List of Symbol Definitions

Transcription

1 List o Symbol Deinitions a long dimension or a section subjected to torsion (in, mm); acceleration due to gravity, t/sec 2, 9.81 m/sec 2 ; unit area (in 2, t 2, mm 2, m 2 ); distance used in beam ormulas (t, m); depth o the eective compression block in a concrete beam (in, mm) a area bounded by the centerline o a thin walled section subjected to torsion (in 2, mm 2 ) A area, oten cross-sectional (in 2, t 2, mm 2, m 2 ) A e net eective area, equal to the total area ignoring any holes and modiied by the lag actor, U, (in 2, t 2, mm 2, m 2 ) (see A net ) A g gross area, equal to the total area ignoring any holes (in 2, t 2, mm 2, m 2 ) A gv gross area subjected to shear or block shear rupture (in 2, t 2, mm 2, m 2 ) A net net eective area, equal to the gross area subtracting any holes (in 2, t 2, mm 2, m 2 ) (see A e ) A nt net area subjected to tension or block shear rupture (in 2, t 2, mm 2, m 2 ) A nv net area subjected to shear or block shear rupture (in 2, t 2, mm 2, m 2 ) A p bearing area (in 2, t 2, mm 2, m 2 ) A throat area across the throat o a weld (in 2, t 2, mm 2, m 2 ) A s area o steel reinorcement in concrete beam design (in 2, t 2, mm 2, m 2 ) A s area o compression steel reinorcement in concrete beam design (in 2, t 2, mm 2, m 2 ) A v area o concrete shear stirrup reinorcement (in 2, t 2, mm 2, m 2 ) A web web area in a steel beam equal to the depth x web thickness (in 2, t 2, mm 2, m 2 ) A 1 area o column in spread ooting design ((in 2, t 2, mm 2, m 2 ) A 2 projected bearing area o column load in spread ooting design ((in 2, t 2, mm 2, m 2 ) ASD b b E b Allowable Stress Design width, oten cross-sectional (in, t, mm, m); narrow dimension or a section subjected to torsion (in, mm); number o truss members; rectangular column dimension in concrete ooting design (in, mm, m); distance used in beam ormulas (t, m) eective width o the lange o a concrete T beam cross section (in, mm) width o the lange o a steel or concrete T beam cross section (in, mm) b o perimeter length or two-way shear in concrete ooting design (in, t, mm, m) b w B B 1 B s width o the stem o a concrete T beam cross section (in, mm) spread ooting dimension in concrete design (t, m); dimension o a steel base plate or concrete ooting design (in, mm, m) actor or determining M u or combined bending and compression width within the longer dimension o a rectangular spread ooting that reinorcement must be concentrated within or concrete design (t, m) 1

2 c c i c o c 1 c 2 distance rom the neutral axis to the top or bottom edge o a beam (in, mm, m); rectangular column dimension in concrete ooting design (in, mm, m) distance rom the center o a circular shape to the inner surace under torsional shear strain (in, mm, m) distance rom the center o a circular shape to the outer surace under torsional shear strain (in, mm, m) coeicient or shear stress or a rectangular bar in torsion coeicient or shear twist or a rectangular bar in torsion CL,q center line C C b C c C D C D C F C C u C F C H C i C L C m C M C p C r C v C V C s C t d compression label; compression orce (lb, kips, N, kn); dimension o a steel base plate or concrete ooting design (in, mm, m) modiication actor or LRFD steel beam design column slenderness classiication constant or steel column design; compressive orce in the concrete o a doubly reinorced concrete beam (lb, k, N, KN) load duration actor or wood design size actor or wood design orm actor or circular sections or or square sections loaded in plane o diagonal or wood design lat use actor or wood design size actor or wood design shear stress actor or wood design incising actor or wood design beam stability actor or wood design modiication actor or combined stress in steel design wet service actor or wood design column stability actor or wood design repetitive member actor or wood design web shear coeicient or steel design glulam volume actor or wood design compressive orce in the compression steel o a doubly reinorced concrete beam (lb, k, N, KN) temperature actor or wood design diameter o a circle (in, mm, m); depth, oten cross-sectional (in, mm, m); perpendicular distance rom a orce to a point in a moment calculation (in, mm, m); critical cross section dimension o a rectangular timber column cross section related to the proile (axis) or buckling (in, mm, m); eective depth rom the top o a reinorced concrete beam to the centroid o the tensile steel 2

