AND CENTROID

The center of gravity or centroid are required parameters in order to determine the moment of inertia of a body. Although these two are often used interchangeably, these terms do differ.

Center of mass is the summation of mass divided by the total body mass in formulation. It is differentiated with the center of gravity with only the introduction of the gravitational acceleration g. Center of mass and center of gravity are used for regular shapes.

Centroid, on the other hand, has the same principle but only used for composite bodies, that is, bodies of different combined shapes. Centroids has similar basic procedure though parameters differ between centroid of a line, centroid of an area, and centroid of a volume.

Click here for pdf notes on Center of Gravity and Centroids

ANALYSIS OF STRUCTURES

credits from Engineering Mechanics - Statics by Hibbeler

The two main methods of analyzing structures are the method of joints and the method of sections. The former method is used when many points or joints are considered in the structure. This method is a longer method as it completes the other members' forces to reach that point in consideration. Method of joints is more on a step by step analysis just to reach a certain joint under study.

The latter method - method of sections - is a faster method especially if there are only specified or few joints or members in consideration. Method of sections utilize a cutting plane from where the unknown member forces should be dissected.

Analysis using any of these two methods would always start in finding the reactions at the supports. These reactions are those added applied loads to be considered besides the readily applied load in the structure (always given).

Frames and machines on the other will consist of the method of frames. This method is a totally different approach from the first two methods. This method includes disassembling the parts to check on the internal forces of each member.

Click here for pdf notes on Analysis of Structures

EQUILIBRIUM OF FORCES

Equilibrium is described in two ways:

1. A particle is at rest,
2. A particle is moving in uniform motion, that is, there is no acceleration.

credits from Palfinger UK

Adopting Newton's second law, F=ma, if we use zero for acceleration (at rest or uniform motion), we get the equation:

                                             F=0

The basic formula can be computed even more easily when the forces are converted to just two perpendicular axes x and y. Thus, the components of forces are used to easily add or subtract collinear forces.

Click here for pdf notes on Equilbrium of Forces

ESTIMATING SURFACE COVERING

Surface covering, such as paint, not only protect the surface but also decorate the wall. Different kinds of surface protection materials are as follows:

credits from Weiler Painting

1. Paint
2. Varnish
3. Shellack
4. Wallpaper

The main procedures for the application are:

a. Surface preparation

b. Diluting the paint into desired consistency

c. Determination of number of coatings.

Click here for pdf notes on Painting

ESTIMATING FORMWORKS

credits from RMD Kwikforms

Although not a part of the resulting structure, formworks, scaffolding and staging are necessary in order to continue with the construction. 

Formworks still have the maximum frequency before materials are worn. Usually they can be reused. However, forms are lumber limiting their use for maximum of two times.

Scaffoldings and staging, on the other hand, already utilizes steel pipes, making their use longer because the material is stronger and more durable.



Click here for pdf notes on Formworks

2.0. FUNDAMENTALS OF FLOW

Hydrodynamics is easier introduced by the understanding of some basic principles - conservation of mass principle, the energy principle, and the principle of momentum. These principles are used in understanding the phenomena during fluid flow.

Two methods are developed to meet the concerns of fluid flow:

credits from Comsol

1. Lagrangian method which analyzes the velocity and acceleration changes of an arbitrary particle.
2. Eulerian method where velocity and pressure changes of a particle are studied at specific points at a certain time.

Fluid behavior also appears in different variations:

• Steady vs unsteady
• Uniform vs non-uniform
• One dimensional vs multi-dimensional
• Viscid vs inviscid
• Compressible vs incompressible
• Ideal vs real

Click here for pdf notes on Fundamentals of Flow

3.0. ESTIMATING MASONRY

The most commonly used material in masonry works is the concrete hollow blocks. Estimation of masonry works involving CHB includes the following items:

credits from India MART

1. Concrete hollow blocks
2. Cement for mortar and plaster
3. Sand for mortar

Different procedures in calculating the number of CHB are available. Most of which utilize the area of spans using CHB.

Click here for pdf notes on Masonry

3.1. CONCRETE HOLLOW BLOCKS (CHB)

Dimensions of concrete hollow blocks are standardized at 16 inches length by 8 inches height (0.40m x 0.20m). The only dimension which varies is the thickness. CHB thicknesses range from 4 inches to 8 inches. 

