STRC14 Bridges Concrete Members 0716

Structural Engineering Exam Review Course

Bridges (Concrete Members)

Bridge Design: Concrete Members Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.

©2016 Professional Publications, I

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Bridge Design: Concrete Members

Lesson Overview •

Concrete Beams for Bridges •

Cast‐in‐Place concrete with Grade 60 Reinforcement

•

Precast Concrete Beams with High‐Strength Steel Cable

•

Bending Moment Strength

•

Shear Strength

•

Deflection and Fatigue

•

AASHTO Requirements



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Learning Objectives You will learn how to •

•

•

•

•

determine the ultimate bending strength of concrete of concrete beams

•

determine shear strength

•

determine detailing of steel of steel reinforcement

•

determine the cracking moment of beams

describe various precast construction practices design composite construction of precast concrete use AASHTO to estimate prestress losses

verify the fatigue and other service level conditions for concrete STRC ©2015 Professional Publications, Inc.


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Prerequisite Knowledge You should already be familiar with •

elastic mechanics of stress of stress

•

AASHTO loading calculations

•

ACI 318 concrete beam design and calculation

•

ultimate load and service load combinations

•

definitions of structural of structural fundamentals (creep and fatigue)



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Referenced Codes and Standards AASHTO AASHTO LRFD Bridge Design Specifications (AASHTO, 2012)



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Concrete Strength Design Concrete strength design uses ultimate strength calculations. •

Whitney stress block for concrete compression

•

uniform stress of 0.85 of 0.85 ´c

•

depth of compression of compression stress, a, is portion of compression of compression depth, c

•

yield stress for tension steel

•

effective depth, d = = distance from compression face to centroid of tension of tension steel



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Concrete Strength Design •

cross‐section stress and force •

•

•

•

•

total compression force on concrete and compression steel = total tension force on steel sum moment of each of each force about centroid of cross of cross‐section

similar to ACI 318 procedures Effective compression flange width is given by AASHTO Sec. 4.6.2.6.1 as tributary width. Print and laminate AASHTO Appendix A5 for use on the exam.



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Load and Resistance Factor Design procedure •

apply load factors to external loads •

•

overestimate the largest loads needed to support load combinations per AASHTO Table 3.4.1‐1

•

apply reduction factor to internal strengths •

•

underestimate the likely failure strength of the of the element phi factors per AASHTO 5.5.4.2



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Example: T‐Beam Design Example 8.11



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Example: T‐Beam Design Example 8.11



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Example: T‐Beam Design



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Deflection Requirements optional AASHTO limits •

service level live load including impact •

for bridges with vehicles and no pedestrians

 max 

•

•

Table 8.3 Recommended Minimum Recommended Minimum Depths

L

800 for bridges with vehicles and pedestrians L  max  1000

Table 8.3 lists suggested minimum depths for reinforced concrete superstructures. STRC ©2015 Professional Publications, Inc.


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Cracking Moment procedure •

•

•

Determine the service level moment when cracking of tension of tension face occurs.

•

Use elastic stress mechanics on gross area of concrete. of concrete. Ignore influence of reinforcing of reinforcing steel.

•

Assume concrete will crack when tension stress reaches modulus of rupture, f r .

Locate centroid of cross of cross‐section.



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AASHTO Cracking Moment AASHTO’s simplified formula for cracking moment is

where these conditions apply



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Minimum Reinforcement AASHTO minimum reinforcement is specified by conformance to the following. Mr ≥ min(1.33Mu, Mcr ) Mr = ϕMn Mu = factored moment Mcr as specified on previous slide.



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Example: Minimum Reinforcement Example 8.13



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Example: Minimum Reinforcement Example 8.13



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Example: Minimum Reinforcement



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Example: Minimum Reinforcement



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Control of of Cracking Cracking •

Smaller bar size and smaller spacing of steel of steel means less cracking of concrete of concrete cover.

•

AASHTO exposure factor •

•

•

For class 1 conditions, cracks can be tolerated with limited effect on corrosion and appearance.

