SS

Area of Footing

Area of Footing = total wall or column load + weight of footing + any soil on top of footing / allowable soil bearing pressure • Earth Pressure on a wall (P) = 30 lb/ft3 x height of wall

Flat plate system

Basically a Two-Way slab with no supporting beams, only columns. • Reinforced slab spans in both directions directly into columns at 25' with 6" - 12" thickness • Typically used for light loads, short spans, when floor-floor height must be minimized, and/or when simple under-side of slab appearance is required • Has low shear capacity and low stiffness

Trusses need to be designed so member

Trusses need to be designed so member is symmetric on both sides of centroid axis in the plane of the truss • Typical depth-to-span ratios range from 1:10 to 1:20 • Typical spans: 40' - 200' and typical spacing: 10' - 40' o.c. • Residential & light commercial trusses are smaller, 2x4 or 2x6 members at 24"o.c. • Flat trusses require less overall depth than pitched trusses • Roof loads transferred from decking to purlins attached to truss at panel points • If concentrated loads between panel points or uniform loads applied to top chords, member must be designed for axial loading as well as for bending...Like beams • Compression in top chord & tension in bottom chords • Forces in a parallel chord truss increase towards center • If concentrated loads or uniform loads on any chord member between panel points, member must resist bending stresses • Steel trusses with double angles back-toback with 3/8" or 1/2" gusset plate with tee sections or wide flange • Wood trusses: web members between double top and bottom chords or with all members in same plane connected with gusset plate • With light loads, bars or rods can be used for tension members • Centroidal axes of intersecting members must meet at a point to avoid eccentric loading

Cavity Walls

Two masonry skins (eg: brick exterior and cmu interior) with a hollow space between. • Cavity is used for drain water out of wall through weep holes • May be grouted and reinforced or ungrouted A cavity wall is a double wythe wall, but a double wythe wall is not always a cavity wall (kinda like, a square is a rectangle, but a rectangle isn't always a square)

Composite Construction

Two or more materials designed to act together to resist loads (reinforced concrete construction is the most typical example)

Double Wythe Masonry Walls

Two units thick • Material for both wythes may be the same and may be grouted/reinforced or ungrouted

Glulam Type Width Spacing Spans Top/Bottom Use Adv

Type Width 3-1/8", 5-1/8", 6-3/4", 8-3/4" Spacing: varies Spans: 15-60' Top/Bottom: Several layers of timber bonded together with glue and connected with plates and/or bolts Use: Columns and beams, commercial, public Adv: can be left exposed, can be tapered or curved

I joist Type Width Spacing Spans Top/Bottom Use Adv

Type: I joist Width: 1-3/4" -3-1/2" Spacing: 12"-24" Spans: 8'-24' Top/Bottom: 9-1/2" - 16" depth OSB webs and microllam (thick plywood) flanges connect to wall with hangers Use: Res, light commercial Adv: Efficient strl shape as shop fabrication eliminates common defects

Joist Type Width Spacing Spans Top/Bottom Use Adv

Type: Joists Width: 2 nom Spacing: 12" or 16" oc Spans: 20-25' Top/Bottom: Bridging supports bottom edge,sheathing holds top in place Use: Between beams or bearing walls Adv: Tried and True method

ultimate goal of an arch

Ultimate goal of arch design is that thrust must be resisted • For a given span thrust is inversely proportional to the rise/height of the arch • If rise is reduced by one half, the thrust doubles Tie rods: hold two lower portions together Foundations are designed to to prevent thrust • Shape of arch selected for aesthetic appeal not always ideal shape for loading • Typical arch spans: • Wood: 50' - 240' • Concrete: 20' - 320' • Steel: 50' - 500'

Load (p)

a force applied to a body (also called an external force)

Moment of Inertia

measure of an object's resistance to changes to its rotation.

Composite Structural Member

more than one material working together (eg: reinforced concrete, box beam, flitch beam)

Forces (or Loads) on Architectural Structures: Deconstructive Agents

reduce capacity of structural element • Fire: the biggest issue! Heavy timber construction is the most preventative form. • Chemical corrosion: parking lots are the worst. • Erosion: wind/water • Insects/Plants/Animals

Post-tensioned concrete

steel tendons are laid out in desired direction and concrete is poured on top. When concrete is cured tendons are tensioned and force is transferred to the concrete through end anchorages.