• 4 inches (0.10m) thick CHB is typically used for CHB partitions.
• 6 inches (0.15m) thick CHB is used for exterior walls.
• 8 inches (0.20m) thick CHB is used for special walls.

3.1.1. THE FUNDAMENTAL METHOD

This method uses the dimensions of block - 8inches height by 16 inches length (0.2x0.40m). Vertical and horizontal layers of the wall will be computed by dividing the wall's height (length) by a unit CHB. The total number of CHB will be the product of the vertical layers by the horizontal layers.

3.1.2. THE AREA METHOD

The area method is based on the number of CHB that will fit a square meter then having this compared with the area of wall to be estimated.

Example 3.1.1 Estimating CHB using the two methods 
Example 3.1.2. Estimating CHB in a concrete structure (Two methods)
Example 3.1.3. Estimating CHB of an irregular wall

3.2. MORTAR

Mortar can be mixed with sand-cement or sand-cement-gravel mixture. Although the mixture with gravel will yield higher strength, most construction procedures apply sand-cement mixture for workability. 

There are two uses of mortar in block laying:

• Cell filler - mortar placed inside CHB cells to keep the masonry into one solid structure. The CHB thickness affects the volume of the hollow cells in a CHB. Regardless of the thickness of the CHB, CHB is made with standard size of 8"x16" using 1" thick concrete sides. The cell length also remains the same at 3".

credits to Medium

• CHB laying - mortar used to stick the various layers of CHB. The standard thickness used for laying CHB is half an inch (12mm) or 0.012m.

3.2.1. THE VOLUME METHOD

Cell filler considers 4 cells in each CHB - 3 internal cells and 2 of half end cells- with the varying volume of each cell. Estimation of the materials for mortar will be through a table with different mixture classes as well.

CLASS	PROPORTION	CEMENT	CEMENT	SAND
		40kg	50kg
A	1:2	18.0	14.5	1.0
B	1:3	12.0	9.5	1.0
C	1:4	9.0	7.0	1.0
D	1:5	7.5	6.0	1.0

3.2.2. THE AREA METHOD

This method is much simpler as it uses a table with the standard volume of mortar needed in each square meter area.

CHB SIZE	CHB NUMBER	A	B	C	D	SAND
		(40kg)	(40kg)	(40kg)	(40kg)
cm	per sqm	bags	bags	bags	bags	cu.m.
10 x 20 x 40	12.5	0.792	0.522	0.394	0.328	0.0435
15 x 20 x 40	12.5	1.526	1.018	0.763	0.633	0.0844
20 x 20 x 40	12.5	2.260	1.500	1.125	0.938	0.1250

3.2.3. THE HUNDRED BLOCK METHOD

This method is similar with the are method but using a table per 100pcs of CHB instead of per square meter of CHB.

CHB SIZE	A	B	C	D	SAND
	(40kg)	(40kg)	(40kg)	(40kg)
cm	bags	bags	bags	bags	cu.m.
10 x 20 x 40	6.336	4.176	3.152	2.624	0.3480
15 x 20 x 40	12.150	8.104	6.072	5.064	0.6750
20 x 20 x 40	18.072	12.000	9.000	7.504	1.0000

Example 3.2.1. Estimating mortar materials in a wall

Example 3.2.2. Estimating mortar materials in a concrete structure

3.3. PLASTER

Plaster is only made of cement and fine sand. It is applied typically at half an inch (0.0125m) thickness.

Again, the estimation of plaster comes in two methods:

• Volume method. This method implores using the area of the wall to be plastered multiplied by the design thickness of the plaster. The total volume will then be multiplied by the factors of concrete mixture from the same table used for mortar-volume method.

CLASS	PROPORTION	CEMENT	CEMENT	SAND
		40kg	50kg
A	1:2	18.0	14.5	1.0
B	1:3	12.0	9.5	1.0
C	1:4	9.0	7.0	1.0
D	1:5	7.5	6.0	1.0

• Area method. Another table is provided for this method. The only parameter needed is the area of the wall to be plastered.

