2D Frame Analysis Tutorial: Portal Frame Under Distributed Load

Steel connections and joints constitute approximately 50% of frame costs and are critical to structural integrity, requiring proper design according to Eurocode 3 Part 1-8. Connections are defined as locations where two or more elements meet, while joints are zones where multiple members interconnect. Simple joints allow rotation and transfer only shear force, rigid joints transfer moments and require columns to be designed as beam-columns, and semi-rigid joints fall between these extremes. Bolted connections use standard M20 grade 8.8 bolts with 22mm holes, where bolt shear failure (catastrophic) should be avoided in favor of gradual plate bearing failure. Design requires checking bolt shear, plate bearing, and block tearing failure modes, with minimum end distances of 1.2d and pitches of 2.2d and 2.4d. Welded joints use simplified design with effective throat thickness and design shear strength based on minimum ultimate tensile strength of connected parts.

Configure Robot for Eurocode design by modifying job preferences to select appropriate databases and codes: materials (EN 1993 for steel), steel sections database, bolt databases (regionally available), and design codes for steel, connections, reinforced concrete, geotech, and load combinations. Verify Eurocode selection for all categories, choosing between general Eurocode or national annexes. Apply member types with proper properties: configure lateral buckling lengths for beams (upper flange ~0.1L for continuous bracing, lower flange full span), and enable automatic K-factor calculation for columns based on beam-column stiffness interactions. Define supports (pinned, fixed, semi-rigid) and apply dead, live, and wind loads. Create multiple frame copies to compare support conditions. Generate automatic load combinations through Loads > Automatic Combinations, verifying Eurocode selection. Create member groups for efficient design: group columns and beams separately for each frame type. Execute steel member design through Design > Steel Member Design, specifying ULS combination. Interpret results showing controlling members, best sections, and verification status. Address practical considerations like maintaining consistent section sizes between beams and columns for simplified connections.

According to the AISC 360 design code written by the American Institute of Steel Construction (the most widely used steel structure design code worldwide), for competently formed butt welds using correct filler material or electrode for tension, compression, and shear cases, the strength of the joint is determined by the strength of the base metal, not the joint configuration itself. This means that concerns about joint angle having no effect on strength are unfounded when proper welding procedures are followed.

Framed connections in steel structures are joints that connect beams to columns, where the beam is connected to the column through flanges and web, with the flange plates typically welded or bolted to the column flanges and the web plate welded to the column web, creating a rigid structural connection that transfers loads between structural members.

This comprehensive section covers structural connection design for civil engineering. Bolted connections use bolts in place of rivets for non-vibrating structures, loaded in tension, shear, or both. Three bolt types: Turn and Finish (small, 152.5mm tolerance), Black and Unfinished (hexagonal/square, temporary fasteners, A2 designation), and HSFG (Class 8.8/10.9, medium carbon steel, best for stress reversal). Joint types: Lap Joint (single/double shear, less strength, no cover plate, eccentric) and Butt Joint (single/double cover, stronger, zero eccentricity). Welded joints offer advantages: no holes, faster fabrication, better appearance, more economical, less working space, no noise. Fillet weld specifications: effective throat = 5/8 × minimum plate thickness, minimum weld size 3-8mm based on thickness, returns = 2 × weld size. Combined stresses: normal and shear τ = √(f_a² + 3f_v²) / (√3 × γmw), combined bearing and bending τ = √(f_b² + f_v² + 3q²). Tension member design involves net area calculation (A_net = (b - d) × t + Σ(d_i²/4g_i)), slenderness ratio limits (400 permanent, 350 with reversal, 180 other), and failure modes: net section rupture (Td = 9A_eFy/γmo), gross section yielding (Td = AFy/γmo), and block shear failure.

This section advances to complex structural analysis techniques and multi-story frame modeling. The instructor explains envelope diagrams that combine all load combinations to show maximum and minimum values at each point, producing two lines for beams (maximum positive and negative moments). The section introduces a 6-story, 3-bay frame model with different floor heights (5m ground floor, 3.5m upper floors) and bay dimensions (3.5m and 7.7m). The instructor demonstrates deleting unnecessary members, setting boundary conditions (fixed supports at base), and systematic member naming conventions (C for columns, B for beams, with floor numbers and Z-axis before X-axis). The section covers applying loads to multiple members simultaneously, different types of live loads (continuous and alternating spans), and wind load distribution to windward and leeward faces for different wind directions.

