Definition & Function
A beam is a structural element that primarily resists loads applied laterally to its axis. Its mode of deflection is by bending. When loaded, a beam develops internal stresses: compression at the top fibers and tension at the bottom fibers (for positive moment). IS 456 Cl. 23
Live/Dead Loads → Slab → Beam → Column → Foundation → Soil.
Beams act as the "connectors" that distribute concentrated slab loads into the vertical support system.
In Reinforced Concrete (RCC), beams are composite members where:
• Concrete resists compressive forces.
• Steel Reinforcement resists tensile forces (which concrete cannot do effectively).
• Stirrups (Shear Reinforcement) resist diagonal shear and hold longitudinal bars in place.
Types of Beams
Beams are classified based on support conditions, geometry, and material. General Classification
Loading & Behavior
Beams are subjected to various load types, resulting in Bending Moments (M) and Shear Forces (V). IS 875
Key Load Effects
- Sagging Moment (+ve): Concave up. Compression on top, tension on bottom. Typical of mid-span in simply supported beams.
- Hogging Moment (-ve): Concave down. Tension on top, compression on bottom. Typical of supports in continuous/fixed beams.
- Shear Force: Acts perpendicular to the beam axis. Maximum near supports. Causes diagonal cracks if not reinforced.
- Torsion: Twisting moment. Critical in spandrel beams or beams with eccentric loads.
Per IS 456 (Cl. 23.6), the total vertical deflection (including creep and shrinkage) shall not exceed:
• L/250 (Total deflection since casting)
• L/350 (Deflection after construction of partitions)
• L/300 (Finishes sensitive to cracking)
Where L is the span length.
Design Principles (Limit State Method)
Modern beam design follows the Limit State Method (LSM) as per IS 456:2000. The design ensures safety against Collapse (Strength) and Serviceability (Cracks/Deflection). IS 456 Cl. 23
1. Flexural Design (Bending)
The section is designed to resist the factored bending moment ($M_u$). The neutral axis depth ($x_u$) must be checked to ensure it is under-reinforced ($x_u \le x_{u,max}$).
Where $b$ = width, $d$ = effective depth, $f_y$ = yield strength, $f_{ck}$ = characteristic strength.
2. Shear Design
Shear stress $\tau_v = V_u / (b \times d)$ is calculated. If $\tau_v > \tau_c$ (concrete shear capacity), stirrups are provided to take the excess shear $(\tau_v - \tau_c)$.
Where $A_{sv}$ = area of stirrup legs, $s_v$ = spacing.
3. Development Length
Bars must extend beyond the point of theoretical need by a length $L_d$ to ensure bond strength.
$L_d = (\phi \sigma_s) / (4 \tau_{bd})$
For Fe415 in M20 concrete, $L_d \approx 47\phi$.
Reinforcement Detailing
Proper detailing prevents premature failure and ensures ductility, especially in seismic zones (IS 13920). IS 456 Cl. 26 & IS 13920
- Min Bars: Minimum 2 bars at top and 2 at bottom along full length.
- Max Steel: Total area $\le 2.5\%$ of gross cross-section ($bh$).
- Positive Moment (Mid-span): Steel at bottom. At least 50% of negative moment steel at support must continue to mid-span.
- Curtailment: Top bars (negative moment) can be curtailed at points where moment demand drops below capacity, but must extend by $L_d$ past the cutoff point.
- Type: Must be Closed Stirrups (no open U-stirrups) for seismic safety and confinement.
- Spacing:
• Near supports (High Shear): $s_v \le 0.75d$ or $d/4$.
• Max spacing anywhere: $0.75d$ (vertical) or $300$mm.
• Minimum shear reinforcement required even if concrete capacity is sufficient (to prevent sudden failure). - Diameter: Min 6mm (or 8mm preferred in practice).
- Hooks: $135^\circ$ bend with straight extension of $10d_b$ (seismic detail).
Effective cover (center of bar to surface) typically 25-30mm for mild exposure, 40mm for moderate/severe. This protects steel from corrosion.
Flanged Beams (T-Beam & L-Beam)
In monolithic construction, the slab and beam cast together act as a single unit. The slab acts as a wide "flange" in compression, significantly increasing the moment capacity without adding depth. IS 456 Cl. 23.1.2
Effective Flange Width ($b_f$)
The portion of the slab that actually contributes to compression. Calculated as:
- T-Beam: $b_f = b_w + (l_0/6) + 6D_f$
- L-Beam: $b_f = b_w + (l_0/12) + 3D_f$
- Where $l_0$ = distance between points of zero moment.
Neutral Axis Location
- Case 1: N.A. lies within flange ($x_u \le D_f$). Analyze as rectangular beam of width $b_f$.
- Case 2: N.A. lies in web ($x_u > D_f$). Requires complex stress block integration considering the stepped shape.
Deep Beams & Special Cases
When a beam's span-to-depth ratio is small, it behaves differently ("Arch Action"). IS 456 Cl. 29
- Definition: Simply supported if $L/D < 2$; Continuous if $L/D < 2.5$.
- Behavior: Linear strain distribution (Bernoulli hypothesis) does NOT apply. Diagonal compression struts form directly from load to support.
- Design: Requires special detailing. Main reinforcement is distributed in bands near top and bottom faces. Web reinforcement (horizontal & vertical) is mandatory to control diagonal cracking.
- Example: Transfer girders supporting walls above, foundation grade beams on rock.
Failure Modes
Understanding how beams fail helps in designing safer structures.
Related Topics
Further reading and resources related to beam engineering: