structural technology

FORMULAS TO REMEMBER

Area: [units = inch2]

Area of a Rectangle = b d Area of a Circle = r2 Area of a Triangle = 1 b h 2 Area of a Bolt, = d2 [where d = diameter] Cable, Tube, Bar 4 Equilibrium: M = 0; V = 0; H = 0

Force: {units = kips & pounds}

F = M [Force = Moment ] d distance RETAINING WALL DESIGN {units = kips & pounds}

F = w h2 [Force exerted on the = (fluid pressure provided) X (height)2] 2 Retaining Wall 2 Remember: pcf = psf [pounds per cubic feet = pounds per square foot] ft one foot width of wall SHEAR DIAGRAM SHEAR FORCE {units = kips & pounds}

R = V = w l [Shear Resisting Force= (uniform load per ft) X (distance)] 2 2 BEARING TYPE SHEAR CONNECTIONS {units = kips & pounds}

R = Fv Abolts [Resistance = (allow.shear stress) X (A of bolt cross sections. Remember to Shear Failure to multiply A by total # of bolts)]

Remember: Stress = P Therefore, P = Stress X Area A Moment: {units = (k ft); (lb ft); (k in); (lb in)} TAKING MOMENTS ABOUT A POINT TO FIND EQUILIBRIUM

M = Fd [Moment = force X distance] UNIFORM LOAD {units = (k ft); (lb ft); (lb in)} M = w L2 [Moment = uniform load X (length)2]

8 8

POINT/CONCENTRATED LOAD AT THE CENTER OF A MEMBER

M = P L [Moment = Point Load X length] 4 4

Remember: w l 2 + P L when Point & Uniform loads combine. 8 4

Watch out: There are various types of Point loads.

ECCENTRIC LOAD {units = (k ft); (lb ft); (lb in)}

M = Pe [Moment = force X eccentricity] {Same as M=Fd}

Section Modulus: [units = inch3] S = b d 2 in3 [Section Modulus] 6 S = M [Section Modulus = Moment in Inches Fb Bending Stress] Watch out: Both Moment & Stress should be in # or kips.

Remember: For a Roof Beam, S = M Fb X 1.25 S = I [Section Modulus = Moment of Inertia c (Just know this) (dist. from extreme fiber to nuetral axis)] Understand that S contains Moment of Inertia and c.

Moment of Inertia: [units = inch4] Remember: Moment of Inertia occurs by default about the Centroidal axis. I = b d 3 in4 [Moment of Inertia] 12 I = b d 3 in4 [Moment of Inertia of a rectangle about its base] 3 Ibase= I + A y2 in4 [I @ Base = I + Area X (dist. from centroid to base)2]

Center of Area:

Use the formula M = A d derived from M=Fd to find X and Y A = Sum of Areas of ALL members

Stress: {units = ksi or psi} BENDING / FLEXURAL STRESS {units = ksi or psi} Remember: Max. Bending stress occurs at the extreme fibers. fb = M [Bending Stress = Moment S Section Modulus] fb = M c [Bending Stress = Moment X (dist. from extreme fiber to N/A)] I Moment of Inertia Remember: Greater the c, greater is the Bending Stress.

AXIAL STRESS {units = ksi or psi} Remember: Max. Axial stress occurs along the entire cross-section.

fa = P [Axial Tension or = Axial Tension Force in lbs or kips] A Compression Stress Area in in2 Remember: Axial Stress is the same at both Tension & Compression SHEAR STRESS {units = ksi or psi} Remember: Max. Shear stress occurs at the Nuetral Axis Remember: Shear Stress is the same at both Vertical & Horizontal axis. fv = 1.5 V [Actual Shear Stress = 1.5 X Shear Force] A Area Just understand the fol. 2 formulas. No need to memorize: fv = V Q I b (Statical moment about the [Shear Stress = (Shear force) X nuetral axis of the area above the plane)] (Moment of Inertia) X (width of beam) Q = (section Area) X (dist. from centroid of rect. to the centroid of section above neutral axis) fv = 1.5 V = 3 V A 2 b d Notching on Tension side of a Wood Beam fv = 1.5 V X d [d = overall d of beam] b d d [d = d of the beam that is notched] Use Actual dimensions of the b and d, NOT Nominal dimensions

Short heavily loaded Beams & Beams with large loads at supports fv = V [Actual Shear Stress = Shear Force dt (depth of beam) X (thickness of beam)]

Deflection: {units = inches} SHORTENING OF A COL. OR ELONGATION OF A HORIZ. MEMBER = P L A E [Shortening / Elongation = Force X Length A of cross-section of member X Modulus of Elasticity] Remember: Stress = P A for change in length, Multiply Stress by Length Modulus of Elasticity DEFLECTION OF A BEAM = 5 w L4 384 E I