For class 2 conditions, cracks are to be avoided due to high concern for corrosion and poor appearance.

ratio of flexural of flexural strain to centroid of reinforcement, of reinforcement,



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Control of of Cracking Cracking crack width depends upon •

tensile stress of reinforcement of reinforcement at service levels

•

thickness of concrete of concrete cover on tension face

•

maximum allowed spacing of reinforcement of reinforcement in layer closest to tension face



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Example: Rebar for Crack Control Example 8.14



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Example: Rebar for Crack Control Example 8.14



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Example: Rebar for Crack Control



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Longitudinal Skin Reinforcement Longitudinal skin reinforcement is required for beams with d > 36 in.



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Fatigue on Reinforcement •

•

•

fatigue based upon fluctuation of tension stress during service levels of load of load constant‐amplitude fatigue threshold defined by AASHTO Eq. 5.5.3.2‐1

Keep stress fluctuation below threshold.



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Fatigue on Reinforcement •

•

•

stress levels determined at fatigue I limit state load Use 150% of design of design vehicle live load including dynamic load allowance, in accordance with AASHTO Table 3.4.1‐1. The dynamic load allowance for fatigue is different than for strength. •

15% for fatigue

•

33% for strength

fatigue loading vs. standard design loading •

•

standard live load consists of (truck of (truck with variable axle spacing or a tandem) plus lane load fatigue loading consists of truck of truck only, with fixed axle spacing instead of variable spacing



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Example: Fatigue of of Reinforcement Reinforcement Example 8.16



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Example: Fatigue of of Reinforcement Reinforcement Example 8.16



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Example: Fatigue of of Reinforcement Reinforcement



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Concrete Shear Design •

strut and tie model (AASHTO Sec. 5.6.3) •

•

•

applicable to pile caps, deep footings, and beams with abrupt changes in cross‐ section

sectional model (AASHTO Sec. 5.8.3) •

typical bridge girder and slabs

•

requires element to meet basic beam theory assumptions

simplified model (AASHTO Sec. 5.8.3.4.1) •

non‐prestressed prestressed beams

•

no tension on beam STRC ©2015 Professional Publications, Inc.


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Concrete Shear Design–Simplified Design Method nomenclature As

area of tension of tension reinforcement

Av

area of shear of shear reinforcement perpendicular to flexural tension reinforcement web width

bv d v

effective shear depth

f y

specified yield strength of reinforcing of reinforcing bars

Mn nominal flexural resistance s

spacing of transverse of transverse reinforcement



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Concrete Shear Design–Simplified Design Method β = 2.0 and θ = 45° if the if the following are true. •

For concrete footings, point of zero of zero shear to the face of the of the column, pier, or wall < 3d

•

For other nonprestressed nonprestressed concrete sections, one of the of the following •

•

Not subject to axial tension and contain at least the minimum amount of transverse reinforcement (AASHTO Sec. 5.8.2.5) Overall depth < 16 in



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Concrete Shear Design–Simplified Design Method A simplified procedure is permissible as specified in AASHTO Sec. 5.8.3.4.1. •

shear strength of concrete of concrete AASHTO Eq. 5.8.3.3‐3

•

effective shear depth, d v AASHTO Eq. C5.8.2.9 ‐1

•

•

•

•

the distance between resultants of tensile of tensile and compressive forces due to flexure need not be smaller than 0.9d e or 0.72h (whichever is greater)

nominal shear capacity of vertical of vertical stirrups given by AASHTO Sec. 5.8.3.3 AASHTO Eq. 5.8.3.3‐4



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Concrete Shear Design–Simplified Design Method •

•

•

•

shear stress of concrete of concrete calculated by AASHTO Eq. 5.8.2.9‐1 as

•

•

V n,max= 0.25 f’ f ’ cbvd v resistance factor for shear and torsion given by AASHTO Sec. 5.5.4.2.1

shear stress dictates requirement for maximum spacing of stirrups of stirrups area of shear of shear steel based on minimum requirement total shear strength



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Example: Concrete Beam Shear Strength A 4000 psi normal‐weight concrete beam has a cross‐section of 16 of 16 in wide and 48 in deep. A single level of three of three no. 9 bars is centered 4 in above the bottom of the beam. No. 5 stirrups are spaced 8 in on center, and V u = 200 kips. What is the design strength of the of the beam using the simplified method? Is the simplified method is suitable?



