1607ENG Week 8 Lecture: Structures and Roofs

Structural Loads – An Introduction

• Structural loads are the prevailing loads on a house.
• The structure is analyzed to determine the required structural support.

Mechanics – Brief Definition

• Mechanics is the part of physics concerned with forces on objects and matter, and the resulting motion.
• An object can change its velocity (accelerate) when acted upon by forces.
• A force is an action on a body that causes it to accelerate (change speed).
• Forces have:
  • Magnitude
  • Direction
• Magnitude is measured relative to the force required to accelerate a 1kg body by 1m/s².

Newton’s Laws

• Newtonian Mechanics: The study of the relationship between accelerations and forces.
• Three key laws:
  • Law 1: If no force acts on a body, the body's velocity cannot change (it cannot accelerate).
    • If a body is at rest, it stays at rest. If moving, it continues to move with the same velocity.
    • If net force = 0, the body cannot accelerate. $<br />\neq = 0$
  • Law 2: The net force on a body is equal to the product of its mass and acceleration.
    • $F_{net} = ma$
    • Forces are vector quantities (magnitude and direction).
    • Expressed in 3 coordinate axes: x, y, and z. != ! + " + # =
  • Law 3: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.
    • $F<em>{AB} = F</em>{BC}$
    • Consider forces acting on each object: $F<em>{AB} = -F</em>{BA}$
    • Forces are equal in magnitude and opposite in direction.

Systems of Units

• Structural loading systems use specific units.
• In 1971, the General Conference on Weights and Measures defined seven base quantities, forming the International System of Units (SI), also known as the metric system.
• Many construction engineering units (e.g., MPa for material strength) are SI-derived units (combinations of SI units).
• Key units for structural engineering:
  • Length: metre (m)
  • Time: second (s)
  • Mass: kilogram (kg)
• Other units: Current in Ampere (A), Temperature in Kelvin (K), Amount of Substance in Mole (mol), Luminous Intensity in candela (cd).

Derived Units

• Structural analysis relates forces (loads) and material resistance (material properties).
• Forces are measured in Newtons (N), an SI-derived unit: force to accelerate 1 kg at 1 m/s². $1 N = 1 kg \cdot \frac{m}{s^2}$
• Moment (torque): rotational effect, measured in Newton metre (Nm).
• Material strength: pressure in Pascal (Pa) or Megapascal (MPa), force per unit area.
  • $1 Pa = \frac{N}{m^2}$
  • $1 MPa = 1 \frac{N}{mm^2}$

Statics

• As in Newton’s First Law, if the sum of forces acting on a body is zero, the body will not accelerate.
• In this state, the body is said to be in equilibrium.
• Statics: The study of the conditions of equilibrium.
• The basic unit of force is a Newton, but in engineering, kiloNewtons (kN) are commonly used.

Components of a Force

• A force can be replaced by two forces (components) if their vector sum equals the given force.
• Resolvingcomponents along Ox and Oy axes.
• Finding components of F parallel and perpendicular to a given direction Ox (at right angles, θ to Ox):
  • $F_x = F \cos \theta$
  • $F_y = F \sin \theta$
  • $F = \sqrt{F<em>x^2 + F</em>y^2}$
  • $\theta = \tan^{-1} (\frac{F<em>y}{F</em>x})$

Rotation, Moment and Torque

• Rotation around a single axis uses an algebraic sign; counterclockwise is positive, clockwise is negative.
• Doorknobs are located far from hinges; force application, location, and direction are crucial.
• Torque (rigid body): force that enables rotation around a fixed axis.
• The ability to rotate depends on:
  • Magnitude of tangential component ($F_t$)
  • Distance from the axis of rotation (moment arm, $r$)
• Torque: $\tau = rF = rF \sin \theta$
  • Often written as: $\\tau = rF \sin \phi$ ; $\tau = F<em>t r$; $\tau = rF</em>t$; $\tau=rF$ (force acts at 90°).