3 (in, mm); symbol in calculus to represent a very small change (like the greek letters or d, see & ) d eective depth rom the top o a reinorced concrete beam to the centroid o the compression steel (in, mm) d b d d x d y D DL e E E c E s a b c c cr m m p depth o a steel W beam section (in, mm); bar diameter o concrete reinorcement (in, mm) nominal bolt diameter (in, mm) depth o a steel W column lange (in, mm) dierence in the x direction between an area centroid and the centroid o the composite shape (in, mm) dierence in the y direction between an area centroid and the centroid o the composite shape (in, mm) diameter o a circle (in, mm, m); dead load or LRFD design dead load dimensional change to determine strain (see s or ) (in, mm); eccentric distance o application o a orce (P) rom the centroid o a cross section (in, mm) modulus o elasticity (psi; ksi, kpa, MPa, GPa); earthquake load or LRFD design modulus o elasticity o concrete (psi; ksi, kpa, MPa, GPa) modulus o elasticity o steel (psi; ksi, kpa, MPa, GPa) symbol or stress (psi, ksi, kpa, MPa) symbol or unction with respect to some variable; ie. (t) calculated axial stress (psi, ksi, kpa, MPa) calculated bending stress (psi, ksi, kpa, MPa) calculated compressive stress (psi, ksi, kpa, MPa) concrete design compressive stress (psi, ksi, kpa, MPa) calculated column stress based on the critical column load P cr (psi, ksi, kpa, MPa) calculated compressive stress in masonry (psi, ksi, kpa, MPa) masonry design compressive stress (psi, ksi, kpa, MPa) calculated bearing stress (psi, ksi, kpa, MPa) s t x v y calculated steel stress or reinorced masonry (psi, ksi, kpa, MPa) calculated tensile stress (psi, ksi, kpa, MPa) combined stress in the direction o the major axis o a column (psi, ksi, kpa, MPa) calculated shearing stress (psi, ksi, kpa, MPa) yield stress (psi, ksi, kpa, MPa) 3

4 F F a F b F b F c F c F connector orce (lb, kip, N, kn); capacity o a nail in shear (lb, kip, N, kn); hydraulic luid load or LRFD design allowable axial stress (psi, ksi, kpa, MPa) allowable bending stress (psi, ksi, kpa, MPa) allowable bending stress or combined stress or wood design (psi, ksi, kpa, MPa) allowable compressive stress (psi, ksi, kpa, MPa); critical unactored compressive stress or LRFD steel design allowable compressive stress perpendicular to the wood grain (psi, ksi, kpa, MPa) resistance capacity o a connector (lb, kips, N, kn) F ce intermediate compressive stress or ASD wood column design dependant on material (psi, ksi, kpa, MPa) F cr F c lexural buckling (column) stress in ASD and LRFD (psi, ksi, kpa, MPa) allowable compressive stress or ASD wood column design (psi, ksi, kpa, MPa) * F c intermediate compressive stress or ASD wood column design dependant on load duration (psi, ksi, kpa, MPa) F e F h F horizontal-resist F n F p F sliding F t F v F x F w F y F u F.S. elastic critical buckling stress is steel design orce component in the horizontal direction (lb, kip, N, kn) resultant rictional orce resisting sliding in a ooting or retaining wall (lb, kip, N, kn) nominal strength in LRFD steel design (psi, ksi, kpa, MPa) nominal tension or shear strength o a bolt (psi, ksi, kpa, MPa) allowable bearing stress parallel to the wood grain (psi, ksi, kpa, MPa) resultant orce causing sliding in a ooting or retaining wall (lb, kip, N, kn) allowable tensile stress (psi, ksi, kpa, MPa) allowable shear stress (psi, ksi, kpa, MPa); allowable shear stress in a welded connection; orce component in the vertical direction (lb, kip, N, kn) orce component in the x coordinate direction (lb, kip, N, kn) allowable weld stress (psi, ksi, kpa, MPa) orce component in the y coordinate direction (lb, kip, N, kn); yield stress (psi, ksi, kpa, MPa) ultimate stress a material can sustain prior to ailure (psi, ksi, kpa, MPa) actor o saety (also see SF) g acceleration due to gravity, t/sec 2, m/sec 2 ; transverse center-to-center spacing (gage) between astener gage lines (in, mm,) G h shear modulus (psi; ksi, kpa, MPa, GPa); relative stiness o columns to beams in a rigid connection (see ) depth, oten cross-sectional (in, t, mm, m); height (in, t, mm, m); 4

