FUNDAMENTALS OF REINFORCED CONCRETE DESIGN By ENGR. VICTOR O. OYENUGA (HND, BSc(Hons), MSc, DIC, PGD(Comp. Sc.), FNSE, FNIStructE, FNICE, MNIOB
Managing Director: Vasons Concept Consultants Ltd (Consulting Engineers and Town Planners)
Engr. V. O. Oyenuga became a Partner of M/S Vasons Concept Group in 1991 and currently the MD/CEO. He worked briefly with Yaba College of Technology and Lagos State Polytechnic, Isolo,
Lagos, where he resigned his appointment in 1989 as a Senior Lecturer and Acting Head of Department of Civil Engineering. His design work include: Teslim Balogun Stadium, Surulere, Lagos, Reconstruction of Petroleum Products Jetties Apapa, Ikeja Plaza and the various projects of Babcock University, Ilishan Remo, his town of birth. He is a Fellow of the Nigerian Society of Engineers and the Nigerian Institution of Structural Engineers.
Engr. Oyenuga is the author of the following publications: 1). Todays’ Fortran 77 Programming 2). Simplified Reinforced Concrete Design, 3). Concise Reinforced Concrete Design 4). RCD2000 Reinforced Concrete Design Programs and 5) Design and Construction of Foundations. Engr. Oyenuga is married with children and they are members of the Seventh-Day Adventist Church in Nigeria.
ABSTRACT Structural design is an art and the ‘artist’ must be convinced of the implications of the final product. The objective of this paper is to highlight the basic load and design fundamentals that must be observed for the economic and safe design of the structure. Various load forms are highlighted and practical examples given. Wind load and its application on the structure are briefly discussed. Ability to trace the load path up to foundation level is discussed. The various design philosophies are enunciated. To assist in the design, values of some important parameters are given in tabular form.
1.0 INTRODUCTION Structural and Civil Engineers deal with forces of nature, which can only be predicted to a reasonable extent. For example, a dam was designed for a 50year rain and one month after its completion a 100year rain fell causing a total damage to the dam structure. Who is to be blamed? Thus, no engineer could say with all certainly that he has got a perfect solution to any design problem. However, as a result of intensive research, experimental and observational data, a level of confidence has been achieved in virtually all aspects of civil/structural engineering to such a level that a ‘near certainty’ can be achieved. The objective of this paper is to discuss the various loads and load forms that must be thoroughly looked into as well as their application in the design of building structures. In most cases, poor load estimation as well as poor load tracing lead to collapse of building structures aside poor materials and workmanship. In addition, some basic design fundamentals are discussed. Structural loads must be properly assessed and successfully transferred to the founding member. The receiving soil must also be of such composition and texture so as to receive the imposed load without undue stress. It is a common believe that all buildings on poor marshy soil be founded on raft foundation. It should be clearly stated here that raft foundation is NOT a solution to all foundation problems. For example, a soil with 20kN/m 2 bearing capacity imposed with 50kN/m2 building on raft foundation will definitely sink, the foundation type notwithstanding The building may, however, not crack, that is, it may tilt in one direction because of the structural rigidity of the foundation and the superstructure frame. Such a building in question may require short pile footings. On the other extreme, building a bungalow on raft foundation may be highly uneconomical since simple wide strip foundation may have been very suitable. The summary of the foregoing is that soil tests and their correct interpretation are necessary even for the most simple structure especially where the soil structure is very doubtful.
2
As a guide the structural form and possible foundation type is shown in Table 1. guidance only and the designer is advised to seek tests information. Table 1: Suggested Appropriate Foundation Type for Building
The information are for
Bungalow
2-storey
Type of Buildings 3-5 storey Medium Rise
High Rise
Strip
Strip
Pad
Pad
Pile
Strip
Wide Strip
Pad
Pile
Pile
Poor Soil 40 – 75kN/m
Wide Strip
Wide Strip
Raft
Pile
Pile
Bad Soil <40kN/m2
Raft
Raft
Short Pile
Pile
Pilr
Soil Type 2
Good soil >100kN/m
Average soil 75 – 100kN/m2 2
Depending on the load type, soil investigation can be limited to penetrometer tests only for relatively good soil and light loads. For heavier loads a combination of both penetrometer tests and borehole tests are required. The structural engineer should convince the client of the paramount importance of soil tests and the fact that money to be expended on the operation is much less than 0.01% of the cost of the structure.