[Deflection = 5 X (w in pounds) X (Length in feet X12)4 (384) X 12 X Modulus of Elasticity X Moment of Inertia] Remember: w # = w # ft 12 Length in inches = Length in feet X 12 Strain: = [strain = Deflection L Original Length] Modulus of Elasticity: E = f [Modulus of Elasticity = Stress Strain] Thermal effects on structures: {units = inches} SHORTENING OR ELONGATION DUE TO CHANGE IN TEMPERATURE = e L t

[Thermal Elongation = (Coeff.of thermal linear expansion) X (Orig.Length) X (Temp Change)]

THERMAL STRENGTH IN A RESTRAINED MEMBER ft = E e t

[Thermal Stress = E X Coeff. of linear expansion X Change in Temp] in a Restrained member

Slenderness Ratio (Loading Capacity): {units = inches} STEEL COLUMN kl is the effective length in feet. SR = k l [Slenderness Ratio = (end cond.) X Unbraced length in inches] r Radius of gyration Remember: Slenderness Ratio should be 200 for a steel column. WOOD COLUMN SR = k l [Slenderness Ratio = (k =1) X (Unbraced Length in inches) b (cross-section width of rectangle)] Remember: Slenderness Ratio should be 50 for a wood column. r = I [Radius of Gyration = Moment of Inertia] A Area Retaining Wall F = w h2 [Force exerted on = (fluid pressure at top of soil) X (height)2] 2 the Retaining Wall 2

RM = 1.5 MOT [DL Resisting Moment = 1.5 (Overturning Moment of the Retaining Wall)] Factor of Safety (FS) for the Resisting Moment requires it .

FS = RM [Factor of Safety = Resisting Moment MOT Overturning Moment] Remember: FS 1.5 SLIDING OF RETAINING WALL FS against Sliding = Sliding Resistance (#) Force causing tendency to Sliding (#) Sliding Resistance = (Total Vert. Load in # on Ftg) X (Coeff. of Friction) Force causing Sliding = (Earth pressure in # @ Base of Ftg) X (h in ft) (2) ft M= (F) h [Bending Moment = Force X (ht at resultant force) 3 Remember: Bending Moment occurs at 1/3rd the height of the retaining wall, where resultant force occurs. Weld: {units = inches} Throat of Weld = Weld Size X (.707) [.707 = 2 ] 2 Capacity of Weld = (Allow. Stress)(Throat)(Weld Size)(Total Weld Length) Allow. Stress = 18 ksi for E60 electrode weld for ASTM A-36 base plate. 21 ksi for E70 electrode weld for ASTM A-36 base plate. ft= P [Stress in the = (Compressive/Tensile Force of the Weld) A throat of the weld (.707) X (Weld Size) X (Total Weld Length)]

Ultimate Strength Design for Concrete:

U = 1.4DL + 1.7LL [Ultimate Load = 1.4(Dead Load) + 1.7(Live Load)]

MU = 1.4 MDL + 1.7 MLL [Ultimate Moment = 1.4(Dead Load Moment) + 1.7(Live Load Moment)]

MU = As fy(d a ) 2 Remember: As is available in a table, ASTM STD REINFORCING BARS [Moment = (strength reduction factor = 0.9) (cross-sectional area of tensile reinforcemnt) (specific yield strength of reinforcemt) {(dist. from extreme compression fiber to centroid of tensile reinforcement) (depth of rectangular stress block) / 2}]

= AS [Percentage of steel to = (area of tensile reinforcemnt)] bd achieve a Balanced Design (beam width) X (d) min = 200 min should be 3 f c fy fy

Live Load Reductions:

R = r (A 150) [Live Load Reduction = (rate of reduction) X {(Tributary Area) 150} Remember: rate of reduction = 0.08 for Floors See table 16-C Roofs Rmax = 40% for single level floors Rmax = 60% for multi-level floors R = 23.1 (1 + DL) LL Remember: Do all 3 checks and then select the lowest value as your final live load reduction.

Thrust in a 3 hinged Arch: Thrust = w L2 [Thrust in a 3 hinged arch = uniform load X (length)2] 8 h 8 X height

The Non-User's Pocket Guide to the Transient Knowledge Necessary for the Structural Divisions of the Architect Registration Exam- ARE

CONCEPT COMMENTS

Memory Trick: SOHCAHTOA (Indian Tribe) used when triangle has a 90 angle.