Yield Point

the amount of stress that causes a material to deform without additional load added

Deflection

the displacement of a structural element under a load

Cast-in-place concrete

typically involves steel reinforcement (rebar), sometime post-tensioning is used

Hook's Law

unit stress is proportional to unit strain up to the elastic limit

A concentrated load vs distributed load

A concentrated load acts at one point on a beam • A distributed load acts over a length of a beam • If the load/unit of length of the beam is constant it's a uniformly distributed load • Simple beams, cantilever beams, and overhanging beams that rest on 2 supports are statically determinate

equilibrant

A force equal in magnitude to the resultant, but opposite in direction and on the same line of action as the resultant is called the equilibrant It is sometimes convenient in the analysis of structure to replace one force with two or more other forces that will produce the same effect on a body as the original force. • These forces are called components of the original force, and the procedure is called resolving forces Two forces equal in magnitude, but opposite in direction, and acting at some distance from each other form a couple • The higher the strength, the less ductile and more brittle it is (so we're lucky our bones are surrounded by tissue) • Temperature will alter the strength...looses modulus of elasticity...not good! • Heat used to melt and shape a member, but once it is shaped, stiffness will still be altered

Eccentric Load

A load imposed on a structural member at some point other than the centroid of the section

Flat slab system

A two way slab with column capitals, drop panels, or both with spans of 30'

Retaining Wall Types

Cantilever wall: (most common type) constructed of reinforced concrete resists forces by the weight of the structure and weight of the soil on the heel of the base slab • A key projects form the bottom to increase the resistance to sliding • 20' - 25' max height due to economics • Counterfort walls: like cantilever walls, with a conterforts spaced at distances approximately half the wall height • Gravity walls: resist forces by own weight and made of non reinforced concrete • Retaining walls fail as a whole by overturning or sliding. • To prevent this, the friction between the footing and the surrounding soil/earth pressure in front of the toe must be 1.5 the pressure that typically causes the wall to slide.

implications of cast in place

Cast in Place Concrete: poured into forms, on decking, or ground at location • Probably the most expensive and slowest structural system • Good for irregular shapes and fireproofing/durability needs • Slip Forming (forming that slides up each floor as it's poured) helps save cost

Connection dowel type fasteners bearing type fasteners

Connection: two or more members joined with one or more fasteners which provide continuity to the members and strength/stability to the system • Dowel Type Fasteners: (nails, screws, bolts) that transmit lateral loads via bearing stresses between the fastener and members of the connection OR that transfer withdrawal loads parallel to the fasteners axis via friction or bearing to the connected materials • Bearing Type Fasteners: (shear plates) that transmit lateral loads only by shear forces via bearing on the connected materials

Coplanar forces Structural forces

Coplanar forces: lines of action all lie within the same plane • Structural forces: any combination of forces (e.g.: truss is sets of concurrent coplanar forces)

Wood Connection Types

Depends on the species/condition of the wood, fire retardant or not, type of load, and angel of load to the grain • Use nails and screws for light loads and timber connectors for large loads • Wood can carry a greater max load for short duration than for long durations • Connections can be adjusted given the type/duration of load

Three general steps in structural design

Determine the loads (compute) • Calculate the stresses (analyze) • Dimension and proportion the members and detail the connections such that the stresses are within the limits for the structural materials (design)

Direct Stress Problems

F = P/A is an investigative formula • St. Venant's Principle for Direct Stress: • The stresses and strains in a body at points that are sufficiently remote from points of application of load depends only on the static resultant of the loads and not on the distribution of loads.

Lift-slab system:

Floor/roof slabs are cast on top of the previous and then jacked up to the desired height

For composite sections

For composite sections, find the moment of inertial of each simple section around its centroid, then transfer to a new axis, typically the centroid of the composite section. The transferred moments of inertia of the simple sections are added to get the moment of inertia for the entire section. Because the section's depth (d) is cubed, it has a greater bearing on the beam' resistance to bending. In other words, the bigger the depth of the beam, the stronger it is.

Forces are also known as loads

Forces are also known as loads. They are an action that has direction (an arrowhead that indicates if it points or pulls), magnitude (pounds or kips), and line of action (a given angle in degrees). When a bunch of forces are acting on the same point, it is called the resultant, and it has the same effect as all of the individual forces combined. Resultants are calculated by simple algebra when all of the magnitudes and lines of action are known. First, resolve the forces into individual vertical and horizontal components using A2 + B2 = C2 and/or SohCahToa. The sum of all of the vertical components gives the vertical component of the resultant, and the sum of all of the horizontal components gives the horizontal component of the resultant. When a force touches a member, the member becomes stressed and it tries to internally resist the external force.