2.0 TYPE OF BUILDINGS In terms of structural framing, a building can be categorized as: (a) A framed building and (b) A non-framed building
2.1 Load Bearing Wall Buildings A non-framed building is a building that is supported on load bearing walls and they are limited to two-storeys only (that is, with rooms at ground floor and one suspended floor). When a building is to be of three storeys or more, there is the tendency for the lower walls to crumble under load. Hence, such buildings must necessarily be framed. On the other hand, a bungalow or two-storey buildings to be built on a marshy soil must be framed since the foundation would be either a raft foundation or a pad foundation. A building on load bearing wall means simply that the loads are transferred through the load bearing walls to the foundation structure. Such walls should have good strength and preferably machine moulded with number of blocks per bag ranging between 25 and 30. The sand should be sharp and not too coarse. Very coarse sharp sand can be mixed with ordinary sharp sand in the ratio of 3:1 in favour of the coarse sharp sand. Experience has shown that very coarse sharp sand develops early strength but relapses later. This is perhaps due to the tiny holes which may have been created during moulding.
2.2 Framed Buildings A framed building consists of slab carried by the beams, which are in turn supported by the columns. The columns transmit the load through the foundation to the soil. For all practical purposes, any building exceeding two-storeys must necessarily be framed irrespective of all foundation soil bearing strata. In the framing operation, the load path must be considered as well as the wind-resisting elements. That is, are the columns and beams robust enough such that they can resist the wind loads? Or shear walls around staircases, lift shafts etc need be introduced to resist the effects of lateral forces? In addition, the geometrical symmetry of the building could be very important especially when raft foundation is to be considered. To avoid uneven ground pressure, the building must be structurally symmetrical as much as possible. The erection of a non-framed building starts from the foundation, which is either strip or wide strip and the building of the walls up to the soffit of the floor slab. The slab is then placed on the walls acting as permanent supports. The slab must be allowed to mature for at least 28days before loading. Experience has shown that one or two weeks old slab are loaded with the props in position. This can lead to collapse of the slab since the strength developed, the props notwithstanding, might not be strong enough to withstand the stresses proposed by the early loading. In addition, the slab may develop uneven soffit making finishing nearly an impossible task. Contrariwise, the frames, that is, foundation, columns, beams, slab, staircases, shear walls etc, of a framed building must be constructed prior to the building of the infill walls. The lower slab and beams must be allowed to mature (at least 28days) before the erection of upper floors and beams. Construction loads that may be due to equipment, prop and fresh floor loads must be born in mind during the design. A high rise ,may necessitate the planting of a crane on one of the floors. Such floors must be designed to ensure that the weight of the train, its contents and frequency of operations (fatigue) can be supported by the floor. Building with cantilevers (‘shoot-out’, in local parlance) must be well constructed to avoid cracks. The reinforcement must be placed at the top and extending beyond the face of the wall or beam into the slab a distance of not less than the span of the cantilever. The optimum distance should be 1.5times the cantilever span. In non-framed buildings, a cantilever span of 600mm is the most economical. Any span over 1.20m may cause building instability. Spans of
3
750mm and 900mm are reasonable but may consume over 30% of the total reinforcements for the slab. A span of 1200mm or more may be difficult to manage in terms of deflection. Buildings tend to be disfigured when large span cantilevers are used. Double cantilever leads to building instability and must be avoided as much as possible. In most construction sites, it is amazing to notice that all the corners of bungalows and two storey buildings have their corners blocks replaced with columns. These columns are rarely linked with beams, at most with mass concrete along the line of external lintels. Some even go to the extent of lining corners of septic tanks and soak-away pits with reinforced concrete beam and columns. Concrete beam and columns are vertical load bearing members while loads exerted by septic tank and soak-away pit soil are purely horizontal. The construction of reinforced concrete columns at corners of non-framed buildings may be counter productive.
