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GR 211Fall 2007

Civil Engineering

ENGR 211 StaticsENGR 211 Statics

Yes there is recitation this week.

Im putting in all grades this week. Contact meabout missing grades after mid-week

Final Thurs Dec. 6th @ 7:30 am Milam 28

Dear118

Alternate Final: send me an email

Wednesday: Review of Class

What I think was important

(Thats what will be on the Final)

Answer as many Qs as possible

Final Exam Closed book, closed

notes

BUT.

You may bring one8- x 11 (max) sheet

with both sidescrammed withwhatever.

Civil Engineering

CablesCables (from Chapter 7 and(from Chapter 7 andAdditional Material on pg. 414FAdditional Material on pg. 414F--K)K)

Analysis

based ontype ofload

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GR 211Fall 2007

Civil Engineering

Loads Distributed UniformlyLoads Distributed Uniformly

Along a Straight LineAlong a Straight Line

0

wa

T=

21

2 y ax=

Civil Engineering

Loads Distributed Uniformly Along a Straight LineLoads Distributed Uniformly Along a Straight Line

0

wa

T=

2 20

1T T a x= +

2 2 2 21 11 ln 12

s x a x ax a xa

= + + + +

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GR 211Fall 2007

Civil Engineering

Golden Gate Bridge

21

2 y ax=

So, a = 2.83 x 10-4 ft-1

Civil Engineering

0

wa

T=

Assume w= 22 kips/ft. (each side)

2.83 x 10-4 =

2 20

1T T a x= +

y = (1.19 x 10-4)x2 m

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GR 211Fall 2007

Civil Engineering

0

wa

T=

Assume w= 22 kips/ft. (each side)

2.83 x 10-4 =

2 20

1T T a x= +

y = (1.19 x 10-4)x2 m

Civil Engineering

Assume w= 22 kips/ft. (each side)

y = (1.19 x 10-4)x2 m

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GR 211Fall 2007

Civil Engineering

Dead Load 41 kips/ft

Live Load 4000 lb/ftCost (1937) $35 million

Today (est.) $1.2 billion

Civil Engineering

11 men died

Safety innovations hard hats and safetynet

19 in Halfway-to-HellClub

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GR 211Fall 2007

Civil Engineering

Catenary Cables

Civil Engineering

Load Uniformly Distributed Along a CableLoad Uniformly Distributed Along a Cable

Catenary Curve

0

wa

T=

( )

1

cosh 1 y axa=

0coshT T ax=

sinh axs

a=

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GR 211Fall 2007

Civil Engineering

Find the Sag & Tmax

T0 = 1.8kN

Cable has mass 2 kg/m

0

w

a T=

Civil Engineering

0

wa

T=

( )

1cosh 1 y ax

a=

= 0.0109

0coshT T ax=

sinh axs

a=

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GR 211Fall 2007

Civil Engineering

Power Lines

ACSR AluminumConductor SteelReinforced

#6 (Code Name Turkey)

0.198 diameter

6 AL x 1 GalvanizedSteel

24.5#/1000 AL

11.6#/1000 Steel

36.1#/1000 Total

Guys

dia. Galvanized SteelWire Rope

Earth Anchors

Civil Engineering

Power Line ExampleTypical Rural Lines

Approx. 300 Spacing

20 Ground Clearance

Sag = 5

Find T0 and length andangle

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GR 211Fall 2007

Civil Engineering

Power Line Example

Typical Rural Lines

Approx. 300 Spacing

20 Ground Clearance

Sag = 5

Find T0 and length and angle

( )

1cosh 1 y ax

a

=

sinh axs

a=

0

wa

T=

Graphical Solution for a cable

y=1/a*(cosh ax -1) for x = 150 ft.

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0.0005

0.00055

0.0006

0.00065

0.0007

0.00075

0.0008

0.00085

0.0009

a, ft-1

y,

ft.

Civil Engineering

Power Line ExampleTypical Rural Lines

Approx. 300 Spacing

20 Ground Clearance

Sag = 5

Find T0 and length and angle

( )

1cosh 1 y ax

a=

sinh axs

a=

0

wa

T=

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GR 211Fall 2007

Civil Engineering

150

1cosh 1

ft

d axdy a

dx dx

=

cosh sinhd

d dxdx

=u

u u

150 150sinh

ft ft dy axdx

=

Find the angletangent to thecable @connection point

Civil Engineering

Find the angletangent to thecable @connectionpoint

( )

1cosh 1 y ax

a=

( )

1cosh 1 y ax

a= @ 140=4.41 ft.

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GR 211Fall 2007

Civil Engineering

Oakland Skyway BridgeOakland Skyway Bridge Most expensive construction project

in California history

Civil Engineering

OSU Grads in chargeOSU Grads in charge

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Civil Engineering

Tacoma Narrows BridgeTacoma Narrows Bridge

19401940

Civil Engineering