MIXTURE	8mm	12mm	16mm	20mm	25mm
CLASS	THK	THK	THK	THK	THK
A	0.144	0.216	0.288	0.360	0.450
B	0.096	0.144	0.192	0.240	0.300
C	0.072	0.108	0.144	0.180	0.225
D	0.060	0.090	0.120	0.150	0.188
SAND	0.008	0.012	0.016	0.020	0.025

Example 3.3.1. Estimating plaster materials for a wall

Example 3.3.2. Estimating plaster materials for a small structure

3.4. WALL FOOTING

Masonry walls require wall footing in cases where there is no grade beam to hold the wall or partition. Unless specified in the plans, wall footings can be configured as shown:

Two methods of estimating wall footing are listed below:

• Volume method. Measure the volume of the concrete from plans and determine the proportions from concrete volume method.

CLASS	PROPORTION	CEMENT	CEMENT	SAND	GRAVEL
MIXTURE		40kg	50kg
		bags	bags	cu.m.	cu.m.
AA	1:1.5:3	12.0	9.5	0.5	1.0
A	1:2:4	9.0	7.0	0.5	1.0
B	1:2.5:5	7.5	6.0	0.5	1.0
C	1:3:6	6.0	5.0	0.5	1.0

• Meter length method. With a table, the Meter Length method estimates concrete materials easily. The length of wall footing is an important factor in using the table.

DIMENSION	A	B	A	B	SAND	GRAVEL
	40kg	40kg	50kg	50kg
cm	bags	bags	bags	bags	cu.m.	cu.m.
10 x 30	0.270	0.225	0.210	0.180	0.015	0.030
10 x 35	0.315	0.263	0.245	0.210	0.018	0.035
10 x 40	0.360	0.300	0.280	0.240	0.020	0.040
10 x 50	0.450	0.375	0.350	0.300	0.025	0.050
15 x 40	0.540	0.450	0.420	0.360	0.030	0.060
15 x 45	0.612	0.510	0.473	0.405	0.034	0.068
15 x 50	0.675	0.563	0.525	0.450	0.038	0.075
15 x 60	0.810	0.675	0.630	0.540	0.045	0.090
20 x 40	0.720	0.600	0.560	0.480	0.040	0.080
20 x 50	0.900	0.750	0.700	0.600	0.050	0.100
20 x 60	1.080	0.900	0.840	0.720	0.060	0.120

Example 3.4.1. Estimating wall footing for a wall

Example 3.4.2. Estimating wall footing for a structure

Example 3.4.3. Estimating wall footing for a structure
Example 3.4.4. Estimating masonry for a wall

3.5. RETAINING WALLS

Retaining walls are constructed for slope protection. The effect of the soil pressure, which is usually triangular, affects the height of the retaining wall.

These walls are made of:

1. Rip-rap
2. Concrete

3.5.1. RIP-RAP

Rip-rap can be constructed with or without grout. Stones used for rip-rap are also in different classes:

Class A. 15 to 25kg rocks [50% weigh more than 20kg]

Class B. 30 to 70kg rocks [50% weigh more than 50kg]

Class C. 60 to 100kg rocks [50% weigh more than 80kg]

Class D. 100 to 200kg rocks [50% weigh more than 1500kg]

The grout proportions for rip rap as volume method is as follows:

STONE CLASS	A	B	C	SAND
	40kg	40kg	40kg
Class A	2.574	1.716	1.287	0.143
Class B	2.448	1.620	1.214	0.135
Class C	2.232	1.488	1.116	0.124
Class D	1.944	1.296	0.972	0.108

Example 3.5.1. Estimating A Grouted Rip-rap

3.5.2. CONCRETE RETAINING WALL

Estimation of concrete retaining wall is similar to slab estimation. The volume of the retaining wall will be determined after which multiplied with the factors presented on concrete volume method.

MIXTURE	PROPORTION	40kg	50kg	SAND	GRAVEL
		CEMENT	CEMENT
AA	1:1.5:3	12.0	9.5	0.50	1.0
A	1:2:4	9.0	7.0	0.50	1.0
B	1:2.5:5	7.5	6.0	0.50	1.0
C	1:3:6	6.0	5.0	0.50	1.0

Example 3.5.2. Estimating A Concrete Retaining Wall

ESTIMATING ROOF MATERIALS

Different roofing materials have been used recently to add glamour to a structure. The basics, however, still work with galvanized iron sheets - plain and corrugated. With the standard sizes of GI sheets available, a similar procedure as to area method is used in some components as well as directly counting number of roofing sheets required with the effective width.

credits from bh38.net

Click here for PDF notes on Roof Materials

Components to be kept in mind while estimating roofing:

• Smaller gauge is most often used in the roofing material (Gauge 26 corrugated sheet) and thicker for the roofing accessories (usually Gauge 24 plain sheet). 
• Side laps are between 1-1/2 and 2-1/2 corrugations making the standard effective width of the roofing sheet as 0.70m and 0.60m respectively.
• End laps can be taken as 0.25 for steep roof slopes and 0.30 for moderate roof slopes.