Frame Truss Gage line Arch

Frame: a structural system that supports other components of a physical construction • Truss: a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure • Gage line: standard dimension from corner edge of an angle to centerline of bolt holes. depends on size of angle • Arch: a curved symmetrical structure spanning an opening and typically supporting the weight of a bridge, roof, or wall above it.

friction pile socketed caissons end bearing piles

Friction Pile: Driven into softer soil. • Friction transmits the load between pile and soil. " • Bearing capacity is limited by whichever is weaker: strength of the pile or soil" • Socketed Caissons: like Belled Caissons, but the hole is drilled deep into the strata. Bearing capacity comes from end baring and frictional forces. • End Bearing Piles: 2-3x cost of spread footings. • Driven until tip meets firm resistance from strata

Hangers Plate Girder Underpinning Shoring

Hangers: combination of dowel and bearing type fasteners that support one structural member and are connected to another member by a combination of dowel and bearing action • Plate Girder: assembly of steel plates, or plates and angles, fastened together to form an integral member • Underpinning: the process of strengthening and stabilizing the foundation of an existing building • Shoring: supporting a structure in order to prevent collapse so that construction can proceed. (e.g.: support beams and floors of building while a column/wall is removed, shoring in trenches for worker safety in excavation)

Arches

Have hinged or fixed supports (though fixed are less common) • Arches are usually top hinged to allow it to remain flexible and avoid developing high bending stresses under live loading and loading due to temperature changes and settlement • Hinged arch is primarily subjected to compressive forces • Conceptually, uniform loads supported across the span form a parabola • Actually, no arch is subject to just one set of loads...there's always compression and bending stresses Supports have vertical reactions and horizontal actions Generally, loads acting on an arch force it to spread out

For an object to be in equilibrium it must

Have no unbalanced force acting on it (aka: it can't move!) • Have no unbalanced moment acting on it (aka: it can't rotate!)

Historic Preservation efforts include upgrades to building structure to protect the building from seismic and wind forces

Historic buildings are especially vulnerable to seismic/wind forces as they have not been designed and constructed to absorb swaying ground motions...can have major structural damage, or outright collapse •More and more communities are beginning to adopt stringent requirements for seismic retrofit of existing buildings. •Although historic and other older buildings can be retrofitted to survive earthquakes, many retrofit practices damage or destroy the very features that make such buildings significant. •Life-safety issues are foremost and there are various approaches which can save historic buildings both from the devastation caused by earthquakes and from the damage inflicted by well-intentioned but insensitive retrofit procedures.

Three important preservation principles should be kept in mind when undertaking seismic retrofit projects:

Historic materials should be preserved and retained to the greatest extent possible and not replaced wholesale in the process of seismic strengthening • New seismic retrofit systems, whether hidden or exposed, should respect the character and integrity of the historic building and be visually compatible with it in design • Seismic work should be "reversible" to the greatest extent possible to allow removal for future use of improved systems and traditional repair of remaining historic materials.

The centrioid of an area is equal to the center of gravity of the area

If a load acts through something's center of gravity, then it has no tendency to rotate, but will translate in the direction of the applied force

Rigid Fames

In rigid frame construction vertical and horizontal members work as a single structural unit • Efficient because three members resist vertical and lateral loads together • Beam are restrained by columns and becomes more rigid to vertical bending forces • Columns resist lateral forces as they are tied together by beam • With single concentrated load, cable assumes shape of two straight lines (not counting the intermediate sag due to the weight of cable) • Since rigid frames only resist loads in tension, instability due to wind must be stabilized or stiffened with heavy infill material (eg: cables attached to ground)

Beam & Girder system

Large girders carry intermediate beams which support a slab with spans of 15'-30' • Easy to form and construct making it economical • Slabs can be penetrated (unlike PT slabs that have tendons)

Two Way Concrete Joist system

Like One Way Joist but with beams in each direction • Typically used in rectangular bays where distance between columns is equal (or close to) in both directions

Drop panel system

Like a Flat Plate system, but the slab thickness is increased around the columns for greater shear failure resistance. • Used with greater live loads or larger spans.