Rise (Rise) SIN RISESlope COS RUN

TAN SLOPERun (Run) a SIN and COS of any angle are between (+/-) 1

Slope 0 < angle < 45 COS > SIN 45 < angle < 90 SIN > COS

Run

Rise (Slope) b

Law of Sines Law of Sines and Cosines are used when triangle has no a = = B right angles.

Sin A Law of Sines is used when you are given more angles a than sides.

Law of Cosines is used when you are given more sides

C than angles

Variations in L.O.A. Properties of a Force: A Force is defined by four properties:

Transmissibility:

Force Addition:

Fo

rces

FORMULAE AND DIAGRAMS

Law of Cosines

A

B

Components of a Force:

b2 = a2 + c2 - 2ac (Cos B)

c2 = a2 + b2 - 2ab (Cos C)

Trig

on

om

etry

/Mat

h

or

a2 = b2 + c2 - 2bc (Cos A)

or

or

Variations in Sense:

Sin C = or

Cos C = or

Tan C = or

c

b

90 triangle

Shallower angles (45) havelarger vertical components

A

P

Py

PX

C

P

Py

PXPy

PX

PPX

Py

P

PX

Py P

Px

Py

Graphic Method for Force Addition:

1

23

Tail of 2 on Head of 1Tail of 3 on Head of 2

1

23

R

Resultant begins at 1s Tail and ends at last Head

3

12

Tails at same P.O.A.

Force Horizontal Vertical

1 +/- +/-

2 +/- +/-

3 +/- +/-

R +/- R X = X +/- R y = Y

1. Point of Application (P.O.A.) 2. Magnitude ( #,kips ) 3. Sense (Arrowhead, Push or Pull, C or T) 4. Line of Action (L.O.A.) , (Angle with horizontal)

The Equilibrant is also defined as a force that has the same P.O.A., Magnitude and L.O.A. as the Resultant but has an opposite sense (Arrow)

The Resultant is also a force and is thus defined by the four properties listed above.

The Resultant of several forces is a single force that has the same effect on a body as all the other forces combined.

P=

P

P

Algebraic Method for finding the Resultant of several forces is used when force magnitudes and lines of action for each force are known

Algebraic Method of Force Addition 1. Resolve each force into vertical and horizontal components 2. The algebraic (+/-) sum of all horizontal components gives the horizontal component of the Resultant. 3. The algebraic (+/-) sum of all vertical components gives the vertical component of the Resultant

Graphic Method is used when a system is in equilibrium and we need to calculate one or more unknown forces that contribute to equlibrium

Graphic Method for Force Addition 1. Arrange all forces Head to Tail then add (independent of order)

2. Resultant begins with its Tail at the Tail of the 1st Force and Head at the Head of the last 3. Resultant can be determined through calculation

P

PX

Py

September, 2004 2004 David J. Thaddeus, AIA PAGE : 1 OF 4


CONCEPT COMMENTSFORMULAE AND DIAGRAMS

Moment Moment = Distance

Summing Moments (M = 0) to establish equilibrium

To find Beam / Truss reactions To maintain equilbrium of members Overturning Moments due to Wind Loads or Hydrostatic Pressure

Couple Unlike a Moment, a Couple is NOT about a certain point, but rather it is about ANY and ALL points.

Moment of a A Couple depends on Force (P), and perpendicular distance (d)

Force X

Mo

men

ts a

nd

Co

up

les

Couple= P x d d d between two Forces that make up the couple. Mo

men

ts a

nd

Co

up

les

(clockwise, CW) P Couple between top Chord (C) and bottom chord (T) in a simply supported truss

Couple between compression in concrete ( top ) and tension in rebar ( bottom ) of reinforced beam

1. ELASTIC RANGE: straight line relationship, slope = E

P 2. PLASTIC RANGE: increase in strain, no increase in Load / Stress

A 3. STRAIN HARDENING: material deforming in section (necking),

and in length

L 4. FAILURE: Material is gone!

Lo 5. YIELD POINT/ YIELD STRENGTH: material is no longer elastic, deformation is permanent

F 6. ULTIMATE STRENGTH: material is about to fail Unit Strain ( L/ L0 ) 7. RUPTURE: Kiss it Good-Bye

8. E: Modulus of Elasticity.Measures material's resistance to deformation

L = (T) L0 Shortening or Elongation of members along their axis Change (Expansion & Contraction) of shape due to Temperature

Examples include Columns, Trusses, Cables, Cross Bracing

b = width

d = depth

c = location of

x

b

Roller: 1 Reaction ( V ) Pin / Hinge: 2 Reactions ( V , H ) Simply Supported: Statically Determinate (Simply Supported) loading = three unknown reactions, and can be solved using the equation of Static equilibrium. Statically Indeterminate loading > 3 unknown Reactions Call your engineer.

