Reinforced Concrete Design for the FE Exam
Reinforced concrete design is a key topic on the FE Civil exam. Concrete is strong in compression but weak in tension, so steel reinforcement is embedded in the tension zone to carry tensile forces. Understanding the interaction between concrete and steel is essential for FE exam success.
Material Properties
Concrete
- Compressive strength (f'c): The primary design property of concrete, measured at 28 days. Common values range from 3,000 to 8,000 psi (20 to 55 MPa).
- Modulus of elasticity: E_c = 57,000 * sqrt(f'c) (in psi units) for normal-weight concrete.
- Tensile strength: Approximately 10 to 15 percent of compressive strength. For design purposes, tensile strength is often neglected.
- Unit weight: Normal-weight concrete is approximately 150 lb/ft^3 (2,400 kg/m^3).
Reinforcing Steel
- Yield strength (f_y): Commonly 60,000 psi (Grade 60) or 420 MPa (Grade 420). This is the stress at which the steel begins to yield.
- Modulus of elasticity: E_s = 29,000,000 psi (200,000 MPa) for all grades of reinforcing steel.
- Modular ratio: n = E_s / E_c. Used in elastic analysis of reinforced concrete sections.
Flexural Design of Beams
Reinforced concrete beams must be designed to resist bending moments. The ultimate strength design method (also called LRFD or strength design) is used:
Assumptions for Flexural Design
- Plane sections remain plane (linear strain distribution)
- Maximum concrete compressive strain at failure is 0.003
- Tensile strength of concrete is neglected
- The concrete stress distribution is approximated by Whitney's rectangular stress block with a depth of a = beta_1 * c, where c is the neutral axis depth
- Steel is elastic-perfectly plastic
Design Moment Capacity
For a singly reinforced rectangular beam, the nominal moment capacity is:
M_n = A_s * f_y * (d - a/2)
Where A_s is the area of tensile reinforcement, d is the effective depth (distance from the compression face to the centroid of the tension steel), and a = A_s * f_y / (0.85 * f'c * b).
The design moment capacity is phi * M_n, where phi is the strength reduction factor (0.90 for tension-controlled sections).
Shear Design
Concrete beams must also resist shear forces. The shear capacity has two components:
- Concrete contribution: V_c = 2 * sqrt(f'c) * b_w * d (in psi units). This represents the shear carried by the concrete alone.
- Stirrup contribution: V_s = A_v * f_y * d / s, where A_v is the area of shear reinforcement (stirrup area), and s is the stirrup spacing.
Total nominal shear capacity: V_n = V_c + V_s
The design shear capacity is phi * V_n, where phi = 0.75 for shear.
Development Length
Reinforcing bars must be embedded in concrete for a sufficient length to develop their full tensile strength through bond. The development length depends on bar size, concrete strength, bar spacing, and cover. Formulas are provided in the reference handbook.
Load Combinations
Reinforced concrete design uses factored loads. The most common load combinations per ACI 318 are:
- 1.4 * D (dead load only)
- 1.2 * D + 1.6 * L (dead plus live)
- 1.2 * D + 1.0 * L + 1.6 * W (including wind)
Where D is dead load, L is live load, and W is wind load. The controlling combination is the one producing the largest factored load effect.
Column Design Basics
Reinforced concrete columns resist axial compression, often combined with bending moment. Key concepts:
- Short columns: Strength governed by material failure (crushing of concrete, yielding of steel).
- Slender columns: Must account for secondary moments due to lateral deflection (P-delta effects).
- Interaction diagram: Shows the relationship between axial capacity and moment capacity. Every column design point must fall within the interaction diagram.
Crack Control and Serviceability
In addition to strength, reinforced concrete members must satisfy serviceability requirements:
- Deflection limits: Beam deflections must not exceed specified limits (typically L/360 for live load, L/240 for total load).
- Crack width control: Cracks are inevitable in reinforced concrete but must be limited in width for durability and appearance.
Practice Strategy
- Know how to calculate the moment capacity of a singly reinforced beam
- Practice shear design calculations including stirrup spacing
- Understand development length concepts
- Be familiar with load combinations and strength reduction factors
- Use the reference handbook for formulas and factors
Reinforced concrete design follows well-established procedures. Learn the steps, practice the calculations, and you will be able to handle concrete design questions on the FE exam with confidence.