Section Modulus

Ratio of beam's moment of inertia to distance from the neutral axis.

Horiztonal shear stress at mid-depth of beam, where stress is a maximum for rectangular sections.

5ωL⁴

384EI

ωL²

8

ωL

2

Maximum shear for simple beam, uniformly distributed load.

*also for beam fixed at both ends, uniformly distributed load.

P

2

PL

4

 PL³ 

48EI

ωL²

2

ωL⁴

8EI

 ωL⁴

384EI

r=√I/A

kL

r

Euler's equation

Maximum stres a column can resist w/o buckling

P    =   π²E  

   A         (L/r)²

• Short compressive members
• Indeterminate columns
• Slender columns

What is typical spacing of open-web steel joists for:

1. Floors
2. Roofs

1. 2'-3'

2. 4'-6'

• 120 for main members
• 200 for secondary and bracing members

1. Sands and gravels
2. Clays
3. Silts
4. Organics

• Pile or caisson foundation
• Concrete grade beam
• Fill

Maximum allowable shear 

One-way shear on plain or reinforced sections

Φ = strength reduction factor (LRFD)

f'_c = design strength of concrete

b_w = footing width

d = effective depth

 V_c = Φ2√f_b'b_wd

Area of steel required?

P = C_oWh

C_o = coefficient of earth pressure

P = 15h²

(assuming 30 lbf/ft³ for weight of soil)

SSH  -    1/16" wider bolt dia

‹ 1/16" oversied bolt dia

LSH -     1/16" wider bolt dia

< 2 1/2 times bolts dia

Columns 8"

Beam/girders 6"w x 10"d

Floor decking 3" thick

Members 5" and wider

Depth > 2" width

≥ 5" x 5"

depth ≤ 2" > width

15% for 2 months, as for snow

25% for 7 days, as for roof load

60% for wind/eq load

100% for impact loads

S = M 

       F_b'

F_b'=F_bC_DC_mC_tC_LC_FC_iC_r

C_D = load duration factor

C_F = size factor

C_m = wet service factor

C_t = high temp

C_L = laterally unbraced

C_i = incised member

S = bd⁶

     6

F_v' = F_vC_pC_mC_tC_iC_H

C_H=extent of cracking in wood member

Live load reduction for public assembly w/ LL ≤ 100 psf

L_o= uniform live load

K_L= LL element factor

A_T= tributary roof load supported by structural member

L > 0.5L_o for (1) floor

L> 0.4L_o for more than (1) floor

L> 0.8L_o for (1) floor w/ LL > 100psf or parking garages

Allowable percentage reduction of load values

r=rate of reduction, =0.08

A=tributary area

r<40% for horizontal

r<60% for vertical members

r< R=23.1(1 +D/L_o)

1.4D

1.2D + 1.6L + 0.5(L_r or S or R)

1.2D + 1.6(L_r or S or R) + f₁L or 0.8W

1.2D + 1.6W + f₁L + 0.5(L_r or S or R)

1.2D + 1.0E + f₁L +f₂S

0.9D + 1.0E or 1.6W

LRFD load combinations to find most critical case

L_r=roof live load

S=snow load

R=rain load

W=wind load

f₁=1.0 for floors in public assembly, parking garage where LL >100psf.  0.5 for other cases

f₂=0.7 for roof w/o shedding, 0.2 for others

D

D + L

D + L + L_r or S or R

D + W or 0.7E + L + L_r or S or R

0.6D + W

0.6D + 0.7E

Stress is internal resistance to an external force

• Tension
• Compression
• Shear

f = P/A

P = force per unit area

A = area

e =∝χΔT

E = ⨍/∈

stress/strain

bd³

12

bd³

3

Describe seismic categorties:

A

B

C

D

A

B

C - 

D - expected to experience severe and destructive shaking but not located near active faults

500 mph

(avg. 250 mph)

• Buildings w/ heights > 400 ft
• Buidlings subject to dynamic effects
• Sensitive to wind vibrations
• Height-to-width ration ≥5

• 1/500 building's height
• 0.0025 times the story height

Type I: general purpose

Type III: high early strength

End bearing pile: driven to bedrock or firm soil

Friction pile: load-carrying capacity developed through friction b/w pile and soil.

H shapes

Round Pipes

Define the following:

A. Reentrant corner

B. Diaphram discontinuity

C. Torsional irregularity

D. Column stiffness variation

Gradient height for:

1. Urban or metro
2. Suburban
3. Open country

1. 1500'
2. 1200'
3. 900'

Under 5 percent.

*5-20 percent to structural cost

24-40'

typical depth 12-36"

Standard (K series) - up to 60'

Long span (LH) - up to 96'

Deep long span (DLH) - up to 144'

20'-30' spans

12-24" joist depths

Light to medium loads where moderate distances must be spanned

Flat plate

Flat slab

Waffle slab

15'-30'

economical for most applications

easy to form

allows penetrations and openings into slab

Up to about 25' with slabs ranging for 6-12"

limited to short spans

useful in situations where the floor-to-floor height must be kept to a minimum

spans up to 40'

heavier loads at slightly longer spans

• slenderness ratio
• flexural strength
• fire-resistance rating

• clip angles with slotted holes
• slip joints
• flexible sealants

Wood - 50-240'

Concrete - 20-320'

Steel - 50-500'

tension, compression, shear

no bending or moment stresses

40-200'

30-160' for hyperbolic paraboloids