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Example: Concrete Beam Shear Strength A 4000 psi normal‐weight concrete beam has a cross‐section of 16 of 16 in wide and 48 in deep. A single level of three of three no. 9 bars is centered 4 in above the bottom of the beam. No. 5 stirrups are spaced 8 in on center, and V u = 200 kips. What is the design strength of the of the beam using the simplified method? Is the simplified method is suitable?

Verify if the if the simplified method is suitable. If it If it is, the location of the of the tension centroid is 4 in. The depth of the of the equivalent stress block is kips   3 in 2   60   A s f y in 2   a  0.85 f cbw  kips   0.85  4 2  16 in   in   3.31 in



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Example: Concrete Beam Shear Strength The centroid is 0.5a, so the centroid is 1.65 in from the top of the of the cross‐section.

The shear strength of steel, of steel, V s, is

 2   0.31 in   60 2

Effective depth, d v , is

V s 

Av f y d v





s  196.9 kips

d v  48 in  4 in  1.65 in

kips 

  42.35 in 

in 2  8 in

 42.35 in This depth is not less than either 0.9d or or 0.72h by inspection.

The shear strength of concrete, of concrete, V c, is Vc  0.0653bv d v

f c

  0.0653 16 in   42.35 in  4

kips in 2

 88.5 kips STRC ©2015 Professional Publications, Inc.


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Example: Concrete Beam Shear Strength The shear strength of the of the beam, V n, is Vn  Vc  V s  88. 88.5 kip kipss  196.9 kips ips

Vdesign   V n   0.90   285.4 kips 

 285.4 kips The beam’s shear strength is not larger than

 

Vn  0.25 f cbv d v   0.25  4

 677.6 kips

To find the design strength, multiply by the phi factor (resistance factor)

kips 

 16 in   42.35 in 

in 2 

 256.9 kips Check the validity of the of the simplified design method. vu 

V u  bv d v

 0.328 So, V n = 285.4 kips. STRC ©2015 Professional Publications, Inc.




200 kips

 0.9  16 in   42.35 in 

kips in 2

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Example: Concrete Beam Shear Strength Compare the results of the of the simplified design method to

 

0.125 f c   0.125   4

 0.500

Therefore, stirrups cannot be more than 12 in apart [OK].

kips 



in 2 

kips in 2

Since the shear stress is not less than the 0.125 f c check, the spacing of stirrups of stirrups should be less than the smaller of 0.4 of 0.4d v or 12 in. ˊ ˊ

0.4d v = (0.4)(42.35 in) = 17.0 in STRC ©2015 Professional Publications, Inc.


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Example: Concrete Beam Shear Strength The minimum area of steel, of steel, Av , is Av 



0.0316bv s f c f y

 0.0316 16 in   8 in  60

 0.13 in

4

kips in 2

kips in 2

2

Two no. 5 stirrup stems are available. Therefore, the simplified method is appropriate because all limits are met.



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Precast Construction precast concrete •

•

post‐tensioning

any concrete cast in fabrication yard instead of cast of cast‐in‐place on job on job site high‐strength steel cable strung through concrete and tensioned to apply compression force to concrete

cable tightened after concrete has cured transfer time when cable tension is first resisted by concrete mild steel (bonded reinforcement)

pretensioning cable tightened prior to casting of concrete

grade 60 reinforcement added to assembly for a variety of reasons of reasons



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Pretension Construction of force to cable prior to concrete curing. Pretensioning is Pretensioning is the application of force •

Cables are installed in forms and held in place.

•

Cables are tensioned against steel frames placed at the ends of the of the element.

•

Concrete is cast and allowed to cure. (While curing, the concrete bonds with cables.)

•

Once concrete is cured, the steel frames are either removed or integrated as part of the element.



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Post‐Tension Construction •

•

•

Locations of cables of cables are installed in forms and held in place. •

pipe or other materials may be used to separate concrete and cable

•

grease of cable of cable may be sufficient

Concrete is cast and allowed to cure. (While curing, the concrete does not bond with cables.) Cables are tensioned against ends of the of the element.