5 sag o a cable structure (t, m); eective height o a wall or column (see e ) h eective height o a wall or column (see e ) h c height o the web in a W section (in, t, mm, m) (also see t w ) h H H A depth o a lange in a T section (in, t, mm, m); height o a concrete spread ooting (in, t, mm, m) hydraulic soil load or LRFD design horizontal load rom active soil or water pressure (lb, k, N, kn) I moment o inertia (in 4, mm 4, m 4 ) I moment o inertia about the centroid (in 4, mm 4, m 4 ) ) Î moment o inertia about the centroid o a composite shape (in 4, mm 4, m 4 ) I c moment o inertia about the centroid o a composite shape (in 4, mm 4, m 4 ) I min minimum moment o inertia o I x and I y (in 4, mm 4, m 4 ) I o moment o inertia about the centroid (in 4, mm 4, m 4 ) I transormed moment o inertia o a multi-material section transormed to one material (in 4, mm 4, m 4 ) I x moment o inertia with respect to an x-axis (in 4, mm 4, m 4 ) I y moment o inertia with respect to a y-axis (in 4, mm 4, m 4 ) j multiplier by eective depth o masonry section or moment arm, jd (see d) J, J o polar moment o inertia (in 4, mm 4, m 4 ) k kg kl kips (1000 lb); shape actor or steel beams, M p /M y : eective length actor or columns (also K); distance rom outer ace o W lange to the web toe o illet (in, mm); multiplier by eective depth o masonry section or neutral axis, kd kilograms kips per linear oot kn kilonewtons (10 3 N) kpa K K ce kilopascals (10 3 Pa) eective length actor with respect to column end conditions; masonry mortar strength designation material actor or wood column design length (in, t, mm, m); cable span (t, m) d development length o concrete reinorcement (in, t, mm, m) dc development length o compression reinorcement in concrete ooting design (in, t, mm, m) l dh development length or hooks (in, t, mm, m) e eective length that can buckle or wood column design (in, t, mm, m) 5

6 n eective clear span or concrete one-way slab design (t, m) lb L pound orce length (in, t, mm, m); live load or LRFD design; spread ooting dimension in concrete design (t, m) L b unbraced length o a steel beam in LRFD design (t, m) L c maximum unbraced length o a steel beam in ASD design or compression buckling limit (t, m); clear distance between the edge o a hole and edge o next hole or edge o the connected steel plate (in, t, mm, m) L d development length o reinorcement in concrete (t, m) L e eective length that can buckle or column design (t, m) L m projected length or bending in concrete ooting design (t, m) L p limiting length o a steel beam in LRFD design or ull plastic strength (t, m) L r roo live load in LRFD design; limiting length o a steel beam in LRFD design or inelastic lateral-torsional buckling (t, m) L u maximum unbraced length o a steel beam in ASD design or stress limit o 0.6F y L length o the one-way shear area in concrete ooting design (t, m) LL live load LRFD Load and Resistance Factor Design m mm M M a mass (lb-mass, g, kg); meters millimeters moment o a orce or couple (lb-t, kip-t, N-m, kn-m); bending moment (lb-t, kip-t, N-m, kn-m); masonry mortar strength designation required bending moment in steel ASD beam design (uniied) (lb-t, kip-t, N-m, kn-m) M A moment value at quarter point o unbraced beam length or LRFD beam design (lb-t, kip-t, N- m, kn-m) M B M c M C M m M n nominal moment capacity o a reinorced concrete beam at the balanced steel ratio ( b ) or limiting strains in both concrete and steel (lb-t, kip-t, N-m, kn-m) moment value at hal point o unbraced beam length or LRFD beam design (lb-t, kip-t, N-m, kn-m) nominal moment capacity o a reinorced concrete beam based on compression orce in a concrete section (lb-t, kip-t, N-m, kn-m) (also see M n ) moment value at three quarter point o unbraced beam length or LRFD beam design (lb-t, kipt, N-m, kn-m) moment capacity o a reinorced masonry beam (lb-t, kip-t, N-m, kn-m) nominal moment capacity o a reinorced concrete beam based on steel yielding and concrete design strength (lb-t, kip-t, N-m, kn-m) 6