Fixed / Moment: 3 Reactions (V , H , M) Continuous: Multiple Reactions Indeterminate Loading:

AE

Neutral Axis

L= PL0

Axi

al L

oad

s G

eom

etry

Deflection

Shear

Bending

Moment

Area (In2)

PSIModulus of Elasticity= Stress / Strain

:

Mo

men

ts a

nd

Co

up

les

Units

in / in

PSI

Str

ess

(F

=P

/A)

Formulas

F: Direct Stress

Unit Strain

E:

Su

pp

ort

Co

nd

itio

ns

Str

ess

/ Str

ain

bd3

12

Radius of = r = I Gyration A

Modulus of Elasticity: E(slope)

Fy

8

1 2 3 4

56

7

Fu

L: deformation, changes in Length (in) caused by Axial Load (P)P : Axial Load (#,k)L0 : Original, undeformed Length (in. not ft.)

A : Cross Sectional Area (in2)E : Modulus of Elasticity (PSI, KSI)

L: Deformation, change in length (in), caused by change in temperature (F) T: Change in temperature : Coefficient of thermal expansion/contraction

A = bd

EA36,A-50= 29,000 KSI

P L L0 L A L E L

Moment

of Inertia (In4) Section

Modulus (In3)

V V

H

V

H

M

(Determinate)

1 2

3

2 1

3

3 3

Force P creates aNegative Momentabout point B

d

A

_+

d

PB

Force P creates aPositive Momentabout point A

P

P

( CCW )

GravityCG ; Center of

x

Y

Y

c

d/2

d

2 2

3 1

If a Member is inadequate in Shear, increasing the Area (either Width (b) or Depth (d)) is effective. If a Member is inadequate in Deflection, increasing the Moment of Inertia (Width (b) is OK; but Depth (d) is cubed and) is much more effective in reducing Deflection. If a Member is inadequate in Bending, increasing the section modulus (width (b) is OK; but Depth (d) is squared and) is much more effective in reducing Bending.

Pin/Hinged connections iclude most wood to wood, bolted steel, and precast concrete connections. fixed connections include most welded steel / steel connections and cast-in-place concrete.

_+CCW CW

A & B are called Centers of Moment, or Centers of Rotation The perpendicular distance (d) is called the Moment Arm, or Lever

Ixx =

=Sxx =Ixx bd2

C 6

12



CONCEPT COMMENTSFORMULAE AND DIAGRAMS

Example 1: M = Moment V =Shear

Equilibruim = Fx = 0; Fy = 0; MAny = 0 Sum of Areas in Shear Diagram = Moment Magnitude of drop = Concentrated Load Between concentrated loads, Moment Diagram Slopes Uniform loads create gradual drop in Shear ( straight line ) Uniform loads create curve (downward cup) in Moment Diagram Overhangs and cantilevers will always have a negative Moment in Moment Diagram. Simply supported beams always have positive Moments

VMAX always occurs at support Moment is minimum

MMAX occurs where V = 0 Uniform load coefficient, w, = slope in Shear Diagram Point of Inflection (P.O.I.) is a point on the Moment Diagram where M = 0 Point of Inflection only happens when a beam has an overhang If Loading Diagram (FBD) is symmetrical, then the Shear Diagram and the Moment Diagram are also symmetrical. Maximum Shear dictates how much Beam area is needed Maximum Moment dictates how much Bema Depth is needed If a hole must be punched out of a Beam to allow for passage of pipe or similar reduction, this must happen at a location of low Shear and low Bending Moment

Method of Method ofSections: Joints:

Web StressesStress increases towards middle Stress increases towards end panels

Sh

ear

and

Ben

din

g M

om

ent

Dia

gra

ms

Tru

sses

Top and Bottom Chord Stress

L < R

L = 5' x 12k = 4k

PossibleZero Members

C

Method of Joints is used to analyze Force / Stress in every member of a Truss Method of Joints is also used to analyze Force / Stress in a member that is close to a support (not in middle of truss) Method of Sections is used to analyze only a few (3 max) members of a truss After cutting a truss in 2 segments, each segment is in Equilibrium F X = 0 ; F Y = 0 ; M ANY = 0 Concentrated Loads in a Truss must be applied at panel points; otherwise we have combined stresses ( T or C + V and M ) Joints that have three or less members framing into them, may potentially have Zero Members

15'

15'

+

-

w , W

P

Load/FBD

V=0

M=0

R = 10' x12k = 8k

12k

10' 5'

15'

L R

+6' 6' 6'

18'

12k 12k

L = 21k R = 21k

6'12'18'