Key Forces in Statics

• Gravity: force due to gravitational attraction between masses. $F = G \frac{m<em>1 m</em>2}{r^2}$
• Weight: magnitude of upward force needed to balance gravity. $W = mg$
• Normal force: force of the ground acting upwards on a building (Newton’s Third Law), perpendicular to the surface.
• Friction: force opposing sliding, parallel to the surface.
• Moment: ‘turning force’ at a distance from a point.
  • Example: person on a diving board.
• Bending: moment on a structural member fixed at both ends creates compression (top) and tension (bottom).
  • Example: books on a bookshelf.
• Torsion: ‘twisting force’.
  • Example: twisting a screwdriver.
• Tension: pulling forces that stretch an object.
  • Example: pulling a rope.
• Compression: pushing forces that squeeze an object.
  • Example: squashing wood in a vice.
• Shear: adjacent pushing or pulling forces that ‘cut’ an object.
  • Example: scissors cutting paper.

Key Forces in Statics – Hydrostatic Forces

• Hydrostatic forces: fluid pressure.
• Atmospheric pressure differentials are often negligible in mechanics and statics.
• Liquid pressures are significant.
• Archimedes' principle: a body immersed in a fluid experiences an upward force ($F<em>b$) equal to the weight of the displaced fluid ($W</em>{fluid}$). $F<em>b = W</em>{fluid}$
• Pressure in a liquid (depth-dependent) and atmosphere (altitude/height-dependent):
  • $P = P_0 + \rho g h$

Key Forces in Statics - Friction

• Static friction: interlocking surfaces prevent motion up to a limit.
• Kinetic friction: frictional resistance between moving surfaces is nearly constant at low speeds.
• Frictional forces arise from interlocking surfaces.
• Friction is unavoidable; it opposes motion.
• It leads to wasted effort but also enables movement (walking, driving).
  • Without friction, cars couldn't move, and pencils couldn't write.

Key Forces in Statics – Friction Equations

• Static Friction: $f<em>s \leq \mu</em>s F_N$ (max = just about to move)
• Kinetic Friction: $f<em>k = \mu</em>k F_N$

Members in a Structure

• Different parts of a frame structure have different jobs.
• Beams: linear members supported at each end, subject to bending (compression on top, tension on bottom).
  • Bearers in flooring systems are beam structures.
  • Beams are generally horizontal, but can also be vertical.
• Columns: linear members taller than they are wide.
  • Stumps and piers are columns.
  • Columns support beams and platforms.
• Tension members: structural elements subject to axial forces that ‘pull’ or ‘stretch’ the member.
  • Frame bracing, truss members, and cables in suspended roofs are tension members.
• Torsion: often a secondary effect; major stresses are bending, compression, and tension.
  • Overhanging balconies (cantilevers) are subject to torsion.
• Shear forces: develop in beams and overall building.

Solving Statics Problems

1. Draw a simplified representation, noting the center of mass (gravity).
2. Choose how to ‘cut’ the diagram for force analysis.
3. Draw a “free body diagram” noting all critical forces (including friction) in their directions.
4. Apply equilibrium conditions.
5. Analyze numbers/equations to determine loads and whether the structure can withstand them.

Roofs - Structures Over Our Heads

• Roofs are critical for house construction.

• Roofs:

  • Protect occupants from weather extremes.
  • Provide a dry internal environment.
  • Provide a route for internal building services.
  • Provide a structure for insulation.
  • Provide a level of privacy.
  • May be integral to the load-bearing structure of the house.

Critical Control Layers – Changing Requirements

1. Water Shedding
2. Water Resisting
3. Air
4. Vapour

Key Parts to a Roof

• Structural Frame
  • Load-bearing structure
• Roof Cover
  • Weatherproof external covering
• Ceilings
  • Internal lining as viewed by occupants
• Roof Lights
  • Glazed or semi-transparent surfaces to promote natural light

Types: Structural Frame and Roof Cover

• Structural Frame:
  • Predominantly timber, but can be steel-framed.
  • Two basic types:
    • Stick built: constructed from assembling individual members of timber using saws, hammers, nails, etc., on-site.
    • Trussed: prefabricated, triangulated assemblies that are hoisted onto walls as a complete two-dimensional frame. Suitable for gable and near-gable applications.
• Roof Cover:
  • Top surface cover for the roof.
  • Main function is weatherproofing.
  • Four potential categories:
    • Tile roof: terracotta or cement tiles, slate, fiber cement or composite material shingles, timber shingles or shakes, and pressed metal tiles.
    • Sheeted roof: uses steel and aluminum-based sheet products with different varieties, profiles, and coatings.
    • Membrane roofs or built-up roofs: a solid base of plywood or concrete with multi-layers of sealant.
    • Concrete roofs: occasionally in Aus., particularly if the roof is to be trafficable.

