Beams, Columns & Connections

Beams and columns are the primary structural elements in most buildings. Beams carry loads horizontally through bending and shear, transferring them to their supports. Columns carry loads vertically in compression, transferring them from floor to floor and down to the foundation. The connections between beams and columns are just as critical as the members themselves — a strong beam connected to a strong column with a weak connection will fail at the connection.

This lesson examines how beams and columns behave under load, the failure modes that engineers must prevent, and the types of connections used to join structural members.

When a load is applied to a beam, the beam bends. The beam must resist two types of internal forces:

Bending (Flexure)

The bending moment varies along the length of the beam. For a simply supported beam with a uniformly distributed load:

• The maximum bending moment occurs at mid-span: M_max = wL²/8
• The moment is zero at the supports

The bending stress in the beam is proportional to the moment and inversely proportional to the beam's section modulus (S) — a geometric property that measures the beam's resistance to bending:

σ = M / S

To prevent failure, the bending stress must not exceed the material's allowable stress.

Beam selection example: If the maximum moment is 100 ft-kips and the steel's allowable bending stress is 30 ksi (kips per square inch), the required section modulus is S = M/σ = 100 × 12 / 30 = 40 in³. The engineer selects a beam from the AISC Steel Manual with S ≥ 40 in³.

Shear

The shear force also varies along the beam. For a simply supported beam with a uniformly distributed load:

• The maximum shear occurs at the supports: V_max = wL/2
• The shear is zero at mid-span

The beam web (the vertical portion of an I-beam) carries most of the shear force. If the web is too thin, it can buckle in shear — a condition called web shear buckling.

Deflection

Even when a beam is strong enough to carry the load without breaking, it may deflect (sag) too much. Excessive deflection causes:

• Cracking of finishes (drywall, tile, plaster)
• Ponding of water on flat roofs
• Visible sagging (aesthetically unacceptable)
• Interference with operation of doors, windows, and mechanical equipment
• Damage to non-structural elements

Building codes and design standards limit deflection to a fraction of the beam span:

• L/360 for floor beams supporting plaster ceilings (live load only)
• L/240 for floor beams (total load)
• L/180 for roof beams (total load)

Where L is the beam span. For a 30-foot (360-inch) floor beam, the maximum allowable live load deflection is 360/360 = 1 inch.

Deflection often controls beam design — especially for longer spans. The beam may be strong enough but too flexible. The engineer must select a deeper or stiffer beam to limit deflection. The key property for deflection control is the moment of inertia (I) — a deeper beam with more material at the flanges has a higher I and less deflection.

Lateral-Torsional Buckling

A beam's compression flange (the top flange under gravity loading) can buckle sideways if it is not laterally braced. This is called lateral-torsional buckling — the beam twists and displaces sideways, losing its bending capacity. Prevention requires:

• Bracing the compression flange at regular intervals (typically the floor deck, roof deck, or dedicated bracing members provide this)
• Using beams with wide compression flanges
• Reducing the unbraced length

Columns carry loads primarily in compression. A short, stocky column fails by crushing — the material is simply compressed beyond its compressive strength. But most columns in buildings are relatively slender, and slender columns fail by buckling — a sudden sideways bowing that leads to rapid collapse.

Euler Buckling

The critical buckling load for a slender column is given by Euler's formula:

Pcr = π²EI / (KL)²

Where:

• E = modulus of elasticity of the column material
• I = moment of inertia of the cross-section (about the weak axis)
• K = effective length factor (depends on end conditions)
• L = actual column length
• KL = effective length

Effective length factor (K):

End Conditions	K value	Description
Both ends pinned	1.0	Standard reference case
One end fixed, one end pinned	0.7	Partially restrained
Both ends fixed	0.5	Fully restrained (theoretical)
One end fixed, one end free (cantilever)	2.0	Free to sway at top

Slenderness ratio (KL/r): This dimensionless number (where r = radius of gyration of the cross-section) is the primary indicator of buckling susceptibility. Columns with higher slenderness ratios are more susceptible to buckling and have lower allowable loads. Building codes limit the slenderness ratio — typically to a maximum of 200 for structural columns.