Modulus of Elasticity

Materials want to put off reaching ultimate strength as long as they can, and the resistance is measured by the Modulus of Elasticity. Resistance, or the Modulus of Elasticity (E) is therefore a ratio of the stress acting on the member (f) to the amount of strain (ε ) (E = f/ε) To make things easier for the designer, the building code lists typical Modulus of Elasticity values for most materials. A more common calculation designers must solve is finding the total deformation of the member (e). It is a ratio of the force (P) and Length (L) to the Area (A) and Modulus of Elasticity (E) (e = PL/AE)

Modulus of Elasticity Reaction

Modulus of Elasticity: a material's resistance to non permanent (or elastic) deformation • Reaction: the force acting at the supports of a beam that holds it in equilibrium

Finding Equilibrium

Objects that are at rest are at static equilibrium

yield point

Once the elastic limit is reached, the material which change length at a faster ratio than the applied force until it gets to the yield point. The yield point is when the material continues to deform with little to no load applied. It's the point of no return...because after that the material will rupture once it hits its ultimate strength

Single Wythe Masonry Walls

One unit thick • Non structural wythe of brick is called veneer • No requirements for reinforcing or grouting and rely on a substrate for support

Post Beam Simple Beam Cantilever Beam Overhang Beam Fixed End Beam

Post: long, sturdy piece of timber or metal set upright in the ground used to support • Beam: a member that supports loads perpendicularly to its longitudinal axis • Simple Beam: rests on a support at each end and ends are free to rotate • Cantilever Beam: supported at one end and restrained from rotation at that end • Overhanging Beam: rests on 2+ supports and has one or both ends cantilevered beyond the support • Fixed End Beam: fixed against rotation at both ends

implication of preengineered metal

Pre-Engineered Metal: standardized metal components are engineered to maximize use of the material's structural properties and includes structure, metal roof, and metal wall panels (or tilt-up concrete panels) • Use without modifying standard design • It's actually pretty difficult to modify as structure is designed close to max limit • Light Gauge system with 20 - 30 year life span • The least expensive way to quickly enclose a large area

implications of precast concrete

Precast Concrete: cast offsite and trucked in and installed with a crane • Subject to wide price swings depending on how it's used • Can be an expensive solution • Prices are competitive with other systems when there are numerous pieces of the same size/shape • Formwork is one of the most expensive components • Can save time as it is prefab and can be erected quickly • Don't have to worry about fire proofing

One Way Concrete Joist system (pan joists

Prefab metal pan forms are used to create frame to support light/medium loads with spans of 20' - 30' and depths of 1' - 2' • Formed with prefab metal pan forms spaced 24" - 36" apart in one direction

Singe tee/double tee system

Prestressed ribs (one or two) with a 2" topping slab connected. • Typically used for larger spans

Selecting a Structural System

Primary consideration is resistance to loads • Anticipated loads are calculated given the known weights of materials, equipment, other dead loads, and requirements of international and local building code (the most stringent of which applies) • Unanticipated loads like changes in use, snow, ponding of water, degradation of the structure must also be considered • Building use and function is a major consideration • What's the occupancy type (wouldn't use the same system for a parking garage and a school) • Client's programmatic needs (hospital surgery needs major mechanical systems above ceiling and below ICU on floor above)

Resilience Ductility

Resilience: ability of material to absorb energy while undergoing elastic range stresses • Ductility: ability of a material to absorb energy prior to fracture...toughness!

Purpose of structural design

Resolution of the conflict between the vertical direction of most load forces and the horizontal dynamics of mankind (eg: gravity and the way we work) Structure is a 3-D art form, like sculpture, but it exists with a purpose • Most structural failures are during construction All structures will be destroyed eventually • Many structural failures are caused by improper load assumptions. • Most concerning types of stress in building design and construction are tension, compression and shear

Waffle slab

Ribs formed with reusable prefab metal/fiberglass forms and span up to 40' • Provides the largest spans of conventional concrete floor systems

Sections

Sections are just that...a slice of a member where forces can be examined further

Air Supported Structures

Simplest form, single membrane anchored continuously at ground level, inflated, and stabilized with cables over the top of the membrane. • Only resist loads in tension and are held in place with constant air pressure that is greater than the outside air pressure • The double skin inflatable structure is created by inflation of a series of voids

Spread footing wall footing column footing strap/cantilever footing mat foundation

Spread Footing: Most economical...$ method. • Delivers load directly to soil over a large area • Area of the footing = load/safe bearing capacity. • Wall Footings" Most common method • Under a continuous foundation wall that supports a bearing wall • Column Footing: one footing supports one column • Combined Footing: when 2+ columns are too close to each other or a property line for separate footings, one footing is poured for them all • Strap/Cantilever Footing: like a combined footing, but columns are far apart • Mat Foundations: Very expensive...$$$ method. • Typically it's only used when the strata is weak, • It acts as one continuous foundation.