Ceilings and Roof Lights

• Ceilings:
  • Dominant functions:
    • Top enclosure to internal spaces.
    • Stopping intrusion of drafts and dust.
  • Typically made from fibrous plasterboard.
  • Can be flush jointed or raked to the roof slope with exposed rafters and purlins.
  • Structural link between the roof, walls, and ceiling system.
• Roof Lights:
  • Historically, windows in roofs had waterproofing, structure, and durability problems.
  • Modern solutions are more accessible.
  • Four types:
    • Dome light: mass-manufactured units designed to slot into tile or sheet roofs.
    • Southlight: vertical (or near) window facing south, built into the roof structure.
    • Roof slope windows: mass-manufactured, suitable for room-in-roof designs.
    • Dormer windows: built into the roof where attics are part of the design.

Relevant Standards

• Roofs are subject to the same loading requirements as walls and must comply with NCC 2019 Volume 2, Part 3.0.
• Timber roofs = timber standards.
• Timber floors are subject to the standards for framing as defined in Part 3.4.3 of NCC 2019 Volume 2:
  • Design of timber structures: AS 1720.1.
  • Design of nail plated timber roof trusses: AS 1720.5.
  • Residential timber-framed construction – non-cyclonic areas: AS 1684.2.
  • Residential timber-framed construction – cyclonic areas: AS 1684.3.
  • Residential timber-framed construction – non-cyclonic areas (simplified): AS 1684.4.
  • Installation of particleboard flooring: AS 1860.2.
• Timber frames in Queensland are also subject to Schedules A, B, C of Book 2 of the “Queensland Government, Department of Agriculture, Fisheries and Forestry - Construction timbers in Queensland, Book 1 and Book 2…”

Relevant Standards - Steel

• Steel frames = steel standards
• Steel frames are subject to the standards for framing as defined in Part 3.4.4 of NCC 2019 Volume 2:
  • Steel structures: AS 4100 - design, fabrication, erection, and modification of steelwork in structures. Applies to buildings, structures and cranes constructed of steel.
  • Cold-formed steel structures: AS/NZS 4600 – cold formed steel sheet, strip, plate or bar <25 mm used for load-carrying in buildings.
  • The building lies outside earthquake prone areas.
  • The building is not subject to snow loads.
  • Part 3.4.4.4 Corrosion protection: all structural steel requires protection against corrosion (except those built into a masonry wall).

Even More Codes and Standards

• NCC Volume 2 2019:
  • Parts 3.1.3 Termite risk management
  • AS 3623 1993, Domestic metal framing
  • AS/NZS 4600, Cold-formed steel structures
  • AS 1170 Series, Minimum design loads on structures
  • AS 4055, Wind loadings for housing
  • AS 1397, Steel sheet and strip – Hot-dipped zinc-coated or aluminium/zinc coated.
  • AS 3600 series, Termite management

Reminder: Steel Terminology

• UC – Universal Column
• UB – Universal Beam
• TFB – Tapered Flange Beam
• PFC – Parallel Flange Channel
• TFC – Tapered Flange Channel
• BT, CT – Structural Tees
• EA – Equal Angle
• UA – Unequal Angle
• WB – Welded Beam
• WC – Welded Channel
• SHS – Square Hollow Section
• RHS – Rectangular Hollow Section
• CHS – Circular Hollow Section

Stick Built Roofs

• Now less common, Stick Built Roofs are built from individual members of timber.