6k

R = 4kL = 2k

L = 6'/18' x 6k = 2k

R = 12'/18' x 6k = 4k

C C

T T T T T

T T T T

C C C C C

C C C C

C C C C C

T T T T T

C

C T

A Truss is inherently stable due to triangulation Truss is stable in its own plane but needs bridging or cross-bracing perpendicular to its own plane All joints in an honest Truss are Pinned Joints Rigid Joints in a Truss will result in less Deflection than Pinned Joints (Advantage) Rigid Joints in a Truss will result in larger size members than Pinned Joint Trusses since members will have to resist V and M in addition to C or T (Disadvantage) Members carrying Tension can be much smaller than members carrying Compresion m + 3 = 2 j ; where m = Number of Members j = Number of Joints

Example 2:

6' 6' 6'

18'

12k 18k

=w = 1k/ft.

W = 18k

L = 21k + 2k

L = 23 kR = 21k + 4k

R = 25 k

L = 23k R = 25k


The Non-User's Pocket Guide to the Transient Information Needed to Successfully Pass the General Structures Division of the Architect Registration Exam - ARE

CONCEPT COMMENTS

MATERIAL:

DESIGN FOR DESIGN FOR DEFLECTION: actual = CONST.x (W or P) (Lx12"/ft.)3

SHEAR: BENDING: E I

WOOD BEAMS: STEEL BEAMS: CONCRETE BEAMS:Shear: Shear: Shear: Concrete: f 'c

b, d, f 'c

Stirrups: f y f y, , A v, spacing

Bending: Bending Bending Concrete: f'c b, d, f 'c

Fb= 24 KSI Rebars: f y

(full lateral support) f y, (, # rebars), A s

WOOD COLUMNS: STEEL COLUMNS:Slenderness: Slenderness:

kLUNB.

k=0.5kwood= 0.671 E

Col

umns

FORMULAE AND DIAGRAMSB

eam

sG

ener

al B

eam

Des

ign

LUNB./ dLeast

I = bd3/ 12 Deflection

: F b = MMAX SMIN

5 wL4

Fc

W = wL

Fv , F b , E LOAD: GEOMETRY: A = bd Shear

S = (bd2) /6 Bending

f v < F v ; V MAXA MIN

Fv

L, w, W, P, FBD

f b < F b ; F b = MMAXSMIN actual < allow

FV = 3 VMAX 2 A MIN

Fb = MMAX

Sxx tables LUNB , M-Charts(partial lateral support)

woodsteel

r

MMAX = WL / 8

VMAX = W/2

MMAX = PL/4

VMAX = P/2

VMAX = 3P/2

MMAX = PL/2MMAX = PL/3

VMAX = P

23 PL3 MAX = 648 EI

19 PL3 MAX =348 EI

1 PL3 MAX =48 EI384 EI

5 WL3 MAX =384 EI

=

VMAX, M MAX

W = wL

W = w L

MMAX = WL/8

VMAX = W/2

VMAX = 0.6 W

MMAX (+) = 0.08 W L

MMAX (-) = - 0.1 W L

W/2

AWEB

F V = VMAX

h

A VA S

d

b

SMIN

= wL2/ 8 = wL2/8

Fb< 24 KSI

FC , FT , F P

A = b x d

slendernessratio

50 L/d200 KL/r

k=1 k=2

b

d

Beam design must satisfy Shear, Bending Moment and Deflection requirements The Allowable Stress (F) of a species of wood or a Grade of steel depends on the material itself and is tabulated in Manuals and Building Codes The Actual Stress ( f ) is an outcome of the application of a load ( W , P ) on a member When a Load is applied perpendicular to the axis of a member ( Normal Loading), Shear and Bending stresses develop The Strain associated with Bending is called Deflection and the deflected shape of a Beam is the inverse (upside/down) of the Moment Diagram When a load is applied along the axis of a member, Axial Compression and Tension Stresses develop The strain associated with Tension is Elongation and the strain associated with Compression is Shortening For the same Magnitude and span, a Uniform Load will cause less Deflection than a Concentrated Load for the same material and geometry The the same Load and Span, a Cantilever will deflect more than a simply supported beam For the same Load, Material and Geometry a slight increase in Span will create a huge increase in Deflection For the same Load and Span, an increase in the Modulus of Elasticity, E, ( a stronger material), will result in less Deflection For the same Load and Span, an increase in the Moment of Inertia, I , (a deeper member) will result in less deflection The Points of Inflection on the Moment Diagram of the Continuous beam (Left) indicate the locations of curve reversal, and are the locations where reinforcing steel would be flipped from bottom to top of the beam.