Stabilization Counterfots Critical net section Connectors Spacing End Distance Edge Distance

Stabilization: retrofitting of platforms/foundations as building for the purpose of improving the bearing capacity of the supported building. • Counterforts: reinforced concrete webs act as diagonal braces • Critical net section: section where the most wood has been removed • Connectors Spacing: the distance between centers of connectors, the minimum of which is typically given in building codes • End distance: distance measured parallel to the grain from the center of connector to square cut end of member • Edge distance: distance from edge of member to center of connector closest to it

Ultimate strength of common materials used in building

Steel = 58,000 - 80,000 psi Concrete = 3,000 - 6,000 psi (higher strengths possible) Wood =2,000 - 8,000 psi

implication of steel

Steel: beams, columns, floors and roof decks (concrete poured over decking as a structural part of the floor system) • More economical framing system than concrete • Takes less time than concrete to fabricate and erect • More economical when spanning open spaces • Durable • Must be fireproofed

elastic limit

Strain is proportional to the amount of stress applied...but only up to a certain point, which depends on the type of material. that point is called the elastic limit. Once the elastic limit is reached, the material which change length at a faster ratio than the applied force until it gets to the yield point.

Strain Shear Moment

Strain: the deformation of a material caused by external loads. Tensile loads stretch, and compressive loads shorten. • Shear: a strain produced by pressure in the structure when its layers are lateral shifted in relation to each other. Shear force acts parallel to area resisting force Moment: the tendency of a force to cause rotation about a given point or axis

Stress (f) Unit Stress Allowable Stress Factor of Safety

Stress (f): the resistance of a body to a load (also called an internal force) and measured in kips (K) • Unit Stress: stress/unit of area at the section, measured in psi or ksi (kips/sq.in.) • Allowable Stress: maximum permissible unit stress • Factor of Safety: ratio of the ultimate strength of material to its working stress

Strain

Stressed members can't always resist external forces. Strain is the change in size, aka deformation, of a member caused by the forces acting on it. The amount of strain in a unit (ε ) is actually a ratio of the total deformation (e) to the original length of the member (L) (ε = e/L)

Stresses are compression, tension or shear

Stresses can be compression (shorten or crush the member), tension (stretch the member), or shear (two members slide past each other) The amount of stress (f) is calculated by taking all of the force that is touching the material (P) and dividing it by the area that it touches (A) (f = P/A)

Masonry

System has high compressive strength and is weak in tension and bending. • Advantages include strength, flexibility, appearance, fire resistance, sound insulation, doesn't weather (much), and can be used as a thermal mass for passive solar energy • Horizontal joints are reinforced at 16" o.c. to strengthen walls and control cracking. • Joints tie multi-wythe walls together and anchor veneer facing to structural backup wall

line of action

The line of action is parallel to and in line with the force. • If lines of action of several forces pass through a common point, forces are concurrent • If the lines of action don't pass through a common point, the forces are nonconcurrent• The point is called the center of moments or axis of rotation and the distance, called the moment arm or lever arm, is measured in a direction perpendicular to the line of action of the force

Center of Gravity

The point at which the mass of a member is concentrated is called the center of gravity. The actual point at the center of gravity that measurements are taken from is called the centroid. While the centroid is the center, it is not necessarily at the geometric center of the section. Only when a section is symmetrical (a rectangle beam for example) the center is located in the geometric center. Calculating the centroid of a symmetrical object is a simple problem. In the case of a rectangle with base (b) and depth (d) the centroid is at b/2 and/or d/2

solving for equilibrium

The reactions are usually located at each end of a member...lets say a beam. Select one of the Reactions, and use the given forces and dimensions from that reaction point. R1 = P1(L) + P2(L) - R2(L) Then solve for the other reaction by checking equilibrium. All upward forces equal all downward forces. R2 = R1 - P1 - P2

The statical moment of an area with respect to an axis is defined as

The statical moment of an area with respect to an axis is defined as the area multiplied by the perpendicular distance from the centroid of the area to the axis.