Roof Components

• Barge board: found on gabled roofs, disguises rafters at the gable end.
• Ceiling joist: timber or metal that the ceiling is attached to.
• Collar tie: fitted between rafters to prevent spreading.
• Fascia board: attached across the end of the rafters to disguise them.
• Hanging beam: supports ceiling joists.
• Hip rafter: extends from wall plate to ridge in the angle of a hip roof.
• Purlin: horizontal piece supporting rafters or decking.
• Rafter: sloped beams from ridge to eaves.
• Roofing batten: provides a fixing point for cladding materials.
• Soffit bearer: base for soffit lining to be fixed to.
• Struts and props: support and transfer load from purlins to strutting beams.
• Strutting beam: supports roof members, transfers load to load bearing walls.
• Top plate: nailed to the top of wall studs, supports the roof load.
• Truss: framework using triangular shapes, supports roof deck and framing.
• Valley rafter: extends diagonally at a 45° angle from the inside corner of two intersecting wall plates up to the ridge of the roof.

Trussed Roofs

• Another commonly employed roof construction system in Australia.
• Trussed roofs have separate frame components that are delivered preassembled to site.

Truss Characteristics

• Timbers used:
  • Lightweight timber trusses are fabricated from a variety of timbers, including, but not limited to, pinus, hardwood, Oregan and cypress pine, dependent only on local availability. No timber appears particularly better than another.
• Truss types:
  • Generally there are two types of roof trusses used in residential building: simple king post and the ‘W’’ web truss, also called a ‘Fink’ truss.
  • ‘W’ trusses can span up to 10m.
  • Ideally suited to gable roofs but can be modified for hip roofs.
• Four common sub-types:
  • Catilevered ‘W’ truss: specifically designed to allow verandahs in a truss roof.
  • Truncated truss: allows trussed roof to be incorporated into a roof with a hipped shape.
  • Scissor truss: used when a vaulted ceiling is designed, but cost of large timber section is disproportionately expensive.
  • Skillion or sawtooth truss: ideally suited for a lean-to extension to an existing roof or as a roof on its own, often using the vertical post of the truss for a window, e.g. clerestory.
• Jointing and connections
  • The chord and web members of the truss are connected at their intersecting points, called panel points, with integral nail plates.
  • Lightweight timber trusses are generally design to be supported on walls at the extreme ends of the bottom chord. No additional support or alteration to the support points should be undertaken.
  • Trusses need to have adequate bearing across the wall top plates (no deviations across the plate).
  • Roof needs to be tied down to the walls to prevent uplift during high winds.

Trussed Roof Bracing

• Bracing is as important on roof frames as it is on walls to prevent shearing of the structure.
• Timber bracing is available, although metal bracing is the most common: flat strap or angled as in speed bracing.
• These are only effective in tension and must be fitted in opposing pairs.
• Metal bracing should be applied at approx. 30° to the ridge line.

Flat (or near flat), Skillion and Vaulted Roofs

• Alternative roof type in Australia.

Flat Roofs

• Horizontal roof with very little or no pitch (<5°).
• Cheap, fast, and easy to install.
• Can be difficult to waterproof.
• Water tends to pool and drain into the house.
• Requires an extremely waterproof covering.
  • Historically asphalt was used, but it is not durable and not sustainable.
  • More recently, vinyl and rubber-based products such as Ethylene Propylene Diene Monomer (EPDM) have been chosen over asphalt.
  • Sheet metal roofing is possible with specialized products, e.g., Zincalume Lokdek.
  • Pump or syphon system may also be required to ensure the interior remains dry.

Skillion Roofs

• One single flat surface.
• Pitch is much steeper and more noticeable than a flat roof.
• Relatively cheap, fast, and easy to construct.
• No drainage problems associated with flat roofs.
• Often do not need a comprehensive waterproof membrane.
• Historically used for sheds and industrial buildings, but are becoming more popular.
• Exposed rafters as a feature.
• Variations include circular or oval shape or a ‘butterfly’, with opposing pitches meeting at a low ridge in the centre of the roof.
• They are usually metal clad.

Vaulted Roofs

• Self-supporting arch above walls and beneath a roof.
• Create a volume of space overhead.
• Offer a sense of spaciousness.
• Allow for more natural light.
• They do waste energy due to the extra volume within occupied spaces.
• Can be advantageous in tropical environments for air circulation and high-level ventilation.
• Harder to maintain than flat ceilings.
• Walls and floors must be designed and engineered to withstand the different loads created by vaulted roofs.
• Require special trusses that are engineered for a vaulted space.
• Cost more for construction – reinforced framing, moving, adding wiring, insulation and finalising the interior.