Key column design concepts for construction professionals:

• Taller columns buckle at lower loads than shorter columns (same cross-section). This is why columns in tall stories or with high unbraced heights may need to be larger.
• Bracing reduces effective length and increases buckling capacity. Mid-height bracing effectively halves the unbraced length and quadruples the buckling capacity.
• Columns buckle about their weak axis — the axis with the smallest moment of inertia. A W-shape column can buckle about either axis; whichever has the larger KL/r ratio controls.
• Eccentricity matters: If the load is applied off-center (eccentric loading), the column experiences both compression and bending, significantly reducing its capacity. Accurate column alignment during construction is critical.

Connections transfer forces between structural members. The type of connection determines how forces are transferred and how the connected members interact structurally.

Simple (Shear) Connections

Simple connections transfer only shear force (vertical reaction) from the beam to the column or girder. They allow the beam end to rotate freely — structurally, they behave like a pin. Simple connections do not transfer bending moment.

Common simple connection types:

• Single-plate connection (shear tab): A single plate welded to the column and bolted to the beam web. The most common connection type in steel-framed buildings.
• Double-angle connection: Two angles bolted or welded to the beam web and to the column flange or supporting member.
• Seated connection: An angle or plate (seat) welded to the column flange; the beam sits on the seat like a shelf.
• End-plate connection: A plate welded to the end of the beam and bolted to the column (can be designed as simple or moment connection depending on configuration).

Moment (Rigid) Connections

Moment connections transfer shear force, axial force, AND bending moment from the beam to the column. They prevent the beam end from rotating relative to the column — the beam-column angle remains constant (rigid). Moment connections create a rigid frame (moment frame) that can resist lateral loads.

Common moment connection types:

• Welded flange, bolted web: The beam flanges are welded directly to the column flange with complete joint penetration (CJP) groove welds. The web is bolted with a shear tab. This is the classic moment connection.
• Extended end-plate: A plate welded to the entire end of the beam (flanges and web) and bolted to the column with high-strength bolts above and below the beam flanges.
• Bolted flange plate: Steel plates are bolted to both the beam flanges and the column flanges using high-strength bolts.

Moment connections are significantly more expensive than simple connections (more material, more welding, more inspection). They are used only where needed — in moment frames designed to resist lateral loads.

Bracing Connections

Connections for diagonal bracing members must transfer the axial force (tension or compression) in the brace to the frame. Gusset plates — flat steel plates welded and/or bolted to the beam, column, and brace — are the most common bracing connection.

Bolts and Welds

The two primary fastening methods in steel construction:

High-strength bolts (ASTM A325 and A490):

• Transfer force through shear (bolt shank resists sliding) or bearing (bolt bears against hole sides)
• Slip-critical connections use fully tensioned bolts that clamp the connected parts together; force is transferred through friction
• Bolt sizes are typically 3/4", 7/8", or 1" diameter
• Bolt holes are typically 1/16" larger than the bolt diameter (standard holes)

Welds:

• Fillet welds: Triangular cross-section welds joining two surfaces at approximately 90°. The most common weld type in building construction. Specified by leg size (e.g., 5/16" fillet).
• Groove welds (butt welds): Welds that fill a groove between two members. Complete joint penetration (CJP) groove welds develop the full strength of the connected material and are required for moment connections in seismic zones.
• Partial joint penetration (PJP) groove welds do not penetrate the full thickness and have lower strength than CJP welds.

Welding quality is critical for structural safety. Structural welds require:

• Certified welders (tested per AWS D1.1)
• Welding procedure specifications (WPS)
• Inspection by certified welding inspectors (CWI)
• Non-destructive testing (NDT) for critical welds — ultrasonic testing (UT) or radiographic testing (RT)