SS 02.13.11

Presented by John Schneider, Atlantic Engineering Services

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1. FORCES

TENSION:  elongation of a member

  • simplest force to evaluate (no other factors affect it)
  • lateral bracing (seismic/ wind) should rely on tension first

COMPRESSION: reduction in size of a member

  • buckling of a column is the simplest form of structural failure

SHEAR: slippage along a horizontal plane

  • example: (2) 2x4s loosely stacked will deflect half as much as a single 2×4 with the same applied load
  • these same (2) 2x4s will barely deflect at all if nailed together
    • nails act as shear connections, preventing the two planes from sliding past one another

MOMENT: desire for a member to rotate about a given point (measured in foot-pounds)

STRESS: internal resistance to externally-applied forces

STRAIN: deformation of a member under an applied force

  • unitless force, expressed in “inches per inch”
  • stiffness is resistance to strain

MODULUS of ELASTICITY: coefficient of elasticity of a material

  • STRESS divided by STRAIN
  • measured in pounds per square inch (PSI)

In a simply-supported beam, uniformly loaded, the top fiber is in COMPRESSION and the bottom fiber is in TENSION

  • a truly efficient beam section would be heavier at the top, lighter on the bottom (see illustration) –but a shape like this would be impossible to create in a steel mill

MOMENT of INERTIA: measure of stiffness

SECTION MODULUS: measure of bending stresses

  • Example: a bundle of spaghetti noodles, when bent, the bottom-most noodles will snap instantly

CENTROID: center of gravity of a member

  • always at the center of simple, symmetric sections (W shapes, I beams)
  • no stress at all at this point — transition from tension to compression

2. BEAMS

shear and moment diagrams are graphic representations of the forces acting upon a beam

the top fiber of a beam (in compression) is subject to buckling, just like a column

  • lateral bracing is required to resist buckling/ overturning
    • steel deck, welded to top flange of beams
    • cross-bracing between wood joists

composite construction (1970s)

  • steel shear studs are welded to the top flange of a beam
  • engage the concrete in compression, effectively enlarging the top flange of the beam(s)
  • allows for incredible savings in steel tonnage (and cost)

defelction under the weight of wet concrete (before curing) is usually what governs modern beam design

3. COLUMNS

buckling will occur along the WEAK AXIS — the weak axis needs to be braced to resist buckling

tubes are the most efficient column shape (symmetrical in both axes) but significantly more expensive than W-shapes

UNBRACED LENGTH: distance between braced points along a column

4. CONCRETE

steel is a HOMOGENEOUS material (the same in every direction)

  • usually used in ONE-WAY systems

wood is homogeneous but DIRECTIONAL (grain)

concrete is a NON-HOMOGENEOUS material

  • usually used in TWO-WAY systems
  • extremely strong in compression, weak in tension, reinforcing steel added to tension side of member
  • typical two-way system (FLAT PLATE) usually includes DROP PANELS at each column location to strengthen against PUNCHING SHEAR
  • concrete allows for reduced depth of structural framing, creating more efficient buildings (15 floors could fit in the same overall envelope, perhaps only 12 with steel)

CREEP: phenomenon in concrete construction; permanent deflection over time (usually due to air entrainment in the mix design)

  • lab casework example: 2 inches of deflection over a 32-foot span, during construction(!); none of this casework could be made to fit, self-leveling toppings were required to solve the problem

PRE-STRESSED versus POST-TENSIONED

PRE-STRESSED:  tension is introduced into the reinforcing steel

  • reinforcement contains DEFORMATIONS to promote bond with concrete
  • concrete is poured, allowed to cure, then tension is released
  • creates CAMBER in pre-cast members

POST-TENSIONED:  Ty Lynne, inventor, called it the “load-balancing method”

  • steel cables are draped through a sheath (to prevent bond with concrete)
  • concrete poured around sheath
  • hydraulic jack pulls anchored cables, introduces tension into the slab