This lecture from IIT Delhi's Advanced Structural Analysis course (CVL 756) explains how to extend plastic analysis methods to complex multistory and multi-bay frames by identifying independent mechanisms (beam mechanisms, sway mechanisms, and joint mechanisms) and systematically combining them to find the critical collapse mechanism that satisfies both yield and equilibrium criteria. The computational effort increases significantly with more stories and bays, making plastic analysis more challenging for complex structures compared to simpler single-story or single-bay frames.

Advanced structural modeling involves defining section properties with concrete compressive strength of 3,000 psi and reinforcement yield strengths of 415 MPa (main bars) and 275 MPa (stirrups). Section modifiers adjust stiffness according to NSCP provisions: 0.35Ig for beams and 0.25Ig for slabs. Reinforcement cover calculations ensure proper bond development with values around 53mm for beams. Slab modeling uses membrane type for in-plane force resistance with 125mm thickness. Efficient multi-story generation employs replication techniques copying ground floor elements along grid axes at specified intervals (3m and 2.5m). Frame division at gridline intersections creates proper joints for accurate load transfer analysis. This systematic approach combines section definition, slab modeling, and replication to create comprehensive structural models ready for detailed analysis and design verification.

For multi-story buildings with brace frames in one direction and moment frames in another: (1) Include all floors, roof, brace frames, moment frames, and gravity columns in the model; (2) Account for leaning columns in each direction; (3) Apply appropriate load factors; (4) Calculate notional loads at each elevated level; (5) Mesh columns into four segments; (6) Define stiffness reduction method; (7) Run second-order analysis; (8) Check drift ratios; (9) Optimize member sizes; (10) Perform final strength check with reduced stiffness.

The structural frame is assembled by rotating columns to be parallel to the Z-direction using 90-degree rotations around the X-axis. Beams are moved to connect to columns and copied using linear patterns. Additional beams are rotated around the Z-direction to complete the frame configuration. Three stories are created using linear pattern with 4-meter vertical spacing between floors.

This section covers plastic analysis of portal frames. For portal frames with plastic hinges at both ends and mid-span, collapse load is calculated using kinematic method. External work equals internal work: W × (L/2) × θ = 2Mpl × θ, so W = 4Mpl/L. Combined mechanism analysis considers simultaneous hinge formation on both sides. External work = W × L × θ, Internal work = 4Mpl × θ, so W = 4Mpl/L. Combined mechanism typically gives minimum collapse load.

In rigid plastic analysis of portal frames, plastic hinges form at the weaker sections (columns with moment capacity μ versus beam with 2μ), and the collapse load is determined by equating external work to internal work; for combined mechanisms, the true collapse load of 5μ/l is obtained by superposing the vertical beam mechanism (6μ/l) and sway mechanism (6.67μ/l), which is lower than either individual mechanism.

Plastic analysis of portal frames uses virtual work methods to determine collapse loads. Frames have two mechanism categories: free mechanisms (can move without restraint) and combined mechanisms (beam + sway). Three mechanism types exist: beam mechanism (load on top causes hinges), sway mechanism (horizontal force causes frame sway), and combined mechanism (combination of both). The number of free mechanisms is calculated using me = n - d, where n is total plastic hinges and d is redundant reactions (d = r - 3). For a frame with 4 hinges and 1 redundant, me = 3 mechanisms. The virtual work method applies: External Work = Internal Work. For beam mechanisms: External work = (1/2) × length × height × θ, Internal work = sum of (Mp × θ). For sway mechanisms: External work = Force × displacement, Internal work = sum of (Mp × θ). For combined mechanisms: combine both approaches. The maximum collapse load is the smallest value among all failure modes.

In plastic analysis of portal frames, the collapse load is determined by analyzing different mechanisms (beam mechanism, sway mechanism, and combined mechanism) and selecting the minimum value; for a portal frame with central point load 2W and nodal point load W, the collapse load is found to be 4 times the plastic moment of resistance divided by the span length (Wc = 4Mp/l).

Portal frame design encompasses ultimate and serviceability limit states. Ultimate analysis uses elastic methods (permissible beyond yield per Eurocode/American codes) or plastic analysis examining hinge formation at maximum moment locations: rafter haunches for positive moments, column weakest points for negative moments. Haunches increase strength, preventing hinges at rafter ends. Column bases exist on a pinned-fixed spectrum with spring stiffness assumptions (10% for alpha critical, 20% for deflection). Serviceability deflection criteria vary by country: Spain specifies H/150 (53mm for 8m height) for non-fragile elements, France uses L/250. Cross-section classification determines plastic analysis applicability: Class 1 allows rotation beyond plastic moments (with strain hardening), Class 2 drops below plastic moments when over-rotated, Class 3 cannot reach plastic moment due to local buckling, Class 4 cannot reach yield moment. Plastic analysis requires Class 1 sections.