CE 315: Design of Concrete Structures I
Dr. Tahsin Reza Hossain Professor, Room No-649
Email:
[email protected]
Syllabus • Fundamental behaviour of reinforced concrete • Introduction to WSD and USD methods • Analysis and design of singly reinforced, doubly reinforced and T-beams according to WSD and USD methods • Shear and Diagonal tension • Bond and anchorage according to WSD and USD methods • One-way slab
Books • Design of Concrete Structures – Nilson, Darwin, Dolan
14th Ed
• Structural Concrete- Theory and Design – Hassoun, Al-Manaseer 4th Ed
• Reinforced Concrete- Mechanics & Design – Wight & McGregor 5th Ed
Many more……..
Concrete, Reinforced Concrete (RC), Prestressed Concrete (PC) • What is concrete? Constituents? – Stone like material, cement, coarse and fine aggregate, water, admixture
• A bit of history • Advantages, disadvantages – Easy to make, relatively low-cost, formabilty, weather and fire resistant, good comp strength – Weak in tension
• Reinforced concrete-mild steel • Where to place the reinforcement-examples • Prestressed concrete
Roman Pantheon, unreinforced concrete dome, diameter 43.3m, 25BC, 125AD
Structural forms: buildings •Beam •Column •Slab
Loads
•Dead load attached •Live load not attached •Environmental load •Wind •Earthquake •Snow, soil pressure, temperature •Building codes- ACI, BNBC, IS, Eurocode
Wind Load
Earthquake Loads
Serviceability, Strength and Structural Safety • To serve its purpose, a structure must be safe against collapse and serviceable in use • Strength of the structure be adequate for all loads
• Serviceability – deflection small, hairline cracks, minimum vibration
Strength and safety • If loads and moments, shears, axial force can be predicted accurately, safety can be ensured by providing a carrying capacity just barely in excess of the known demand. • Capacity= Demand
Uncertainity • There are a number of sources of uncertainty in Analysis, Design and Construction • Read 7 points • Consideration given to consequence of failure • Nature of failure is also important
Variability of Loads, Strength, safety Load can be considered as random variable Form of distribution curve (probability density function) can be determined from large scale load survey
Probability of occurrence Area under curve is probability of occurrence Qd design load Sd Design strength
M is also a random variable Beta between 3 and 4 corresponds to a probability of failure of 1:100,000
Partial safety factor • Strength reduction factor X Nominal Strength > Load Factor X Design Load
Why partial factors are different
Concrete
Steel
Design Basis • Strength Design • Load factoredhypothetical overload stage • Material stress level – – – –
Nonlinear inelastic Concrete fc’ Steel reaches fy Both or one
• USD – Ultimate Strength Design
• Service load design • Load unfactored – Service load
• Material stress level – At allowable stresses – Half of fc’ – Half of fy
• WSD – Working Stress Design
Design Codes and Specifications • International Building Code- consensus code • American Concrete Institute ACI Code- Building Code requirement for Structural Concrete -3182008 • AASHTO- American Association of State Highway and Transportation Officials- for bridges • American Railway Engineering and Maintenance of Way Association –AREMA-Manual of Railway Engineering
Bangladesh National Building Code • BNBC • First in 1993 • Up-gradation is in progress
Safety provision of ACI/BNBC Code
Load factors
Probability of overload 1/1000
Strength reduction factor
Probability of understrength 1/100
• Probability of Structural failure 1/100,000
Fundamental Assumption for RC Behavior 1. 2. 3. 4. 5.
Equilibrium Strain in steel=Strain in surrounding concrete Plane cross section remain plane Concrete does not resist any tension The theory is based on the actual stressstrain relationship of concrete and steel or some simplified equivalent.
Read last para
Behaviour of members subject to Axial Loads • Fundamental behaviour illustrated
• Axial Compression – Economical to make concrete carry most loads – Steel reinforcement is always provided • Bending may exist • Cross section reduced
RC Column Square, tied column Tie • Hold longitudinal bar during construction • Prevent bucking under load Circular spirally reinforced column Spiral • same • confinement to concrete
fc’=4,000 psi fy= 60,000psi
•Slow loading •Fast loading •0.85fc’
Elastic behaviour • Up to fc’/2, concrete behave elastic • Also stress and strain proportional • Range extends to a strain of 0.0005 • Steel is elastic nearly to yield 60 ksi, strain 0.002
Valid up to 50 to 60 percent of fc’
Inelastic range
Strength
Strength
Axial Tension • If tension is small, both steel and concrete are elastic
• Larger load than that cracks concrete • At steel yields