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Prestress Engineering •

Design calculations are based upon uncracked concrete elements

•

A, I , S •

calculations based upon elastic mechanic stress theory  

•

P



•

M S

•

cable force intended to apply sufficient compression stress into concrete to prevent large tension stresses from occurring

Cable at centroid of cross of cross‐section is the uniform compression stress over entire cross‐section. Eccentricity of cable, of cable, e, is the offset distance from centroid to develop moment on cross‐section. Most stress calculations are similar, whether or not the section is pretensioned or post‐tensioned.



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Prestress Engineering design for flexure focuses on

history of load of load application

•

maximum stress in tension zone

•

•

maximum stress in compression zone

•

•

•

stresses at transfer stresses at application of post of post‐ construction dead load stresses at application of live of live load stresses at additional loads (wind, seismic, etc.)



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Transfer Conditions AASHTO Sec. 5.9.4.1 specifies the allowable stresses in concrete at the time of cable of cable force transfer.

nomenclature

f ti

top fiber stress immediately after prestress prestress transfer transfer and before time‐dependent prestress prestress losses

f bi

bottom bottom fiber fiber stress immediately after prestress prestress transfer transfer and before time‐dependent prestress prestress losses



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Transfer Conditions AASHTO requirements for stress at time of cable of cable force transfer •

•

maximum allowable stress in pretensioned tendons immediately prior to transfer

nomenclature

f pbt allowable stress in prestressing steel prior to prestress transfer f pt

stress in the prestressing prestressing steel immediately after transfer

maximum allowable stress in post‐ tensioned tendons immediately after transfer



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Example: Determine Kern Point A post‐tensioned beam has a rectangular cross‐section with width b and height h. Determine the kern point (the largest eccentricity of cable of cable from the centroid) if the cross‐section is to be entirely in compression once the post‐tensioning force is applied.



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Example: Determine Kern Point A post‐tensioned beam has a rectangular cross‐section with width b and height h. Determine the kern point (the largest eccentricity of cable of cable from the centroid) if the cross‐section is to be entirely in compression once the post‐tensioning force is applied.

Use elastic mechanics equations.  

P



M S

The first moment on cross‐section is P e, the tensioning force at distance e.



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Example: Determine Kern Point If the If the cross section is to be fully compressed, then stress in the formula should be zero.  

P 1 P 1e



g

0

Sb

g



e

Sb

P 1 P 1e



P1e Sb



M g Pi

 

M g



Sb

g

S b g

S b



P 1 Ag

P 1 Ag STRC ©2015 Professional Publications, Inc.


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Service Load Conditions •

•

•

•

•

stresses calculated using elastic mechanics service load conditions specified by AASHTO load factors for service load combinations load combinations typically = 1.0 allowable stresses of concrete of concrete and steel developed with factor of safety of safety existence of mild of mild steel usually ignored when high strength cables are used



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Example: Service Level Load Conditions Example 8.19



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Example: Service Level Load Conditions



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60

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Ultimate Strength of of Precast Precast Beams •

•

Beams are usually checked for their plastic bending strength. Compare with ultimate level load combinations. (Use strength combination load factors.)

ultimate strength •

•

•

plastic bending strength phi factors as reductions include contribution from mild steel



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Ultimate Strength of of Precast Precast Beams ultimate cable strength •

AASHTO Eq. 5.7.3.1.1‐1

after all strength losses, if a if a cable is expected to have ≥ 0.5 f pu •

•

assumes the center of the of the prestressing prestressing cable is at a distance, d p, from the extreme compression fiber = adjustment for steel type and k = strength



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Ultimate Strength of of Precast Precast Beams compression zone •

•

compression zone factor,  , is given in AASHTO Sec. 5.7.2.2 as

depth of compression of compression zone, considering prestress cable and tension mild steel



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Example: Ultimate Load Conditions Example 8.20



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Example: Ultimate Load Conditions Example 8.20



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Example: Ultimate Load Conditions



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Poll: Ultimate vs. Service Conditions Which of the of the following issues is related to ultimate level load combinations and NOT service load combinations? (A) safety against catastrophic loading (B) deflection of beam of beam (C) stress at time of transfer of transfer (D) fatigue life



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Poll: Ultimate vs. Service Conditions Which of the of the following issues is related to ultimate level load combinations and NOT service load combinations? (A) safety against catastrophic loading (B) deflection of beam of beam

The purpose of checking of checking the ultimate conditions is to ensure that the beam will be able to support the rare but possible peak moment that might occur. The answer is answer is (A).