The three conditions of equilibrium may be stated as follows

The summation of all the horizontal forces acting on the body must equal zero. • The summation of all the vertical forces acting on the body must equal zero. " • The summation of all the moments acting on the body must equal zero

St. Venant's Principle for Direct Stress 9 assumptions

The thing being loaded must be perfectly straight • Load must be applied axially (ie: the center of gravity at the cross section) • Cross section of the thing being loaded must be constant • Cross section under investigation has to be some distance away from the support/loaded ends • Loaded member must be made of a single material • Material must be homogenous (and strong, no soft spots!) • Load must be statically loaded • Elastic range stresses (don't go past yield stress!) • Loading must be pure tension, compression, or shear (no secondary effects)

Three hinged arches

Three hinged arches have an additional hinged connection at apex which makes structure statically determinate (two hinged/fixed arches are statically indeterminate)

A steel building weighs less than a concrete/masonry building of the same parameter what are lbs/sf for timber, steel, conc/masonry, and light loads/pneumatic

Timber = 7-10 lbs/sf typical construction weight/floor • Steel= 15-20 lbs/sf typical construction weight/floor • Concrete/Masonry=150-200 lbs/sf typical construction weight/floor • Light loads/Pneumatic = lightest system, but must deal with wind

Forces (or Loads) on Architectural Structures: vertical loads

Vertical forces are comprised of: • Dead loads : Live Loads • Static : Dynamic • Concentrated: Distributed • Vertical loads are mostly caused by gravity • People (which are both static and dynamic) • Moveable equipment • Vehicles • Rain, Snow, Drifting Snow • Ponding • Buoyancy • Construction Materials (bricks, stockpile, materials, etc) • Dead loads are permanently fixed in a structure, and easier to predict • Live loads move around on their own, or can be moved, and cause vibration. • They are hard to predict and require a higher safety precaution • Produce changing deformations, and are either: • Dynamic: the load changes with respect to time, often suddenly (eg: earthquakes, wind) • Static: the load moves with building accumulation, slowly. • Example: walking in a classroom is static, siting in a chair is dynamic

Forces (or Loads) on Architectural Structures: Materials and Systems:

What do we require of a structural material and of a structural system: • Strength = resist the three stresses (tension, compression, shear) • Tension: the most efficient system we do Primary deformation=elongation (e) Failure mode = tearing • Compression: Primary deformation =" shortening Failure mode"" = " crushing (strength related) buckling (stiffness related) Cross section will bulge • Shear: Primary deformation "= " change in angle Failure mode "" = " torsion • (also Bending: Primary deformation "= " deflection) • Stiffness = resist deformation • Elastic response is temporary • Ineleastic response is permanent • Want deformation to be: • predictable: calculate what happened • small: high resistance • temporary: go away when the load is off • Stability • Durability

moment.

When force is applied to a member, it will try to cause the member to rotate around a point. This called the moment. If the force causes a clockwise rotation, then the moment is positive. If the force causes a counter-clockwise rotation, then the moment is negative. If a member doesn't rotate, then it means that the positive moments applied to it are equal to the negative moments. This is called equilibrium and is calculated by finding the reactions

When selecting a system, it often comes down to

When selecting a system, it often comes down to Time and Money when choosing what will be appropriate. The owner's budget and schedule must be considered as well as the seismic design requirements and conditions • Getting a contractor on board early to help in the selection process will help. Cost Implications vary depending on the type of building, location, and economy

statistical moment

When the section is unsymetrical, the statistical moment is calculated with respect to a neutral axis (typically at the base of the section). It is the area (A) times the distance to center from the neutral axis (X) Divide the section into multiple simple shapes (typically rectangles) and find the area (A) of each, and the distance from the centroid of the simple shape to the neutral axis (x). Do this for each simple shape. Multiply the areas and the distances together for each shape, and add them together. (A1 x D1) + (A2 x D2) = ([A1 + A2] x overall distance to neutral axis X) . Then solve for X. That's the overall centroid.

Moment of Inertia

While the modulus of elasticity measures how stiff a material is (through how it resists stress), the measure of bending stiffness of a section is called the Moment of Inertia.