3.0 TYPE OF LOADING The Advanced Learner’s Dictionary defines load as “that which is to be carried or supported” and Chambers’ Mini Dictionary says ‘a heavy weight’. Hence, from these two basic definitions, we can summary load as the weight of a material that is to be structurally supported. Thus, all loads whether permanent (dead) or transient (live) are weight of the materials in question and at times their impact on the structure e.g. wind load, train impact load and spectators impact load when a goal is scored in a football match. Structurally, the following loads are common. 1. Dead load - weight of the material of construction, permanently present. 2. Permanently superimposed load, that is, a live load that can be considered as permanent on the structure e.g. machine base or plinth. 3. Live load - transient load, that is, a load that can be moved in and out of the structure. 4. Wind load, that is, effect of wind forces or pressure (force/unit area) on the structure. This is a lateral load. 5. Impact load that is, due to impact of the live load. This may be taken as 10-20% of the live load. Load type 1,2, 3 and 5 act vertically while load type 4 acts horizontally. Another horizontal load, though not common in building structure, is breaking load, that is, when a brake is suddenly applied to a vehicle on a bridge. Each of these loads is briefly discussed.
3.1 Dead Load The dead load is the weight of the structure itself, and the structural elements such as the ceiling, cladding and permanent partitions. When machines and equipment are permanently located they can be assumed as dead loads. In case of equipment and machines, the manufacturer would be in a position to give the details. To arrive at a dead load, the member is preliminarily sized. The obtained load which is the product of the member size and its specific weight can be adjusted (or rounded) up so that any little difference in size during actual design will not significantly affect the analysis. For example a 450 x 225mm beam can be assumed to be 5.0kN/m run which includes own weight and finishes rounded up. Table 2 shows some values that could be useful during design.
Table 2: Materials Basic Weight S/N 1. 2. 3. 4. 5. 6. 7. 8.
Materials Concrete
- dense (normal) - light weight Block -225mm hollow - 150mm hollow Wall finishes-both sides Screeding - 37mm thick Terrazzo Paving Roofing felt and screed Asbestos rooting sheet etc. Amanitas and nails
Basic Weight 24.0 7.0 – 18.0 2.87 2.15 0.60 0.80 0.022 2.00 0.40 0.30
Unit kN/m3 -dittokN/m2 -dittokN/m2 kN/m2 kN/m2 kN/m2 kN/m2 kN/m2
The dead weight must be assessed as much as possible. However, an ultimate partial factor of safety of 1.4 is often applied. The application of dead load in design of structure is discussed in this paper.
3.2 Superimposed Permanent Load This can be treated as dead loads.
4
3.3 Live Loads
These are transient loads to be carried by the structure and because of their nature are more difficult to determine precisely. Hence, a more generous partial factor of safety of 1.6 is used. B.S. 6399: Part 1: 1984, deals with the design loading for buildings. Some values from this Code are as stated in Table 3. Table 3: Imposed Load for Slabs S/N 1. 2. 3.
Description Dwelling units Class rooms Place of assembly
4.
Offices
5. 6. 7. 8.
Library Motor Rooms Car Park – Light Pedestrian foot path
- with fixed seating - with no fixed seating - General use - Filling room
Values kN/m2 1.5 3.0 4.0 5.0 2.5 5.0 5.0 7.5 2.5 4.0
3.4 Wind Load A wind load or wind pressure is a lateral load and it is mandatory when a structure is more than five storeys in height. A building with high aspect ratio (ratio of height/width) must also be considered for wind. Unlike pressure due to water or grain which is linear and the magnitude of which depends on height, wind pressure is uniform and not dependent on height. It depends mainly on locality and the isopleths of basic wind speed that is always available show the values of various basic wind speed across the country. The basic wind speed is converted to wind force as follows. Let V be the local basic wind speed. Vs = V S1 S2 S3 m/s and Wk = 0.613 Vs2 N/m2. Where: Vs = Design wind speed in m/s S1 = multiplying factor relating to topology which can be taken as 1.0 S2 = multiplying factor relating to height above ground and wind braking, obtainable from literature and ranges between 0.55 and 1.27. S3 = multiplying factor related to the life of the structure which again can be taken as 1.0 that corresponds to an excessive speed occurring once in fifty years. Wk = the wind load in N per square metre. Normally, these are multiplied by the projected area to determine the wind force on the structure and the wind pressure (W k) is assumed uniform over the entire surface. For purposes of an example, assume a 20-storey building is to be located in Lagos, assuming each storey to be 2.85m, the wind forces calculated per m face of the structure are as shown below. Basic wind speed = 36 m/s S1 = 1.0, S3 = 1.0 and for the value of S2 we have the following conditions: Topographical factor - Open country Building width - Less than 50m Therefore, 5m, 10m 15m, 20m, 30m, 40m, 50m, 60m