(C) stress at time of transfer of transfer (D) fatigue life



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Example: Composite Cross‐Section For the composite cross‐section shown, the prestress force is 500 kips. All concrete is 5 ksi. Topping is added after transfer. The self ‐weight of the of the T‐beam alone is 60 ft‐kips. The self ‐weight of the of the T‐beam with topping is 80 ft‐kips. The superimposed dead load is 100 ft‐kips. The live load (with AASHTO impact) is 200 ft‐kips. Determine (a) the peak tension stress prior to transfer, and (b) the peak compression stress after all loads are applied. STRC ©2015 Professional Publications, Inc.


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Example: Composite Cross‐Section For (a), consider the original T‐section only. Locate the centroid at distance yT from base.

 yA  A  20 in   4 in   20 in    9 in  12 in   18 in    4 in   20 in   12 in  18 in 

yT 

i

i

 11.97 in



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Example: Composite Cross‐Section Determine I , the second moment of inertia of the of the T‐Beam. I   I o  Ad 2



 20 in   4 in  12

3

   4 in    20 in  

in  11.97 in in     20 in 2

12 in  18 in  12

 12 in  18 in   9 in  11.97 in   13,002 in

3

2

4



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Example: Composite Cross‐Section Determine the section modulus for the bottom fiber. s bottom 

I y



13, 13, 002 in 4 11.97 in

 1086 in

3

Determine the section modulus for the top fiber. stop 

I y  h



 1296 in

13, 13, 002 in 4 11.97 in in  22 in

 1296 in

3

3



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Example: Composite Cross‐Section Consider the maximum tension stress on the bottom fiber before transfer. Determine the stress on the original T‐ section. The tension stress on the bottom of the of the beam, f b, is f b 

M SW s bottom

 663

 

 60 ft-kips  12 

in  

lbf  1000   ft   kip 

1086 in 3

lbf in 2



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Example: Composite Cross‐Section For (b), use the properties for the entire cross‐section.

Determine I , the second moment of inertia of the of the full cross‐section.

Locate the centroid at a distance, yT , from base.

I   I o  Ad 2

 yA  A 11.97 in   296 in    23 in   20 in   2 in    296 in    20 in   2 in 

yT 

i

i

2

2

 13.29 in

002 in   296 in  13.29 in  11.97 in   13, 00 4

2



  20 in   2 in     20 in   2 in     12      23 in  13.29 in    3

2

17, 301 in  17,301



2

4

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Example: Composite Cross‐Section Determine the section modulus, s, for the bottom fiber. s bottom 

I y



17,301 17, 301 in 4

The compression stress on top of the of the beam is

13.29 in

 1302 in

For (b), calculate the maximum compression stress on the top fiber due to external loads.

3

80 ftft-kip  100 ftft-kip  200 ftft-kip  Determine the section modulus, s, for the top fiber. f c  stop 

I h y



17,301 in 4 24 in in  13.29 in

 1615 in

 M  all

stop

3

 2824



lbf   in    12  1000 ft   kips   1615 in 3

lbf in 2

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Example: Composite Cross‐Section Calculate the composite section modulus at the top of the of the original section. Check stresses at that location against stresses at the top of the of the topping. S top,original 

17301 in 4 24 in  13.29 in  2 in

 1986 in

3

 60 ft-kips  12 

f b 

1296 in

in 



ft 

3

0.56 kips in  0.56

2

Therefore, the final stress on top fiber is f top  f c  2824 lb lbf in 2

f c 

ft-kips kips  100 100 ftft-ki kips ps    80 ftin  12     ft   200 ft-kips  

1986 in 3  2.30 kips in 2

f top,original  2300

 560

in 2  2860 lbf in 2



lbf

lbf

in 2  governs

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Cracking Moment for Prestressed Beams •

•

•

Estimate when tension stress reaches the level for a crack to form.