Flat, Skillion and Vaulted Roofs - Basic Structural Construction

• More care required than Trussed or Stick Built.
• Reliance on gravity for structural integrity, rather than triangulated frames.
• The individual members in post-and-beam roofs are more important individually than in other roof types.
• One structural failure in a member can lead to collapse.
• Vaulted ceilings often require open rafter couples: restraining forces supplied by bottom chord (truss) or ceiling joist (conventional) are provided by walls and beams design to counter rafter spreading forces.

Flat, Skillion and Vaulted Roofs - Jointing and Connections

• Skillion roof generally use the underside of the rafters and structure to which ceiling is fixed.
• In some cases the normal top plate of a wall framing system is replaced by a beam around the entire perimeter of the house as an alternative structural fixing point. (In brick veneer this changes the aesthetic).
• Beams may also be supported at ends by load-bearing walls.
• Beams may be different types of timber or steel beams or cold formed steel purlins.
• Rafters are connected to internal load-bearing via a birds mouth notch and nailing or fixing plates.
• There can be a tendency in skillion roofs to use brick walls as the point of tie down for roofs. Brick walls in these situations may be higher than external brick and structural capacity needs to be confirmed.

Roof Cladding - Options for What Goes Onto a Roof Structure

Roof Tiles

• Most roof tiles, particularly terracotta, are inexpensive and durable.
• Suited to the Australian climate, as they are not usually subject to high wind or snow loads – with exceptions of course.
• Generally pitch greater than 15°, with the pitches most common being between 17° and 27°. Generally the maximum is 45°, at which point tilers charge extra and some products cannot cope.
• Preference when using roof tiles is to have right-angled building corners and for hip/valley roofs to have intersections that meet at 45° to avoid messing detailing.
• The simpler design the better.
• Sarking:
  • Required under any roof because:
    • It acts as secondary protection against moisture such as wind-borne spray, broken tiles, etc.
    • As a reflective foil to prevent radiant heat gain. A lot of sarking products are now reflective on two sides to prevent heat loss and heat gain.
  • Most manufacturers recommend a specific pitch for their product with/without sarking.

Tile Materials

• Terracotta – wet clay formed and then fired for loss long (50 years outside salty environments).
• Cement or concrete – newer versions have high quality and durability (towards terracotta).
• Slate – natural stone cut material, can be expensive. Good life if limited solar loads.
• Fibrocement shingles – multi-notched fiber-reinforced cement. Notched system allows material saving.
• Timber shingles and shakes – durable timber species, mainly imported from North America.
• Metal tiles – cold-formed in long lengths of galvanized steel or aluminum.

Roof Sheets

• Product is now steel rather than iron and has an aluminium/zinc coating rather being hot dipped galvanised (zinc).
• Three major improvements in current roofing from earlier products:
  • Available in long lengths, limited only by trucking.
  • Pre-painted colored sheets available.
  • Fixing methods greatly improved to reduce leakage.
• Many profiles also now available, however traditional corrugations still popular – allows curved roofs.
• Modern products have been developed with specific profiles and non-punctured fixings to allow near-flat roofs (down to a pitch of 1:50 = 1.2°). These products dominate flat roofs in Australia.
• Aluminium sheets – normally commercial sector.
• Fibrocement sheets – occasionally popular, but require complicated waterproofing and flashing.
• Water collection:
  • Run off from sheet roofs is immediate and near-complete, making roof sheeting ideal for water collection and reuse.
• Wind:
  • Sometimes poor reputation.
  • Sheet roofing is suitable for cyclonic wind conditions if the house structure is properly constructed and sheeting is fixed correctly.
• Sarking:
  • Sarking is important for any condensate runoff underneath a metal surface.
• Insulation:
  • Insulation should always be installed.
  • Quantity and type will be dependent on climate and roof construction.
  • Require specialist for best method to insulate to prevent problems occurring with condensation.