K values: Fixed-fixed: K = 0.65 (both ends moment-connected) Fixed-pinned: K = 0.80 (one end moment, one end pin) Pinned-pinned: K = 1.00 (both ends pinned — typical residential) Fixed-free: K = 2.10 (cantilever column — AVOID)

Practical: For a pinned-pinned HSS 4×4×1/4 column:

• 8' height: capacity ~95 kips

• 10' height: capacity ~85 kips

• 12' height: capacity ~70 kips

• 14' height: capacity ~55 kips (getting borderline for interior columns)

Rule of thumb: Every 2' of additional height costs ~15% of column capacity.

Base Plate Design

Sizing Formula

Base plate area ≥ Factored axial load / (0.85 × f'c × φ)

Where: f'c = concrete strength (typically 4,000 PSI) φ = 0.65 (bearing on concrete)

Typical ML Systems Base Plates

| Column | Base Plate | Thickness | Anchor Bolts | Footing Size | |--------|-----------|-----------|--------------|--------------| | HSS 4×4 | 8"×8" | 1/2" | (4) 5/8" A307 | 24"×24"×12" | | HSS 6×6 | 10"×10" | 5/8" | (4) 3/4" A307 | 30"×30"×14" | | W10×33 | 12"×12" | 3/4" | (4) 3/4" A325 | 36"×36"×16" | | Moment base | 14"×14" | 1" | (6) 7/8" A325 | 42"×42"×18" |

DfD Base Plate Detail

• Stub plate cast into foundation at pour — flush with top of slab

• Column base plate bolted to stub plate with A325 bolts

• At deconstruction: unbolt column from stub plate, crane-lift column away

• Stub plate remains in foundation for Cycle 2 reuse

• Critical: Stub plates sized for N+2 column loads (multi-cycle over-engineering)

Bolt Specifications

A325 vs A490

| Property | A325 (Group A) | A490 (Group B) | |----------|---------------|---------------| | Tensile strength | 120 ksi | 150 ksi | | Proof load | 85 ksi | 120 ksi | | Shear capacity (per bolt, 3/4") | ~15.9 kips | ~19.9 kips | | Bearing capacity | Governed by plate thickness | Same | | Installation | Snug-tight or turn-of-nut | Turn-of-nut or TC bolts | | Reuse | Yes (DfD compatible) | No (ASTM prohibits reuse) | | Galvanizing | Available (hot-dip) | NOT available | | ML Systems choice | Primary — all connections | Avoid (non-reusable) |

Bolt Sizing for Residential Steel

| Bolt Diameter | Shear (A325-N) | Typical Use | |---------------|----------------|-------------| | 1/2" | 7.07 kips | Light connections, hangers | | 5/8" | 11.0 kips | Beam-to-beam, secondary | | 3/4" | 15.9 kips | Standard ML Systems connection | | 7/8" | 21.6 kips | Moment connections | | 1" | 28.3 kips | Heavy moment, base plates |

Bolt Pattern Rules

• Minimum edge distance: 1.5× bolt diameter from edge of plate

• Minimum spacing: 3× bolt diameter center-to-center

• Standard pattern: 3" gauge, 3" pitch for 3/4" bolts

• Even number of bolts per connection (2, 4, 6) — never odd

Connection Types

1. Simple Shear (Pinned) — Most Common

• What: Beam sits on column, transfers vertical load only, allows rotation

• Hardware: Clip angle, single plate ("shear tab"), or seated connection

• Bolts: 2-4 bolts through web

• Use: Standard beam-to-column where no lateral resistance needed

• DfD: Excellent — unbolt clip angle, crane-lift beam away

2. Bolted End-Plate Moment Connection — ML Systems Preferred

• What: Steel plate welded (shop only) to beam end, field-bolted to column flange

• Capacity: Transfers moment (bending) + shear — rigid frame behavior

• Bolts: 4-8 bolts through end plate into column flange

• Use: Open floor plans, lateral resistance, cantilevers

• DfD: Good — all field connections are bolted, shop welds are permanent but stay with the beam

• Advantage over field-welded: No HAZ concerns with HSLA, faster erection, reversible

3. Seated Connection (Knife/Unstiffened)

• What: Angle or tee bracket bolted to column, beam flange bears on seat

• Use: Light loads, easy erection (beam sets on shelf like a bookshelf)