L/3 L/3 L/3

P P

P

PL/3

P

P

P

L/4 L/4 L/4 L/4

PP

3P/2

PL/2

P

L/2 L/2

P/2

PL/4

P/2L

w

W/2

WL/8

W/2 W/2

w

W/2

W/2

WL/8

W/2

w

L L L0.4W 1.1W 1.1W 0.4W

0.6W 0.5W0.4W

0.4W 0.5W 0.6W

d

b f

A W

k11

For all beams; actual = CONST.(W or P)(Lx12"/ft.)3

EI Allowable Deflecion is specified by model codes as a fraction of the span allow = L / 240, L / 360,...

FC = P/A Long and thin ( slender ) columns tend to be governed by buckling Short and fat ( chunky ) columns tend to be governed by crushing

w w

- 0.1WL

0.08WL0.025WL

0.08WL

P.O.I.- -+++

- 0.1WL

... .

September 2004 2004 David J. Thaddeus, AIA PAGE : 4 OF 4

1. StaticsStatics_0001Statics_0002Statics_0003Statics_0004Statics_0005Statics_0006Statics_0007Statics_0008Statics_0009Statics_0010Statics_0011Statics_0012Statics_0013Statics_0014Statics_0015Statics_0016Statics_0017Statics_0018Statics_0019Statics_0020Statics_0021Statics_0022Statics_0023Statics_0024Statics_0025Statics_0026Statics_0027Statics_0028Statics_0029Statics_0030Statics_0031Statics_0032

2. BeamsBeams & Columns_0001Beams & Columns_0002Beams & Columns_0003Beams & Columns_0004Beams & Columns_0005Beams & Columns_0006Beams & Columns_0007Beams & Columns_0008Beams & Columns_0009Beams & Columns_0010Beams & Columns_0011Beams & Columns_0012Beams & Columns_0013Beams & Columns_0014Beams & Columns_0015Beams & Columns_0016Beams & Columns_0017Beams & Columns_0018Beams & Columns_0019Beams & Columns_0020Beams & Columns_0021Beams & Columns_0022Beams & Columns_0023Beams & Columns_0024

3. Wood ConstructionWood Construction_0001Wood Construction_0002Wood Construction_0003Wood Construction_0004Wood Construction_0005Wood Construction_0006Wood Construction_0007Wood Construction_0008Wood Construction_0009Wood Construction_0010Wood Construction_0011Wood Construction_0012Wood Construction_0013Wood Construction_0014Wood Construction_0015Wood Construction_0016Wood Construction_0017Wood Construction_0018Wood Construction_0019Wood Construction_0020Wood Construction_0021Wood Construction_0022

4. Steel ConstructionSteel Construction_0001Steel Construction_0002Steel Construction_0003Steel Construction_0004Steel Construction_0005Steel Construction_0006Steel Construction_0007Steel Construction_0008Steel Construction_0009Steel Construction_0010Steel Construction_0011Steel Construction_0012Steel Construction_0013Steel Construction_0014Steel Construction_0015Steel Construction_0016Steel Construction_0017Steel Construction_0018Steel Construction_0019Steel Construction_0020Steel Construction_0021Steel Construction_0022Steel Construction_0023Steel Construction_0024

5. Concrete ConstructionConcrete Construction_0001Concrete Construction_0002Concrete Construction_0003Concrete Construction_0004Concrete Construction_0005Concrete Construction_0006Concrete Construction_0007Concrete Construction_0008Concrete Construction_0009Concrete Construction_0010Concrete Construction_0011

6. WallsWalls_0001Walls_0002Walls_0003Walls_0004Walls_0005Walls_0006Walls_0007Walls_0008Walls_0009Walls_0010Walls_0011Walls_0012Walls_0013Walls_0014Walls_0015Walls_0016Walls_0017Walls_0018

7. ConnectionsConnections_0001Connections_0002Connections_0003Connections_0004Connections_0005Connections_0006Connections_0007Connections_0008Connections_0009Connections_0010Connections_0011Connections_0012Connections_0013Connections_0014Connections_0015Connections_0016Connections_0017Connections_0018Connections_0019Connections_0020Connections_0021Connections_0022Connections_0023Connections_0024Connections_0025Connections_0026

8. FoundattionsFoundattions_0001Foundattions_0002Foundattions_0003Foundattions_0004Foundattions_0005Foundattions_0006Foundattions_0007Foundattions_0008Foundattions_0009Foundattions_0010Foundattions_0011Foundattions_0012Foundattions_0013Foundattions_0014Foundattions_0015Foundattions_0016

9. GlossaryGlossary_0001Glossary_0002Glossary_0003Glossary_0004Glossary_0005Glossary_0006Glossary_0007Glossary_0008Glossary_0009Glossary_0010Glossary_0011Glossary_0012

