Prelims

1. Lightweight concrete
2. High density concrete
3. Mass concrete
4. Ready-mix concrete
5. Shotcrete

reinforcing steel bars / REINFORCED CONCRETE

(NSCP 2015 Sec 203.3.1)

1.4(D+F)
1.2(D + F + T) + 1.6(L + H) + 0.5(L or R)
1.2D+ 1.6(L or R) + (f1L OR 0.5W)
1.2 D+ 1.0W+ f1L + 0.5(L or R)
1.2+ 1.0E+ f1L
0.9D + 1.0W + 1.6H
0.9D + 1.0E + 1.6H

1.2D+ 1.6L
1.2D+ f1L + 1.0W
1.2D + f1L + 1.0E
0.9D + 1.0W
0.9D + 1.0E

(NSCP 2015 Sec 419.2.2.1)

(NSCP 2015 Sec 429.6.4)

(NSCP 2015 Sec 429.6.5)

1. Plane section remains plane before and after bending.
2. Concrete stress varies from zero at the neutral axis to a maximumat theextreme fiber.
3. Concrete do not carry tensile stress. All tensile stress will be carriedby steel
reinforcement.
4. The steel and concrete are perfectly bond so that no slippage betweenthe two will occur.

Doubly reinforced beams

A composite material consisting of concrete and steel reinforcement.

Concrete is strong in compression.

Concrete is weak in tension.

To provide tensile resistance and help resist bending.

Deformations or lugs on the reinforcing bars.

Yes.

Lightweight concrete, high-density concrete, mass concrete, ready-mix concrete, and shotcrete.

Concrete made with lightweight aggregates to reduce density.

Concrete having a higher density than normal concrete.

Concrete placed in large quantities where heat generation and temperature control are important.

Concrete produced in a batching plant and delivered ready for placement.

Concrete or mortar pneumatically projected onto a surface.

Dead load.

Live load.

Wind load.

Earthquake load.

Fluid load.

Lateral soil or water pressure.

Rain load.

Self-straining effects.

A live-load factor used in certain load combinations.

1.0.

1.0.

1.0.

0.5.

1.2D + 1.6L.

A load combination involving dead, live, and wind loads.

A load combination involving dead, live, and earthquake loads.

Stability involving dead and wind loads.

Stability involving dead and earthquake loads.

No.

Working Stress Design.

Ultimate Strength Design.

0.45f'c.

f'c/11.

3f'c/8.

0.3f'c.

140 MPa.

170 MPa.

200,000 MPa.

Ec = 4700√f'c MPa.

n = Es/Ec.

6.

2n.

Plane sections remain plane after bending.

Concrete stress varies from zero at the neutral axis to maximum at the extreme fiber.

No.

Steel reinforcement.

Perfect bond with no slippage.

Uncracked stage, cracking stage, and cracked transformed-section stage.

The gross concrete section resists bending and behaves elastically.

The concrete reaches its cracking strength and tensile cracking begins.

The cracked transformed section is used for analysis.

fr = 0.62λ√f'c.

Mcr = frIg/yt.

Gross section moment of inertia, neglecting reinforcement.

Distance from the centroid to the extreme tension fiber.

bc(c/2) = nAs(d-c).

I = bc³/3 + nAs(d-c)².

fb = Mc/I.

fc = Mc/INA.

fs/n = M(d-c)/INA.

A beam with reinforcement in both the tension and compression zones.

When the required moment is large but the beam dimensions are limited.

To increase moment capacity when the section cannot be enlarged sufficiently.

Long-term deformation effects that affect compression reinforcement.

Mu must be less than or equal to φMn.

Factored or ultimate moment.

Nominal moment capacity.

Strength reduction factor.

Design or usable moment strength.

φ = 0.90.

A tensile strain exceeding 0.005.

It allows warning and slower failure rather than sudden brittle failure.

A failure involving significant deformation before failure.

A sudden failure with little warning or deformation.

0.004.

A factor relating the equivalent rectangular compression block depth a to neutral-axis depth c.

a = β1c.

C = T.

Compression force in the concrete.

Tension force in the steel.

C = 0.85f'cab.

T = Asfy.

0.85f'cab = Asfy.

a = Asfy/(0.85f'cb).

Area of tensile reinforcement.

Yield strength of reinforcing steel.

Specified compressive strength of concrete.

Width of the beam.

Effective depth from the compression face to the centroid of tensile reinforcement.

Neutral-axis depth measured from the compression face.

Depth of the equivalent rectangular compression stress block.