7 M overturning resulting moment rom all orces on a ooting or retaining wall causing overturning (lb-t, kip-t, N-m, kn-m) M p M r M resis M t M u M ult M y n n.a. N o.c. O p internal bending moment when all ibers in a cross section reach the yield stress (lb-t, kip-t, N-m, kn-m) (also see M ult ) required nominal moment capacity based on design moment or reinorced concrete (lb-t, kipt, N-m, kn-m) (also see M n ) resulting moment rom all orces on a ooting or retaining wall resisting overturning (lb-t, kipt, N-m, kn-m) nominal moment capacity o a reinorced concrete beam based on tensile orce in the steel reinorcement (lb-t, kip-t, N-m, kn-m) (also see M n ) actored moment calculated in concrete design rom load actors (lb-t, kip-t, N-m, kn-m) internal bending moment when all ibers in a cross section reach the yield stress (lb-t, kip-t, N-m, kn-m) (also see M p ) internal bending moment when the extreme ibers in a cross section reach the yield stress (lb-t, kip-t, N-m, kn-m) number o truss joints, nails or bolts; modulus o elasticity transormation coeicient rom steel to concrete neutral axis (axis connecting beam cross-section centroids) Newtons; bearing-type connection with bolt threads included in shear plane; normal load (lb, kip, N, kn); bearing length on a wide lange steel section (in, mm) masonry mortar strength designation on-center point o origin; masonry mortar strength designation pitch o nail or bolt spacing (in, mm) (also see s); pressure (lb/in 2, lb/t 2, kip/in 2, kip/t 2, Pa, MPa); reinorcement ratio in concrete beam design = A s /bd (or possibly A s /bt, A s /bh) (no units) (see ) p A active soil pressure (lb/t 3, kn/m 3 ) p b balanced reinorcement ratio in concrete beam design (see b ) pl P P a P c P cr P e1 P n P o pounds per linear oot orce, concentrated (point) load (lb, kip, N, kn) required axial orce in ASD steel design (uniied) (lb, kip, N, kn) available axial strength or steel uniied design (lb, kip, N, kn) critical (ailure) load in column calculations (lb, kip, N, kn) Euler buckling strength in steel uniied design (lb, kip, N, kn) maximum column load capacity in LRFD steel and concrete design (lb, kip, N, kn) maximum axial orce with no concurrent bending moment in a reinorced concrete column (lb, kip, N, kn) 7

8 P r P u required axial orce in steel uniied design (lb, kip, N, kn) actored column load calculated rom load actors in LRFD steel and concrete design (lb, kip, N, kn) Pa Pascals (N/m 2 ) q shear low (lb/in, kips/t, N/m, kn/m) q allowed allowable soil bearing pressure (lb/t 2, kips/t 2, N/m 2, Pa, MPa) q net q u net allowed soil bearing pressure (lb/t 2, kips/t 2, N/m, Pa, MPa) actored soil bearing pressure in concrete design rom load actors (lb/t 2, kips/t 2, N/m, Pa, MPa) Q irst moment area used in shearing stress calculations (in 3, mm 3, m 3 ) Q connected irst moment area used in shear calculations or built-up beams (in 3, mm 3, m 3 ) Q x irst moment area about an x axis (using y distances) (in 3, mm 3, m 3 ) Q y irst moment area about an y axis (using x distances) (in 3, mm 3, m 3 ) r radius o a circle (in, mm, m); radius o gyration (in, mm, m) r o polar radius o gyration (in, mm, m) r x radius o gyration with respect to an x-axis (in, mm, m) r y radius o gyration with respect to a y-axis (in, mm, m) R orce, reaction or resultant (lb, kip, N, kn); radius o curvature o a beam (t, m); rainwater or ice load or LRFD design R a required strength (ASD-uniied) (also see V a, M a ) R n R x R y s s.w. concrete beam design ratio = M u /bd 2 (lb/in 2, MPa) nominal value or LRFD design to be multiplied by (also see P n, M n ) nominal value or ASD design to be divided by the saety actor reaction or resultant component in the x coordinate direction (lb, kip, N, kn) reaction or resultant component in the y coordinate direction (lb, kip, N, kn) strain (change in length divided by length (no units); displacement with respect to time (t, m); length o a segment o a thin walled section (in, mm); pitch o nail spacing (in, mm) (also see p); spacing o stirrups in reinorced concrete beams (in, mm); longitudinal center-to-center spacing o any two consecutive holes (in, mm) sel-weight S section modulus (in 3, mm 3, m 3 ); snow load or LRFD design; allowable strength o a weld or a given size (lb/in, kips/in, N/mm, kn/m); masonry mortar strength designation S required section modulus required to not exceed allowable bending stress (in 3, mm 3, m 3 ) S x section modulus with respect to the x-centroidal axis (in 3, mm 3, m 3 ) 8