10. Conventional Structural Systems1. Conventional Structural Systems_00011. Conventional Structural Systems_00021. Conventional Structural Systems_00031. Conventional Structural Systems_00041. Conventional Structural Systems_00051. Conventional Structural Systems_00061. Conventional Structural Systems_00071. Conventional Structural Systems_00081. Conventional Structural Systems_00091. Conventional Structural Systems_00101. Conventional Structural Systems_00111. Conventional Structural Systems_00121. Conventional Structural Systems_00131. Conventional Structural Systems_00141. Conventional Structural Systems_00151. Conventional Structural Systems_00161. Conventional Structural Systems_00171. Conventional Structural Systems_00181. Conventional Structural Systems_00191. Conventional Structural Systems_00201. Conventional Structural Systems_00211. Conventional Structural Systems_00221. Conventional Structural Systems_00231. Conventional Structural Systems_00241. Conventional Structural Systems_00251. Conventional Structural Systems_00261. Conventional Structural Systems_00271. Conventional Structural Systems_00281. Conventional Structural Systems_00291. Conventional Structural Systems_00301. Conventional Structural Systems_00311. Conventional Structural Systems_00321. Conventional Structural Systems_00331. Conventional Structural Systems_00341. Conventional Structural Systems_00351. Conventional Structural Systems_0036

11. Long Span Systems2. Long Span Systems_00012. Long Span Systems_00022. Long Span Systems_00032. Long Span Systems_00042. Long Span Systems_00052. Long Span Systems_00062. Long Span Systems_00072. Long Span Systems_00082. Long Span Systems_00092. Long Span Systems_00102. Long Span Systems_00112. Long Span Systems_00122. Long Span Systems_00132. Long Span Systems_00142. Long Span Systems_00152. Long Span Systems_00162. Long Span Systems_00172. Long Span Systems_00182. Long Span Systems_00192. Long Span Systems_00202. Long Span Systems_00212. Long Span Systems_00222. Long Span Systems_00232. Long Span Systems_00242. Long Span Systems_00252. Long Span Systems_00262. Long Span Systems_00272. Long Span Systems_00282. Long Span Systems_00292. Long Span Systems_00302. Long Span Systems_00312. Long Span Systems_00322. Long Span Systems_00332. Long Span Systems_00342. Long Span Systems_00352. Long Span Systems_00362. Long Span Systems_00372. Long Span Systems_00382. Long Span Systems_00392. Long Span Systems_00402. Long Span Systems_00412. Long Span Systems_00422. Long Span Systems_00432. Long Span Systems_0044

12. Trusses3. Trusses_00013. Trusses_00023. Trusses_00033. Trusses_00043. Trusses_00053. Trusses_00063. Trusses_00073. Trusses_00083. Trusses_00093. Trusses_00103. Trusses_00113. Trusses_00123. Trusses_00133. Trusses_00143. Trusses_00163. Trusses_00173. Trusses_0018

13. Earthquake Design4. Earthquake Design_00014. Earthquake Design_00024. Earthquake Design_00034. Earthquake Design_00044. Earthquake Design_00054. Earthquake Design_00064. Earthquake Design_00074. Earthquake Design_00084. Earthquake Design_00094. Earthquake Design_00104. Earthquake Design_00114. Earthquake Design_00124. Earthquake Design_00134. Earthquake Design_00144. Earthquake Design_00154. Earthquake Design_00164. Earthquake Design_00174. Earthquake Design_00184. Earthquake Design_00194. Earthquake Design_00204. Earthquake Design_00214. Earthquake Design_00224. Earthquake Design_00234. Earthquake Design_00244. Earthquake Design_00254. Earthquake Design_00264. Earthquake Design_00274. Earthquake Design_00284. Earthquake Design_00294. Earthquake Design_00304. Earthquake Design_00314. Earthquake Design_00324. Earthquake Design_00334. Earthquake Design_00344. Earthquake Design_00354. Earthquake Design_00364. Earthquake Design_00374. Earthquake Design_00384. Earthquake Design_00394. Earthquake Design_00404. Earthquake Design_00414. Earthquake Design_00424. Earthquake Design_00434. Earthquake Design_00444. Earthquake Design_00454. Earthquake Design_00464. Earthquake Design_00474. Earthquake Design_00484. Earthquake Design_00494. Earthquake Design_00504. Earthquake Design_00514. Earthquake Design_0052