ESTIMATING LUMBER IN CONSTRUCTION

credits from Projitech

Although the use of lumber is quite limited nowadays to ornamental parts of the structure, it would still be best to learn the use of it in the major members like they were before. Some countries still prefer lumber over the other materials especially for residences.

Unlike the volume measured in cubic meters for concrete and length, also in meters for steel reinforcement, lumber uses board feet in measurement. A board feet is defined as the volume of lumber given its width (in inches) by length (in inches) and thickness (in inches). But with measurement of length in inches being cumbersome, the formula introduces a divisor of 12 to account for the length of the lumber in feet.

courtesy of Hardwood Distributors Association

Click here for PDF NOTES on lumber

7.0. ESTIMATING CONCRETE REINFORCEMENT

So reinforcing bars are vital components of a concrete structure. One requirement before the construction kicks in is to submit a detailed list of reinforcement. There are structural parts whereby it is easy to determine the number of rebars needed or its equivalent weight; however, there are many members requiring direct count method - which is more tedious but better detailed.

The main structural members where detailed estimates of reinforcement is required are:

1. Footings

2. Columns and posts

3. Beams and girders

4. CHB walls

5. Slab - one way and two way

Click here for pdf notes on Estimating Concrete Reinforcement

7.1. STANDARD WEIGHT OF PLAIN OR DEFORMED ROUND STEEL BARS IN KG

DIAMETER	5.0m	6.0m	7.5m	9.0m	10.5m	12.0m	13.5m
	kg	kg	kg	kg	kg	kg	kg
8mm	1.98	2.37	2.96	3.56	4.15	4.74	5.33
10mm	3.08	3.7	4.62	5.544	6.47	7.39	8.32
12mm	4.44	5.33	6.66	7.992	9.32	10.66	11.99
13mm	5.21	6.25	7.83	9.38	10.94	12.5	14.07
16mm	7.9	9.47	11.84	14.21	16.58	18.95	21.32
20mm	12.33	14.8	18.5	22.19	25.89	29.59	33.29
25mm	19.27	23.12	28.9	34.68	40.46	46.24	52.02
28mm	24.17	29	36.25	43.5	50.75	58	65.25
30mm	27.75	33.29	41.62	49.94	58.26	66.59	74.91
32mm	31.57	37.88	47.35	56.82	66.29	75.76	85.23
36mm	39.96	47.95	59.93	71.92	83.91	95.89	107.88

7.2. BAR SPLICE, HOOK AND BEND

a. SPLICE LENGTH:

In steelwork estimating, splicing, hooks, and bends should be accounted for.

Example 7.2.1. Determining Splice Lengths


b. HOOK LENGTH

Hooks are often placed with lateral ties or stirrups to hold the shape of the ties.  Usually, hook length (for one side) is nine times the diameter of the rebar.

          



c. BEND LENGTH

Bends are often placed with bigger diameter bars as it is hard to make hooks on them.  Bends are considered to anchor a member to another, such as column to a footing. Bend length is considered as sixteen times the bar diameter. In other cases, bends are taken from plans' specifications.

          


d. DEVELOPMENT LENGTH

This length is required of the bar to transfer the stress it is carrying into the concrete. Most often development length is computed as:

          