9 S y section modulus with respect to the y-centroidal axis (in 3, mm 3, m 3 ) SC SF S4S t slip critical bolted connection saety actor (also see F.S.) surace-our-sided thickness (in, mm, m); time (sec, hrs) t thickness o the lange o a steel beam cross section (in, mm, m) t w thickness o the web o a steel beam cross section (in, mm, m) T U U bs v V V a V c V n V s V u V u1 V u2 w tension label; tensile orce (lb, kip, N, kn); torque (lb-t, kip-t, N-m, kn-m); throat size o a weld (in, mm); eect o thermal load or LRFD design shear lag actor or bolted connections reduction coeicient or block shear rupture velocity (t/sec, m/sec, mi/h); shear orce per unit length (lb/t, k/t, N/m, kn/m) (see q) shear orce (lb, kip, N, kn) required shear in steel ASD design (uniied) (lb, kip, N, kn) shear orce capacity in concrete (lb, kip, N, kn) nominal shear orce capacity or concrete design (lb, kip, N, kn) shear orce capacity in steel (lb, kip, N, kn) actored shear calculated in concrete design rom load actors (lb, kip, N, kn) actored one-way shear calculated in concrete ooting design rom load actors (lb, kip, N, kn) actored two-way shear calculated in concrete ooting design rom load actors (lb, kip, N, kn) load per unit length on a beam (lb/t, kip/t, N/m, kn/m); load per unit area on a surace (lb/t 2, kip/t 2, N/m 2, kn/m 2 ): width dimension (in, t, mm, m) w c weight o reinorced concrete per unit volume (lb/t 3, N/m 3 ) w u W actored load per unit length on a beam rom load actors (lb/t, kip/t, N/m, kn/m); actored load per unit area on a surace rom load actors (lb/t 2, kip/t 2, N/m 2, kn/m 2 ) weight (lb, kip, N, kn); total load rom a uniorm distribution (lb, kip, N, kn); wind load or LRFD design x a distance in the x direction (in, t, mm, m) x xˆ the distance in the x direction rom a reerence axis to the centroid o a shape (in, mm) the distance in the x direction rom a reerence axis to the centroid o a composite shape (in, mm) 9

10 X y y ŷ bearing-type connection with bolt threads excluded rom shear plane a distance in the y direction (in, t, mm, m); distance rom the neutral axis to the y-level o a beam cross section (in, mm) the distance in the y direction rom a reerence axis to the centroid o a shape (in, mm) the distance in the y direction rom a reerence axis to the centroid o a composite shape (in, mm) z the distance rom a unit area to a reerence axis (in, t, mm, m) (also see d x and d y ) Z plastic section modulus o a steel beam (in 3, mm 3 ) lateral design value or a single astener in a timber connection (lb/nail, k/bolt) ' symbol or eet " symbol or inches # symbol or pounds = symbol or equal to c 1 symbol or approximately equal to symbol or proportional to symbol or less than or equal to symbol or integration coeicient o thermal expansion (/C, /F); angle, in a math equation (degrees, radians) angle, in a math equation (degrees, radians) ratio o long side to short side o the column in concrete ooting design coeicient to determine the stress block height in concrete beam design elongation (in, mm) (also see e) P s T elongation due to axial load (in, mm) shear deormation (in, mm) elongation due to change in temperature (in, mm) beam delection (in, mm); an increment LL beam delection due to live load (in, mm) max maximum calculated beam delection (in, mm) TL beam delection due to total load (in, mm) x beam delection in beam diagrams and ormulas (in, mm) T change in temperature (C, F) strain (also see s) t thermal strain 10

11 b c t v c diameter symbol; angle o twist (degrees, radians); resistance actor in LRFD steel design and reinorced concrete design resistance actor or lexure in LRFD design resistance actor or compression in LRFD design resistance actor or tension in LRFD design resistance actor or shear in LRFD design design constant or slenderness evaluation or steel columns in LRFD design Poisson s ratio; coeicient o static riction speciic gravity o a material (lb/in 3, lb/t 3, N/m 3,kN/m 3 ); angle, in a math equation (degrees, radians); shearing strain (no units); load actor in LRFD design D dead load actor in LRFD steel design L b g live load actor in LRFD steel design angle, in a trig equation (degrees, radians); slope o the delection o a beam at a point (degrees, radians) pi (180) radial distance (in, mm); radius o curvature in beam delection relationships (t, m); reinorcement ratio in concrete beam design = A s /bd (or possibly A s /bt, A s /bh) (no units) balanced reinorcement ratio in concrete beam design reinorcement ratio in concrete column design = A st /A g maximum reinorcement ratio allowed in concrete beam design or ductile behavior max c engineering symbol or normal stress (axial or bending) engineering symbol or shearing stress shearing stress capacity in concrete design (psi; ksi, kpa, MPa) load per unit length on a beam (lb/t, kip/t, N/m, kn/m) (see w); load per unit area (lb/t 2, kips/t 2, N/m 2, Pa, MPa) summation symbol saety actor or ASD o steel (uniied) relative stiness o columns to beams in a rigid connection (see G) 11