Wk Wk Wk Wk Wk Wk Wk Wk
= = = = = = = =
(0.83 x 36)2 x (0.95 x 36)2 x (0.99 x 36)2 x (1.01 x 36)2 x (1.05 x 36)2 x (1.08 x 36)2 x (1.10 x 36)2 x (1.12 x 36)2 x
0.613 0.613 0.613 0.613 0.613 0.613 0.613 0.613
= 547N/m2 = 717 “ = 779 “ = 810 “ = 876 “ = 927 “ = 961 “ = 997 “
Note: The values of S2 are taken from Table 13 of Reinforced Concrete Designer’s Handbook by C. E. Reynolds and J. C. Steedman, 10th Edition. Thus the higher the level of consideration of the forces, the higher the pressure. The building should be broken down to storeys corresponding to the heights above for purpose of application of these loads. In this case we have: Grd to 2nd floor slab 2nd to 3 floor slab
= 0.55kN/m2 = 0.72kN/m2
5 rd
3 to 5 floor slab 5th to 7 floor slab 7th to 10th floor slab 10th to 14th floor slab 14th to 17th floor slab 17th to roof level
2
= 0.78kN/m = 0.81kN/m2 = 0.99kN/m2 = 0.93kN/m2 = 0.96kN/m2 =1.00kN/m2
Each is multiplied by the projected width of the building to obtain the force per m run. These in turn can be calculated as point loads and applied at the floor level as illustrated in Figure 1. 5th
Figure 1: 7.8kN/m.
2850
22.23kN
2850
21.38kN
4th 3rd
7.2kN/m 2850 6.6kN/m
Please note:
2nd
19.67kN
2850
22.33 = 7.8 x 2.85kN;
1st
21.38 = (7.8 x 7.2) x 0.5 x 2.85kN., and so on.
3.4 Load Combination Every structure must be able to carry the loads imposed and it is always a combination of loads. The commonest are dead plus live loads and dead plus live plus wind loads. Each of the combinations must be accompanied with the appropriate partial load factor as enunciated in the codes of practice. For residential buildings of not more than five storey the load combination is limited to dead plus live loads only. Table 2.1 of B.S. 8110: Part 1: 1997, reproduced here as Table 4 gives the various values of the partial factor of safety. Table 4: Load Partial factor of safety for various load combinations Load Type Load Combination Dead Imposed Adverse Beneficial Adverse Beneficial 1. Dead and imposed 1.4 1.0 1.6 1.0 (and earth and water pressure 2. Dead and wind (and 1.4 1.0 earth and water pressure) 3. Dead and wind (and 1.2 1.2 1.2 1.2 earth and water pressure)
Earth Water & Pressure 1.4
Wind -
1.4
1.4
1.2
1.2
4.0 DESIGN OF STRUCTURES 4.1 Design Objective A reinforced concrete design must satisfy the following functional objectives:
Under the worst system of loading, the structure must be safe.
Under the working load, the deformation of the structure must not impair the appearance, durability and/or performance of the structure and
The structure must be economical, that is, the factor of safety should not be too large to the extent that the cost of the structure becomes prohibitive with no additional major advantage except for robustness.
These requirements call for good assessment of the intending loads, right choice of materials and sound workmanship. To ensure these, the various components forming the reinforced concrete and the concrete itself must pass the various tests as detailed in the controlling code of practice.
6 The determination of the size of the structural member and the amount of reinforcement required to enable it withstand the forces or other effects to which it will be subjected is the object of design or detailed design. Detailed design is, however, only one of the two main parts of structural design, the other being the primary design. This is the initial planning or arranging of the members so that the external forces or loads on the structure are transmitted to the foundation in the most economical manner consistent with the purpose of the structure. This is borne out of experience, from a study of existing structures and from comparison of alternative designs. 4.2 Shearing Force and Moment Envelopes - Slab and Beam Design Most designers assume uniform loading of full dead and live loads on the structure. The implication of this is to produce maximum bending moments and shearing forces at the supports. Alternate loading of maximum and minimum loads on the other hand will produce higher span moments especially at the end support. This could be beneficial. Section 3.2.1.2.2 of B.S.8110:Part 1: 1997 states that it will be sufficient to consider two loading cases as follows: a) All spans loaded with 1.4Gk + 1.6Q and b) The spans loaded alternatively with (1.4Gk + 1.6Qk) and 1.0Gk Where:
Gk = Characteristic dead load, Qk Characteristic live load.