7.3. REINFORCEMENT REQUIREMENTS OF STRUCTURAL MEMBERS

There are parts of reinforcement that an estimator should be familiar with:

a. CHB WALLS

• Vertical reinforcement
• Horizontal reinforcement

b.  FOOTING REINFORCEMENTS

• Footing slab reinforcement for small and medium size
• Beam reinforcement for large foundations
• Dowels

c. POST AND COLUMN REINFORCEMENTS

• Main vertical reinforcement
• Lateral ties

           1. Outer ties

           2. Inner ties

           3. Straight ties

• Spiral ties

d. BEAM AND GIRDER REINFORCEMENTS

• Main reinforcement

            1. Straight bars

            2. Bend bars

•     Stirrups

             1. Open stirrups

             2. Closed stirrups

• Cut Bars

              1. Over and across the support

              2. Between supports

              3. Dowels

e. FLOOR SLAB REINFORCEMENT

•  Main reinforcement

               1. Straight main reinforcing bars

               2. Main alternate reinforcing bend bars

• Temperature bars
• Cut additional alternate bars over support (beam)
• Dowels        

7.4. PROCEDURE OF ESTIMATING CONCRETE REINFORCEMENT

• Columns, beams, girders, and the like are best determined using direct counting.
• For lateral ties, stirrups, spirals, dowels, cut bars, and the like, estimation should be done one at a time. The length of bars should include the additional length of bends and hooks.
• After determining the length of lateral ties, stirrups and the similar reinforcements, select the commercial size yielding the least wastage.
• Tie wire for reinforcement joints and intersections should be done to the minimum required length based from the diameter of the bars to be tied with.

7.5. REINFORCEMENT OF CHB WALLS

Specifications for the reinforcement of CHB walls are usually written on the plan and specifications. The different ways to estimate them are as follows:

1. By direct counting method. Vertical and horizontal wall reinforcements are directly counted from the plans. Length includes hooks, bends or splices.
2. By the unit block method. 
3. By the area method. Estimation of wall reinforcements with the help of a table. The presented values include allowances for bends, hooks and splices.

VERTICAL REINFORCEMENT

SPACING	LENGTH OF BARS	LENGTH OF BARS
	PER BLOCK	PER SQ.M.
cm.	m.	m.
40	0.235	2.930
60	0.171	2.130
80	0.128	1.600

HORIZONTAL REINFORCEMENT

SPACING	LENGTH OF BARS	LENGTH OF BARS
LAYERS	PER BLOCK	PER SQ.M.
	m.	m.
2	0.264	3.30
3	0.172	2.15
4	0.138	1.72

Example 7.5.1. Estimating CHB Wall Reinforcement

7.6. TIE WIRE FOR STEEL REINFORCEMENT

No. 16 galvanized iron wire (#16 GI Tie Wire) is used to secure reinforcements in place for concrete pouring. Ordering tie wire does not come per length but per kilograms or roll. One roll is 45 kilograms which can be converted to 2285 meters. Thus making 53 meters per kilogram.

The length of each tie wire ranges from 20 cm to 40 cm for small and medium size steel bars. For 10mm, 12mm, 13mm, or 16mm rebars, tie wire length should be 25cm or 30cm (max), folded at the center.

KILOGRAM PER NUMBER OF CHB

VERTICAL	HORIZONTAL	TIES	TIES
SPACING	SPACING	25cm	30cm
cm	layer	kg	kg
40	2	0.0042	0.0051
40	3	0.0031	0.0038
40	4	0.0028	0.0033
60	2	0.0028	0.0034
60	3	0.0021	0.0025
60	4	0.0018	0.0022
80	2	0.0021	0.0025
80	3	0.0016	0.0019
80	4	0.0014	0.0017

Example 7.6.1. Estimating Tie Wire for CHB Reinforcement

7.7. INDEPENDENT FOOTING REINFORCEMENT

Procedure for estimating footing reinforcement is as follows:

1. Know the actual size of the footing - it's width and length.
2. Identify the bar size and the number from the plans.
3. Always keep in mind that clear cover of reinforcements, when exposed to soil, is 3 inches or 75mm.
4. If the pan does not call for a hook or bend of the reinforcement, the length of the bar is equal to the length of the width less the concrete cover at both ends.
5. If not specified in the plans, better to identify the spacing of bars in the footing to determine the exact number of bars needed.