• DfD: Excellent — very simple to reverse

4. Moment Connection Types (By Rigidity)

| Type | Rigidity | Bolts | Best For | |------|----------|-------|----------| | Extended end plate | Full moment | 6-8 | Primary lateral system | | Flush end plate | Partial moment | 4-6 | Secondary frames, moderate spans | | Top-and-seat angle | Partial moment | 4 | Light moment, wind bracing | | Shear tab only | Pinned (zero moment) | 2-3 | Gravity-only connections |

Deflection — The Real Design Driver

Why Deflection Governs in Residential

In residential construction with typical spans (15-25'), the beam almost always has enough STRENGTH but too much DEFLECTION. This is because:

Deflection Formulas (Simply Supported)

Uniform load: δ = 5wL⁴ / (384EI) Point load center: δ = PL³ / (48EI) Two point loads: δ = Pa(3L² − 4a²) / (24EI) [loads at distance 'a' from supports]

Reducing Deflection (Without Changing Span)

| Strategy | Effect | Cost | Notes | |----------|--------|------|-------| | Deeper section (↑I) | Best — I grows as d³ | Low | W12 vs W10 = ~70% more I | | Heavier section (same depth) | Moderate | Low | Thicker flanges = more I | | Composite action (concrete on steel) | ~2× stiffness | Moderate | Shear studs to precast — BUT kills DfD | | Cambering | Visual fix only | Low | Pre-bend beam upward = looks flat under load | | Continuous spans | ~60% less deflection | Design complexity | Beam runs over interior column | | Moment connections | ~20-40% less | Moderate | End fixity reduces midspan deflection |

ML Systems Deflection Strategy

Advanced Beam Concepts

Castellated Beams (Hexagonal Web Openings)

• Standard W-shape cut in zigzag pattern, offset, and re-welded → ~50% deeper beam with hexagonal holes

• Depth increase: 1.5× original depth at same weight

• Stiffness increase: ~2.5× due to depth³ relationship

• MEP routing: Ducts, pipes, conduit pass through web openings

• Span increase: 20-30% longer spans vs parent section

• DfD note: Re-welding is shop-only; field connections still bolted

• Use case: Long-span living areas where MEP needs to run through structure

Cellular Beams (Circular Web Openings)

• Same concept as castellated but with round holes — smoother aesthetics

• Better for exposed steel — clean circular openings look intentional

• Slightly less structural efficiency than hex openings

• Use case: Exposed ceiling in loft/industrial aesthetic homes

Vierendeel Trusses (Rectangular Openings)

• Frame-like truss with NO diagonal web members — only verticals

• Large rectangular openings between chords — perfect for windows, doorways, MEP

• Less efficient than diagonal trusses (bending in chords, not just axial)

• Use case: "Wall of glass" — Vierendeel spans above a window wall, carrying roof/floor load while allowing full-height glazing

• Connection: Moment connections at all chord-to-vertical joints (rigid frame behavior)

Stub Girders

• Short beam stubs welded to bottom chord, full-depth openings between stubs

• Use case: Very long spans (30-45') with integrated MEP zones

• Rare in residential — more common in commercial

Cantilever Design

Rules

• Maximum cantilever: ≤ L/3 of back span (structural) or ≤ L/4 (comfort)

• Example: 20' back span → max 6.7' cantilever (structural), 5' recommended

• Deflection at tip: δ = PL³/(3EI) — deflection grows as L³, so small increases in length = large deflection increases

• Uplift at back support: Cantilever creates net uplift — must be anchored or counter-weighted

Cantilever Connection

• Requires moment connection at the support point (not a simple pin)

• Bolted end-plate moment connection = DfD compatible

• Back span beam must be heavier than cantilever (counterbalance + load path)

• Floor vibration: Cantilevers are inherently bouncy — target natural frequency > 8 Hz

ML Systems Cantilever Applications

| Feature | Typical Cantilever | Beam | Notes | |---------|-------------------|------|-------| | Bay window bump-out | 2-3' | W10×22 | Minimal — well within limits | | Covered entry porch | 4-6' | W12×26 | Standard — moment at wall line | | Balcony | 4-8' | W14×30 | Need railing load (200 PLF) at tip | | Dramatic overhang | 8-12' | W16×36+ | Requires engineering review, heavy moment connection |

Floor Vibration Control

Why It Matters

Steel-framed residential floors can feel "bouncy" compared to heavy wood/concrete floors because steel is lighter (less mass to dampen vibration).

Natural Frequency Target

fn = 0.18√(g/δ) ≈ 0.18√(386/δ)

Where δ = instantaneous deflection in inches under design load Target: fn > 8 Hz (imperceptible to occupants)