Hence, if Gk = 5.8 and Q = 1.5 we have the following loading regime on the slab in Figure 2. 1.4Gk + 1.6Q = 1.4(5.80) + 1.6(1.5) = 10.52kN/m2 1.0Gk = 1.0 x 5.80 = 5.80kN/m2 Figure 2: 10.52kN/m 6000
5000
6000
10.52kN/m
10.52kN/m
5.80kN/m 5000
6000
6000
These should be analyzed and the maximum results picked for the purposes of design. The single case loading can be used with moment re-distribution.
4.1 Load Assessment Load on superstructures must be assessed starting from the roof to the walls (or roof beams) to the slab, beam, columns and foundations. Column and foundation loads may be determined from the static loads, that is, floor area supported by the column multiplied by the floor load per square metre. To this is added the beam and wall loads and the column own weight. Column Design Design of beams and slabs do not pose much problem to most designers. However, column design does. Structurally column can be categorized into axially loaded, uniaxially loaded and biaxially loaded. Most designers, due to either laziness or ignorance, assume all columns to be purely axial. This is generally not in the best interest of the job. Should the designer, nevertheless, insist, the values in the following table could be used to convert the loads to axial and the columns designed as such. The values in the Table 5 are quite conservative Table 5: Column Axial Load Multiplier Column/Storey Axial Uniaxial Biaxial
Top 1.0 4.5 6.0
Next to Top 1.0 2.0 2.3
Lower 1.0 1.4 1.8
4.4 Foundation Design The major objective of foundation design is to prevent settlement of the structure. It should be noted that raft foundation is not a solution to all foundation problems and not an antidote to settlement. A poorly designed raft foundation can still settle but may settle uniformly or by tilting avoiding cracks in the structure.
7
Soil/geotechnical investigations must be carried out prior to any foundation and where possible, the building could be broken down into several sections and different types of foundations used. This is illustrated in the example shown as Figure 3. In this figure, a proposed Church building at Ikate, Surulere, Lagos, the congregation area is lightly loaded and the side columns could be supported on single pad, while the rear columns could be joined together on a continuous reinforced concrete footing. In real life, the soil permissible bearing capacity is 45kN/m 2. In view of the heavy loading towards the front (Ground floor, First floor and Second floor), a raft foundation would be the most suitable. Efforts should be made to ensure that the resulting bearing pressure under each type of foundation is the same. The foundations could be linked up with ground beams.
2nd Floor - Offices
1st Floor – Church Gallery
Altar
6000
Congregational
6000
Sitting
6000
6000
3600
5400
4200 4200 Altar
5400
4200
Figure 3: Church Project in Lagos – Plan and Section.
Entrance Porch
5.0 CONCLUSION
8
To conclude, here is a quotation from Man on the Job leaflets, published by Cement and Concrete Association, United Kingdom, titled “IT DEPENDS ON YOU”. It says: A good concrete job is only good, strong, long-lasting, good-looking and economical to build, if every man on the job shares in making it so. A good concrete building or road or bridge does not only depend on a good designer or a clever engineer: it depends on good materials, accurate batching, the right amount of water and thorough mixing: it depends on well-placed reinforcement, well-made formwork, careful compacting: it depends on good finish. No stage is unimportant. One man’s carelessness can let down the whole job: every man’s care can make it a job to be proud of. SO IT REALLY DOES DEPEND ON YOU Good structural design must be backed up by good construction materials, good workmanship, and good supervision. Structures are to be designed to provide safe accommodation and not a coffin for mass burial.
References: 1.
Simplified Reinforced Concrete Design, by Victor O. Oyenuga, 2nd Edition, Asros Ltd., Lagos, 2005.
2.
Design and Construction of Foundations, by Victor O. Oyenuga, Asros Ltd., Lagos, 2004.
3.
BS 8110: Parts 1 and 2, Structural Use of Concrete, BSI, United Kingdom.
4.
Reinforced Concrete Designer’s Handbook by C. E. Reynolds and J. C. Steedman, 10th Edition.