Mn = Asfy(d-a/2).

d-a/2.

φMn.

φMn = 0.90Mn.

Mu ≤ φMn.

ρmin = 0.25√f'c/fy.

ρmin must not be less than 1.4/fy.

As,min = 0.25√f'c/fy × bd.

ρact = As/(bd).

Use ρ = ρmax.

Use ρmin or 4/3ρact depending on the applicable provision.

Use ρ = ρact.

To ensure the reinforcement amount satisfies the required limits and ductility provisions.

Determine ρmin and ρmax.

Determine ρact.

Compare ρact with ρmin and ρmax.

Determine As = ρbd.

Solve C = T and determine a, considering whether the steel yields.

Check the assumptions.

Determine φ.

Determine the moment capacity.

Rn = ρfy(1 − ρfy/(1.7f'c)).

Mu = φRn b d².

Solve Rn.

Solve ρ, ρmin, and ρmax.

Solve As.

Compute a and c.

Check whether the section is tension-controlled.

It is designed as a doubly reinforced beam according to the module.

It is designed as a singly reinforced beam and the number of bars is determined.

Singly Reinforced Beam.

Doubly Reinforced Beam.

0.003.

To determine strain distribution and help classify the reinforcement behavior.

Steel strain is checked to determine whether the reinforcement yields and whether the section is tension-controlled.

Its strength and behavior may not satisfy the required design conditions.

To maintain ductile behavior.

To simplify the representation of the concrete compression stress distribution.

a = β1c.

Compression force equals tension force.

d-a/2.

Mn = T(d-a/2).

Mn = C(d-a/2).

The factored design moment is set equal to the design moment strength.

To account for uncertainties and reduce nominal strength to a design strength.

The tensile reinforcement has a tensile strain exceeding 0.005.

Nominal strength is Mn, while design strength is φMn.

Service loads are actualnfactored loads, while factored loads are increased using load factors for strength design.

1.2.

1.6.

300 kN·m.

411.57 = 1.2(250) + 1.6Mll.

69.73 kN·m.

As = 4(π/4)(25²).

1963.50 mm².

As = 9(π/4)(28²).

5541.77 mm².

150,000 mm².

0.03695 or 3.695%.

Approximately 264.62 mm.

c = a/β1.

Approximately 0.807.

Approximately 327.9 mm.

0.003.

εt = 0.003(d-c)/c.

0.00158.

No.

No.

Because the appropriate strength reduction factor φ depends on the section's strain classification.

Recheck the strain classification and the applicable NSCP procedure before using φ = 0.90.

To verify that the assumed steel behavior and strength reduction factor are valid.

Concrete compression force and steel tension force.

It is neglected in the tensile zone.

The tensile reinforcement.

The concrete compression block.

C = T.

Mn = force × lever arm.

d-a/2.

It increases the tensile force and generally increases moment capacity, subject to design limits.

It increases the lever arm and therefore generally increases moment capacity.

It increases the available concrete compression force.

It determines the lever arm between compression and tension forces.

To ensure the beam has sufficient design strength for the factored moment while satisfying reinforcement and ductility requirements.

To keep stresses within allowable limits under service loads.

To check strength using factored loads and reduced nominal strength.

Behavior under service or unfactored loads such as stress and cracking.

Ultimate or factored load capacity.

WSD uses service loads, while USD uses factored loads.

Stress is determined using the transformed section and elastic bending relationships.

Mu ≤ φMn.

To represent steel reinforcement as an equivalent concrete area for elastic analysis.

Steel area into an equivalent concrete area.

nAs.

2nAs.

Moment of inertia about the neutral axis.

Stress is zero at the neutral axis.

It increases linearly under the elastic assumptions.

It increases according to the strain and transformed-section relationship.

Because the concrete section is assumed to remain uncracked and participate in tension and compression.

Because concrete tensile resistance is neglected after cracking and steel is transformed using n.

Gross section moment of inertia.

Cracking moment.

Modulus of rupture of concrete.

Modulus of elasticity of concrete.

Modulus of elasticity of steel.

Modular ratio.

Reinforcement ratio.

Minimum reinforcement ratio.

Maximum reinforcement ratio.

Actual reinforcement ratio.

Minimum required steel area.

Relating the equivalent rectangular compression block depth to neutral-axis depth.

To determine the tensile force when reinforcement yields.

To determine the concrete compression strength.

To reduce nominal strength to design strength.

To represent the nominal moment capacity of the beam.

To represent the factored ultimate moment demand.

To represent the beam's design moment strength.

Mu ≤ φMn.