•

γ values are related to prestressing and mild steel strength.

Use the concrete modulus of rupture of rupture as the expected tensile strength. AASHTO formula

AASHTO Eq. 5.7.3.3.2‐1



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Example: Cracking Moment Example 8.21



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Example: Cracking Moment Example 8.21



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Example: Cracking Moment



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Shear Strength of of Prestressed Prestressed Beams nomenclature

of prestressing essing steel A ps area of prestr of shear reinforcement Av area of shear

bv

web width

d v effective shear depth f  c

specified compressive strength of concrete of concrete

f cpe compressive stress in concrete, due to final prestressing force only, at bottom fiber of the of the section f pc compressive stress in the concrete, due to final prestressing force and applied loads resisted by precast member, at centroid of composite of composite section of member required f ps average stress in prestressing steel when nominal resistance of member STRC ©2015 Professional Publications, Inc.


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f r

modulus of rupture of rupture

f y

specified yield strength strength of reinforcing of reinforcing bars moment causing flexural cracking at section due to externally applied loads

M cre

unfactored dead load moment acting on precast member M dnc total unfactored

M max maximum factored moment at section due to externally applied loads M n nominal flexural resistance s S c

longitudinal spacing of shear of shear reinforcement

section modulus at the bottom of the of the composite member

of the precast member S nc section modulus at the bottom of the STRC ©2015 Professional Publications, Inc.


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nominal shear strength provided by concrete

V c

V ci

nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment

V cw nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in the web V d

shear force at section due to unfactored unfactored dead load

V i

factored shear force at section due to externally applied loads occurring simultaneously with M max

V p

vertical component of effective of effective prestress force at section



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Shear Strength of of Prestressed Prestressed Beams •

•

shear strength calculated at ultimate level forces

•

moment causing flexural cracking

shear strength of concrete of concrete nominal shear capacity of concrete, of concrete, V c , given by lesser value of V V ci or V cw

AASHTO Eq. 5.8.3.4.3‐2 •

nominal shear capacity given by

AASHTO Eq. 5.8.3.4.3‐1



AASHTO Eq. 5.8.3.4.3‐3

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Shear Strength of of Prestressed Prestressed Beams •

nominal shear capacity of vertical of vertical shear reinforcement

•

Effective shear depth, d v, is the distance between the results of the of the tensile and compressive forces due to flexure.

AASHTO Eq. C5.8.2.9‐1

AASHTO Eq. 5.8.3.3‐4



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Shear Strength of of Prestressed Prestressed Beams adjustment and factors •

•

•

slope of prestr of prestressing essing cable causes a vertical force on the beam shear stress on concrete resistance factor (phi value) given by AASHTO Sec. 5.5.4.2.1 as ∅  0.90



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Example: Shear Strength of of Precast Precast Girder Example 8.22



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Example: Shear Strength of of Precast Precast Girder



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92

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95

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Friction Losses •

•

•

Friction of the of the cable is based on both wobble and curvature. AASHTO determines friction loss, from the equation

,

For prestressing prestressing cable, values of wobble and curvature friction coefficients are given in AASHTO Table 5.9.5.2.2b‐1 as



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Example: Friction Losses Example 8.23



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Example: Friction Losses Illustration for Illustration for Ex. Ex. 8.22 and Ex. and Ex. 8.23



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Example: Friction Losses



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Elastic Shortening Losses nomenclature

of elasticity of concrete of concrete at time of initial of initial prestress E ci modulus of elasticity

E p

modulus of elasticity of elasticity of prestr of prestressing essing steel

of prestressing essing steel due to prestress prestress and self ‐ F cgp compressive stress at centroid of prestr weight of girder of girder at transfer

ni

modular ratio at transfer

N

number of identical of identical prestressing prestressing tendons

 f

loss of prestr of prestress ess due to elastic shortening

pES



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Elastic Shortening Losses •

•

Prestressing force is reduced because it compresses the original concrete length. Losses occur due to the elastic shortening of concrete. of concrete.