14. Wind Design5. Wind Design_00015. Wind Design_00025. Wind Design_00035. Wind Design_00045. Wind Design_00055. Wind Design_00065. Wind Design_00075. Wind Design_00085. Wind Design_00095. Wind Design_00105. Wind Design_00115. Wind Design_00125. Wind Design_00135. Wind Design_00145. Wind Design_00155. Wind Design_00165. Wind Design_00175. Wind Design_00185. Wind Design_00195. Wind Design_00205. Wind Design_00215. Wind Design_0022

15. Notable Buildings6. Notable Buildings and Engineers_00016. Notable Buildings and Engineers_00026. Notable Buildings and Engineers_00036. Notable Buildings and Engineers_00046. Notable Buildings and Engineers_00056. Notable Buildings and Engineers_00066. Notable Buildings and Engineers_00076. Notable Buildings and Engineers_00086. Notable Buildings and Engineers_00096. Notable Buildings and Engineers_00106. Notable Buildings and Engineers_00116. Notable Buildings and Engineers_00126. Notable Buildings and Engineers_00136. Notable Buildings and Engineers_00146. Notable Buildings and Engineers_00156. Notable Buildings and Engineers_00166. Notable Buildings and Engineers_00176. Notable Buildings and Engineers_00186. Notable Buildings and Engineers_00196. Notable Buildings and Engineers_00206. Notable Buildings and Engineers_00216. Notable Buildings and Engineers_00226. Notable Buildings and Engineers_00236. Notable Buildings and Engineers_00246. Notable Buildings and Engineers_00256. Notable Buildings and Engineers_00266. Notable Buildings and Engineers_00276. Notable Buildings and Engineers_00286. Notable Buildings and Engineers_00296. Notable Buildings and Engineers_00306. Notable Buildings and Engineers_00316. Notable Buildings and Engineers_00326. Notable Buildings and Engineers_00336. Notable Buildings and Engineers_00346. Notable Buildings and Engineers_00356. Notable Buildings and Engineers_00366. Notable Buildings and Engineers_00376. Notable Buildings and Engineers_00386. Notable Buildings and Engineers_00396. Notable Buildings and Engineers_00406. Notable Buildings and Engineers_00416. Notable Buildings and Engineers_00426. Notable Buildings and Engineers_00436. Notable Buildings and Engineers_00446. Notable Buildings and Engineers_00456. Notable Buildings and Engineers_00466. Notable Buildings and Engineers_00476. Notable Buildings and Engineers_00486. Notable Buildings and Engineers_00496. Notable Buildings and Engineers_00506. Notable Buildings and Engineers_00516. Notable Buildings and Engineers_00526. Notable Buildings and Engineers_00536. Notable Buildings and Engineers_00546. Notable Buildings and Engineers_00556. Notable Buildings and Engineers_00566. Notable Buildings and Engineers_00576. Notable Buildings and Engineers_00586. Notable Buildings and Engineers_00596. Notable Buildings and Engineers_00606. Notable Buildings and Engineers_00616. Notable Buildings and Engineers_00626. Notable Buildings and Engineers_00636. Notable Buildings and Engineers_00646. Notable Buildings and Engineers_00656. Notable Buildings and Engineers_0066

16. FORMULAS TO REMEMBERto Shear Failure to multiply A by total # of bolts)]AUNIFORM LOAD {units = (k ft); (lb ft); (lb in)}POINT/CONCENTRATED LOAD AT THE CENTER OF A MEMBERBENDING / FLEXURAL STRESS {units = ksi or psi}fb = M [Bending Stress = MomentS Section Modulus]fb = M c [Bending Stress = Moment X (dist. from extreme fiber to N/A)]Remember: Greater the c, greater is the Bending Stress.AXIAL STRESS {units = ksi or psi}

fa = P [Axial Tension or = Axial Tension Force in lbs or kips]A Compression Stress Area in in2Remember: Axial Stress is the same at both Tension & CompressionSHEAR STRESS {units = ksi or psi}(Moment of Inertia) X (width of beam)

SHORTENING OF A COL. OR ELONGATION OF A HORIZ. MEMBER

A ERemember: Stress = PAModulus of Elasticity

384 E I(384) X 12 X Modulus of Elasticity X Moment of Inertia]Remember: w # = w #ft 12Retaining Wall

Sliding Resistance = (Total Vert. Load in # on Ftg) X (Coeff. of Friction)Throat of Weld = Weld Size X (.707) [.707 = (2 ]U = 1.4DL + 1.7LL [Ultimate Load = 1.4(Dead Load) + 1.7(Live Load)]Remember: As is available in a table, ASTM STD REINFORCING BARS

R = r (A 150)[Live Load Reduction = (rate of reduction) X {(Tributary Area) 150}Rmax = 40% for single level floorsR = 23.1 (1 + DL)

17. AREStructures

structural technology

Documents