5. STRUCTURAL STEEL

material strength

  • early ’80s: 36 ksi max (known as “A36 steel”)
  • mid ’80s: 50 ksi max (due to improved production methods)
  • seismic deisgn usually relies on the use of SACRIFICIAL MEMBERS
  • designed to yield first under excessive strain
  • A36 steel is usually specified for cross-bracing
  • A36 steel (lesser quality) is actually MORE EXPENSIVE than A50 or A60 steel (less abundant, more difficult to fabricate)

6. LATERAL FORCES

Bernouli’s principle – velocity is inversely proportioanl to pressure (shower curtain example)

  • wind passing around a building has increased velocity at the corners (creating a decrease in pressure)
  • this creates an increase in pressure across the building’s face (SUCTION)
  • structural engineers need to consider both areas separately in design (closer stud spacings, heavier guage materials, etc, at corners…)
  • similar to ballasted roof design principles (more ballast at corners, less at center of roof, etc)

Lateral bracing:

shear walls: masonry stair/ elevator shaft construction

braced frames: braces act in tension

  • cross bracing resists wind in both directions
  • eccentric bracing avoids doors and windows, etc

moment frames: heavier material, fully-welded (labor-intensive and expensive)

Example: Equitable and Del-Monte Buildings along North Shore

  • both very similar buildings (six stories, spec office space)
  • Equitable used a moment frame design
  • Del Monte used eccentric chevron braced frame design (concealed by masonry piers along face of building)
  • end result was Del Monte used ONE-THIRD of the steel that was used in Equitable (significant cost savings)

Building Code governs the design of buildings in a seismic area

  • IBC consolidated several other codes, incorporated UBC guidelines — intent is to keep a building standing during seismic activity
  • increase in mass near the top of a building is considered a code violation, for example (increases the moment arm of the building in a seismic event)
  • Northridge earthquake demonstrated vertical movement as well as horizontal (first recorded case — influenced future code requirements) (see handout page L6)
  • moment-frame connections are now welded top and bottom when designed for a seismic zone (MUCH more stringent/ complex than BOCA code requirements)

Why would seismic design be necessary in Pittsburgh?

  • subgrade conditions may be less than favorable (New Mexico earthquake resulted in “soil liquefaction”)
  • geotechnical report is used to detemine soli quaility
  • “Occupancy category” of building may require seismic design principles (see handout pages L7-L11)
  • Site Class definitions (see handout page L9) (code language states that “if you dont know, pick ‘D'”)
  • the component parts of the building also must comply (see handout page L11)
  • Class C requires ductwork, lighting, etc to be braced; Class D requires this in hospitals
  • example:  Morgantown, WV, office building originally required $500,000 worth of bracing for MEP items due to its occupancy class and the soil conditions
  • A SHEAR WAVE VELOCITY TEST (see handout page L10) eliminated this requirement (test costs about $8000)

7. LONG-SPAN STRUCTURES

MOMENT OF INERTIA means that a steel beam relies in the flanges being held apart by the web — the depth of the steel member increases its stiffness

Deeper the steel, the stiffer the member — Vierendeel trusses are full-story deep structural members

Deflection always governs in the design of long-span structures

Trusses are analyzed using the “method of joints” — summation of moments about the same point (basic statics)

  • sum of all forces must equal zero
  • all forces act axially (along the web members)
  • all forces can be broken into simpler force vectors using trigonometry
  • “magic” zero-force member — no forces acting upon it (may be used as a trick question on the exam)

PLATE GIRDERS are built-up shapes specially designed and fabricated to solve high-load situations (examples: Childrens’ Hospital, Mellon Client Services Center)

8. REVIEW OF SAMPLE QUESTIONS (see handout pages Q1-Q8)

  • Question 7: live-load reduction (based on the likelihood that a column will be fully-loaded at any given time) — NOT PERMITTED for roofs (due to snow load conditions)
  • Question 8: soil-bearing capacity (simple math)
  • Question 9: P-delta effect — loading on a column is not always concentric, which introduces moment into the column
  • Question 19: simplest seismic design would avoid re-entrant corners
  • Question 23: the column in question is seeing TWICE the amount of load as the exterior columns (due to its increased tributary area)
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