Example7.7.1. Estimating Isolated Footing Reinforcement
Example 7.7.2. Estimating Isolated Footing Reinforcement of a Small Structure

7.8.  POST AND COLUMN REINFORCEMENT

Estimates of posts and columns include:

1. The main or vertical reinforcement
2. Lateral ties
3. Spiral ties or circular column ties

MAIN REINFORCEMENT:

Estimate the main reinforcement of columns using the direct count method with the following lengths to note:

1. Floor to floor height. Most plans show height of floors based on floor to floor distances. If otherwise specified, then add the thickness of the beam included.
2. Depth of footing from the ground floor. Column height is usually measured from the bottom of the footing to the ground floor.
3. Development length of column to footing. Development length is usually 10 times the bar diameter of the column.
4. End splices. Splicing of reinforcement should be done in staggered mode - meaning, the lengths of bars used should not be the same. The ideal distribution is 33% but bar scheduling using 33% will be difficult. Most designers use 50%. Splicing points should be locations of minimal moment, that is, the last quarter of a span.

LATERAL TIES:

For the length of the ties, determine the concrete cover used. For columns, concrete cover ranges from 25mm to 40mm. Most designers use 25mm. Hooks for ties are taken as 2 inches each end.

The length of lateral ties can be computed as:

credits to Engineering Feed

The number of lateral ties required is estimated by direct count. 



Example 7.8.1. Estimating Column Reinforcement (Low-rise)
Example 7.8.2. Estimating Column Reinforcement (High-rise)
Example 7.8.3. Estimating Multiple Lateral Ties

7.9. BEAMS AND GIRDERS REINFORCEMENT

Estimating the reinforcement for beams and girders is similar but a bit more complicated with estimating columns.

The main reinforcements are estimated similarly as with columns. But beams can have cut bars, which makes the difference. As per design, there could be different configurations between the top bars with the bottom bars in beams. Splicing is of beam reinforcement is located on the compression side.

credits to Orazio.it

Extra bars can be cut or bent. Any of these are done based on economic reasons. The lengths of cut bars is based on the tension-compression functionality of the bar.

credits to Reinforcement Detailing

Example 7.9.1. Estimating a simple Beam Reinforcement
Example 7.9.2. Estimating a Continuous Beam Reinforcement
Example 7.9.3. Estimating a Continuous Beam Reinforcement-II

7.10. SPIRAL AND COLUMN TIES

There are three considerations in the installation of spirals:

1. The center to center spacing of the spiral should not exceed 1/6 of the diameter core.
2. The clear spacing between spirals is within the range 5.0cm to 7.5cm.
3. The clear spacing between spirals should be less than 1.5 times of the gravel.

NUMBER OF SPIRAL REINFORCING BARS PER METER HEIGHT

*Values given includes the end lap or splice allowance.

COLUMN	PITCH	NO. OF TURN	NUMBER	OF STEEL	BARS FROM
DIAMETER		PER METER HT
cm	cm		6.00m.	9.00m.	12.00m.
30.0	5.00	21.0	2.604	1.706	1.269
30.0	6.25	17.0	2.108	1.381	1.027
30.0	7.50	14.3	1.778	1.165	0.866
32.5	5.00	21.0	2.894	1.896	1.410
32.5	6.25	17.0	2.342	1.535	1.141
32.5	7.50	14.3	1.975	1.294	0.962
35.0	5.00	21.0	3.183	2.085	1.55
35.0	6.25	17.0	2.577	1.688	1.255
35.0	7.50	14.3	2.172	1.423	1.058
37.5	5.00	21.0	3.472	2.275	1.692
37.5	6.25	17.0	2.811	1.842	1.393
37.5	7.50	14.3	2.370	1.524	1.154
40.0	5.00	21.0	3.762	2.465	1.833
40.0	6.25	17.0	3.045	1.995	1.484
40.0	7.50	14.3	2.567	1.682	1.251
42.5	5.00	21.0	4.051	2.654	1.974
42.5	6.25	17.0	3.281	2.149	1.598
42.5	7.50	14.3	2.765	1.812	1.347
45.0	5.00	21.0	4.340	2.844	2.115
45.0	6.25	17.0	3.513	2.302	1.712
45.0	7.50	14.3	2.962	1.940	1.443
47.5	5.00	21.0	4.630	3.033	2.256
47.5	6.25	17.0	3.748	2.455	1.826
47.5	7.50	14.3	3.159	2.070	1.539
50.0	5.00	21.0	4.919	3.223	2.397
50.0	6.25	17.0	3.982	2.609	1.940
50.0	7.50	14.3	3.357	2.199	1.635
55.0	5.00	21.0	5.498	3.602	2.678
55.0	6.25	17.0	4.451	2.916	2.168
55.0	7.50	14.3	3.752	2.458	1.828
60.0	5.00	21.0	6.077	3.981	2.96
60.0	6.25	17.0	4.919	3.223	2.396
60.0	7.50	14.3	4.146	2.717	2.02
70.0	5.00	21.0	7.234	4.740	3.524
70.0	6.25	17.0	5.856	3.837	2.853
70.0	7.50	14.3	4.936	3.234	2.405
80.0	5.00	21.0	8.391	5.498	4.088
80.0	6.25	17.0	6.793	4.451	3.31
80.0	7.50	14.3	5.726	3.752	2.790
90.0	5.00	21.0	9.549	6.256	4.652
90.0	6.25	17.0	7.730	5.064	3.766
90.0	7.50	14.3	6.366	4.171	3.101
100.0	5.00	21.0	10.706	7.014	5.216
100.0	6.25	17.0	8.667	5.678	4.222
100.0	7.50	14.3	7.137	4.676	3.477