Plank/ Beam/Framing Width Spacing Spans Top/Bottom Use Adv

Width: 4" or 6" Spacing: 4' or 6' or 8' Spans: 10'-20' Top/Bottom: Wood decking span between beams, underside finish ceiling Use: Between girders or bearing walls, residential Adv: Easy to insulate

Box Beam Width Spacing Spans Top/Bottom Use Adv

Width: up to 30" Spacing: varies Spans: 50' Top/Bottom: Plywood panels glued & nailed to 2x4 Use: Residential, Commercial, Public Adv: Looks like solid timber, custom made

Truss Width Spacing Spans Top/Bottom Use Adv

Width: varies Spacing: 24" oc Spans: 24-40' Top/Bottom: 12 - 36" depth made of strand wood members connected with plates Use: Residential, Commercial, Public Adv: MEP can pass thru

implication of wood

Wood: wood columns, beams, and framing floors, roofs and walls • Smaller commercial or residential Economical up to 3 stories Inexpensive for non-fire resistive construction

Forces (or Loads) on Architectural Structures: Internal Forces

cause secondary stresses which can be greater than primary stresses • The result of system or material characteristics • Movements (if resisted) are elastic (temporary) or inelastic (permanent) strains. • Shrinkage: some takes place early (eg: concrete) • Humidity Changes (eg: wood) • Thermal Changes (eg: steel, metal, thin shell) • Fabrication Errors (eg: incomplete concrete pour) • Prestressing (they're all the same

Forces (or Loads) on Architectural External (applied) loads:

causes primary stresses. Horizontal forces are comprised of: • Forces with horizontal components (SEE: LATERAL FORCES) • Wind: hurricanes, tornados (no warning or unpredicted) • Ice: Expansion force (as it freezes), footings below frost lines • Earthquakes: (the biggest concern, and hardest to design for, the best we can do is have good warning systems) Effects of earthquakes are: • ground rupture (in the fault zone) • ground failure (sliding, settlement, liquefaction) • tsunami (seismic sea waves, called a "seich" on inland bodies of water) • ground shaking (vibration, repetitive dynamic motion) • People: pushing on a window, balcony, etc • Vehicles: impact loads (collisions), sudden starts and stops • Machinery: generators, oscillating equipment, vibration of equipment • Earth or Water: pressure on below grade structure • Transportation and Erection: (in transport to site and put in place) • Lighting: powerful • Blast: explosions

Purpose of structures in the built environment

connect two points (eg: bridge) • withstand natural forces (eg: dam) span and enclose space (eg: building)

Truss

framework consisting of rafters, posts, and struts

Precast structural members

high-strength steel cables are pre-stressed/stretched and concrete is poured on top. When concrete reaches minimum allowable strength cables are cut from formwork and compressive stresses are transferred to concrete that resists tension forces of own weight/live load

Section Modulus

is the ratio of a cross section's second moment of area to the distance of the extreme compressive fibre from the neutral axis

Pile Foundations

used when soil is unsuitable for spread footings (e.g.: expansive soils or clay near surface) by transmitting loads through soil to a more secure bearing farther below • Located in groups or in alignment under a bearing wall • Load transferred from wall to pile caps. • Piles are either driven (timber, steel, precast conc) or drilled (caissons) Belled Caissons: holes are drilled to firm strata and concrete poured. • They're basically really, really deep spread footings"

Charpy V-Notch Test

• A ductility test where a piece of material has a v-notch cut into the to top • Tests how much energy it takes to make the notch go through the whole piece • If it breaks quickly with not much energy, then the material is brittle • If it breaks slowly and takes a lot of energy, then it is ductile

Force Collinear forces Concurrent forces Non concurrent forces

• Force: the push or pull exerted on an object, including its magnitude, direction, and point of application • Collinear forces: vectors lie along the same straight line • Concurrent forces: lines of action meeting at common point • Non concurrent forces: lines of action do not pass through a common point

Steel , beam and girder spans

• Most commonly used structural material due to its high strength, availability, adaptability, ductility (can deform and return to original shape/bends before it breaks) • Suited for multi-floor construction due to strength and structural continuity • Beams span shorter distances of 8' - 10' • Girders span longer distances of 25' - 40

wood Connections are typically designed for 10 year loading duration, PLUS any of the given factors:

• Permanent Loading beyond 10 years = + 0.90 • Snow Loading (2 month duration) = + 1.15 • 7 day duration = + 1.25 • Wind or earthquake = + 1.60 • Impact loads = + 2.00