(calculated at centroid of concrete of concrete cross‐section) •

•

•

For a pretensioned beam, the loss of prestress due to elastic shortening is given by AASHTO Sec. 5.9.5.2.3a as

For a post‐tensioned beam, AASHTO Sec. 5.9.5.2.3b gives the loss of prestress as

modular ratio of transfer, of transfer,



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Elastic Shortening Losses calculation procedure 1. Assu ssume a force loss due to elastic shortening. 2. Calc Calcul ulat ate e stress loss using provided formulas. 3. Mult Multip iply ly stress loss by area of prestress prestress to get force loss. 4. Check force loss against assumed value and then iterate if necessary. if necessary.



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Example: Elastic Shortening Losses The beam of Ex. of Ex. 8.23 is prestressed rather than post‐tensioned. The concrete strength at transfer is 4.5 ksi, and the force at midspan is 1000 kips, which considers friction losses but not elastic shortening. The moment of inertia of inertia is 589,680 in4. Determ Determine ine the loss of prestressed force due to elastic shortening.



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Example: Friction Losses Illustration for Illustration for Ex. Ex. 8.23



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Example: Elastic Shortening Losses The modular ratio at transfer is

Estimating that a 8% loss will occur due to elastic shortening, the force in the prestressing prestressing member immediately after transfer is

The modulus of elasticity of elasticity of the of the concrete at transfer is

Pi   P o  1  0.08 kips   0.92   1000 ki

 920 kips AASHTO Eq. C5.4.2.4 ‐1



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Example: Elastic Shortening Losses If the If the loss is 4%, the concrete stress at the centroid of the of the prestressing member, f cgp , is then

 1 e  eM f  P   A  I   I    1 in  30.8 in  800 in   920 kips   589, 680 in  589, 

For a prestressed prestressed beam,

 f

pES

2

i

cgp

2

2

g

cgp

kips    n f   7.38  2.011  in   14.8 ki kips in  14.

i

g

g

g

2

4



2

    

 f

pES

kips    P  A f   5.36 in  14.8  in    79.5 kips 2

ES

ps

pES

2

in  12,50 12,500 0 inin-kips   30.8 in 589, 589, 680 in 4

2.011 1 kips kips in  2.01

2



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Long Term Losses of of Prestress Prestress Force Prestress force is reduced after transfer (i.e., the time when the cables are released). creep deformation of the of the concrete due to sustained loading shrinkage reduction in concrete volume due to water loss during curing relaxation steel cable at high tension slowly stretches



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Long Term Loss AASHTO Eq. 5.9.5.3‐1 estimates long‐ term prestress prestress loss, ∆ f pLT , due to creep of concrete, shrinkage of concrete, of concrete, and relaxation of steel. of steel.



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Example: Long Term Losses Example 8.25



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Example: Long Term Losses Example 8.25



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Example: Long Term Losses



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Poll: Sources of of Prestress Prestress Losses Which of the of the following is not a loss that occurs at the time or prior to transfer? (A) elastic shortening (B) creep (C) curvature friction (D) wobble friction



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Poll: Sources of of Prestress Prestress Losses Which of the of the following is not a loss that occurs at the time or prior to transfer? (A) elastic shortening (B) creep

Creep is the deformation of a of a material due to sustained loading. It occurs during several years after the prestressing tendons are installed and tensioned. The answer is answer is (B).

(C) curvature friction (D) wobble friction



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Learning Objectives You have learned how to •

•

•

•

•

determine the ultimate bending strength of concrete of concrete beams

•

determine shear strength

•

determine detailing of steel of steel reinforcement

•

determine the cracking moment of beams

describe various precast construction practices design composite construction of precast concrete use AASHTO to estimate prestress losses

verify the fatigue and other service level conditions for concrete STRC ©2015 Professional Publications, Inc.


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Lesson Overview •

Concrete Beams for Bridges •

•

Cast‐in‐Place concrete with Grade 60 Reinforcement Precast Concrete Beams with High‐Strength Steel Cable

•

Bending Moment Strength

•

Shear Strength

•

Deflection and Fatigue

•

AASHTO Requirements



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STRC14 Bridges Concrete Members 0716

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