Example 7.10.1. Estimate the spiral Reinforcement

7.11. REINFORCEMENT FOR ONE WAY CONCRETE SLAB

A slab will be designed as one-way when one side is less than half the other.

For one way slab, the only functional beams carrying the load are the long span. In this case side B. With the moment imposed on the long span beams, main reinforcement will also be along this span. The rebars placed along the shorter span is only to avoid shrinking of concrete or to avoid cracks. These bars are called temperature bars (distribution bars, straight bars).

Similar to the configuration of a beam, the main reinforcement will be placed in tension areas. That is, the upper portion of the slab on both ends, and the bottom portion in the middle part.

TABLE FOR AREA METHOD: ONE WAY SLAB

BAR SPACING	NUMBER	OF STEEL	BARS PER	SQUARE	METER	TIE WIRE	LENGTH
	5.0m	6.0m	7.50m	9.0m	12.0m	25cm	30cm
10.0	4.493	3.667	2.856	2.320	1.834	0.242	0.291
12.5	3.911	3.186	2.483	2.015	1.593	0.197	0.236
15.0	3.524	2.866	2.234	1.812	1.433	0.163	0.195
17.5	3.247	2.637	2.056	1.667	1.319	0.141	0.169
20.0	3.039	2.465	1.192	1.558	1.233	0.126	0.152
22.5	2.878	2.332	1.819	1.473	1.166	0.111	0.133
25.0	2.749	2.225	1.737	1.405	1.113	0.101	0.121
27.5	2.643	2.138	1.669	1.350	1.069	0.091	0.109
30.0	2.554	2.065	1.612	1.304	1.033	0.086	0.103

Example 7.11.1. Estimating A One-Way Slab Reinforcement

7.12. REINFORCEMENT OF TWO-WAY SLAB

For two-way slab, all the surrounding beams carry load and are to be designed with main reinforcement. The temperature bars are placed under the slab on the sides of the slab with a quarter of the length. Estimation of bars is similar with one way slab main reinforcement. 

TABLE FOR AREA METHOD: TWO-WAY SLAB

BAR SPACING	NUMBER	OF STEEL	BARS PER	SQUARE	METER	TIE WIRE	LENGTH
	5.0m	6.0m	7.50m	9.0m	12.0m	25cm	30cm
cm						kg	kg
10.0	4.953	3.995	3.05	3.047	2.000	0.364	0.437
12.5	4.409	3.549	2.703	2.734	1.775	0.279	0.335
15.0	4.047	3.252	2.471	2.524	1.626	0.238	0.286
17.5	3.788	3.039	2.306	2.377	1.520	0.208	0.25
20.0	3.594	2.88	2.182	2.266	1.440	0.185	0.222
22.5	3.443	2.756	2.085	2.179	1.378	0.168	0.202
25.0	3.322	2.656	2.008	2.109	1.328	0.156	0.187
27.5	3.223	2.575	1.945	2.053	1.288	0.146	0.175
30.0	3.141	2.507	1.892	2.005	1.254	0.138	0.165

Example 7.12.1. Estimating Reinforcement of Two-way Slab

7.13. CONCRETE PIPE REINFORCEMENT

Concrete pipes also need longitudinal reinforcement and hoops.

Example 7.13.1. Estimating Reinforcement of a Concrete Pipe