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Department of Civil Engineering, Faculty of Engineering, Mahidol UniversityEGCE 406: Bridge DesignHomework 4 (Due Tuesday, September 14th 2010)

Develop an Excel worksheet to calculate the stresses in a prestressed concrete

member at initial and service stages based on AASHTO LRFD Specifications. The

worksheet must have the following features:

Able to input material and section properties Able to input the prestressing force, number of strand, and eccentricity. Able to input (or calculate) moments due to dead load, superimposed dead

loads, and live loads on a simple-supported member.

Able to calculate allowable stresses from the input compressive strengthaccording to the AASHTO specifications.

Able to calculate stresses on the top and bottom fiber in the member for initial(immediately after transfer) and final (service) stages.

Able to plot a simple feasible domain for the critical section Able to plot prestress envelope at every 10% of the span

The example given in class may be used as a guideline and to check your results.

However, you do not need to follow it closely (you may be as creative as you want).

After successfully develop the worksheet, use this worksheet to find the number of

strands and the tendon profile for the following beam:

Assume

fci = 40 MPa, fc = 55 MPa,

fpu = 1860 MPa, fpi = 1300 MPa,

= 0.8, fpe = 1040 MPa

Aps (each) = 98.71 mm2

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PrestressedConcreteBeam AASHTOLRFDMaterials Concrete PrestressingSteel

f'ci 40 MPa fpu 1860 MPa 0.8

f'c 55 MPa fpi 1300 MPa fpe 1040 MPa

Section Concrete PrestressingSteel

Ac 131250 mm^2 Zt

1.91.E+07 mm^3 #strands 4

Ic 3.04E+09 mm^4 Zb 8.91.E+06 mm^3 Aps(each) 98.71 mm^2 Fi 513292

yt 158.9 mm kt 67.91 mm Aps 394.84 mm^2 F 410634 kN

yb 341.07 mm kb 145.76 mm e0 266.07 mm 1/Fi 1.948E06 kN

Load

Span mm MidspanMoments

WD N/mm MD 7.30E+07 Nmm 73 kNm

WSD N/mm MSD 1.00E+07 Nmm 10 kNm

WL N/mm ML 8.17E+07 Nmm 82 kNm

WT N/mm MT 1.45E+08 Nmm 145 kNm

AASHTOAllowableStress

fti = 0.25(f'ci)

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FeasibleDomain

e0(inch)

= 0.8 0 3.00E06 1/Fi

MminftiZt = 9.94E+07 146 444 I

Mmin+fciZb = 2.87E+08 68 793 II

MmaxfcsZt = 4.11E+08 146 1394 IIIa

MmaxfcsZt = 3.08E+08 146 2162 IIIb

MmaxfcsZt = 4.87E+08 146 1679 IIIc

Mmax+ftsZb = 9.53E+07 68 289 IV

dc,min = 75 mm 266 266 V

Donotdele 341.07 341. 07

600

400

200

0

200

400

600

0.0E+00 5.0E07 1.0E06 1.5E06 2.0E06 2.5E06 3.0E06

e0

(mm)

1/Fi

CaseI

CaseII

CaseIIIa

CaseIIIb

CaseIIIc

CaseIV

CaseV

yb

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