InstructionsThis spreadsheet will analyse a simply supported, rectangular, pre-stress concrete beamClick on the Stresses tab at the bottom of the worksheet to determine an acceptable size for the beamThe size will be determined by the moments that the beam are subjected to.if you are not sure what to enter in a cell, just hold the cursor over the cell marked with a red tab in the cornerand a comment with some advice will be displayedEnter values (in the green cells) for the dead and imposed moments and trial values for P, e and ZNOTE so that formulae are not accidently overwritten, the cells have been 'locked'.If you wish to change a 'locked cell' - for example, if you do not have a rectangular cross section, you may wish to insert your own values for Ig and Zchoose Tools, Protection, Protect Sheet. The click on the protect worksheet and contents of locked cells check box

like this

Stressesenter the beam specification and loads here and see if the concrete stresses have been exceededLOADINGMoment Due to Dead load (Md)0kN-mMoment Due to Superimposed Dead Load (Msi)0kN-mMoment due to imposed load (Mi)0kN-mTransfer Moment (Mt)0kN-mMaximum Service moment0kN-mUltimate moment0kN-mCONCRETE SPECIFICATIONConcrete cube strength (fcu)50MPaType of prestressingConcrete Strength at Transfer (fci)50MPaConcrete modulus of Elasticity (Ec)32000MPa2partial material safety factor for concrete1.5plottingArea of Pre-stress3000mm2workingtransferfcwftwfctfttUltimate strength of Pre-stress1616MPa-10-11.7647058824-16.53.1819805153-25.03.180Pre-stress modulus of elasticity205000MPa-10-11.7647058824-16.53.1819805153-25.03.18100partial materail safety factor for pre-stress1.05Peff100kNstress in pre-stress at transfer39MPa0eccentricity e0mmcheck beam is deep enough to achieve this eccentricity% loss of prestress15%P Transfer118kNMax allowable concrete compressive stress - Working (fcs)16.5MPaMethod of prestressingMax allowable concrete tensile stress - Working (fts)3.18MPaMax allowable concrete compressive stress - Transfer (fct)25MPaMax allowable concrete tensile stress - Transfer (ftt)3.18MPaClass of Prestresssed MemberZmin0.000E+00mm3Beam DimensionsOverall Depth D100mmBreadth B100mmeffective depth50mmGross area (A)1.00E+04mm2Actual Section Modulus, Bottom Fibre (Zbot)1.67E+05mm30Actual Section Modulus, Top Fibre (Ztop)1.67E+05mm30Gross second moment of area (Ig)8.33E+06mm4ytop50ybot50Working stress - TOP-10.00MPastress okayWorking stress - Bottom-10.00MPastress okayTransfer stress - Top-11.76MPastress okayTransfer stress - Bottom-11.76MPastress okay

Stresses

service stresses (working)Transfer StressesfcwftwfctfttStress (MPa)Depth from soffet of beam (mm)Concrete Stresses

profilethis spreadsheet calculates the allowable cable profile for the beam entered in the 'stresses' spreadsheet.enter the minimum and maximum moments that occur along the beam and the graph will plot the allowable cable profilestress in the bottom fibre at transfer governsstress in the top fibre at transfer governsstress in the bottom fibre at working governsstress in the top fibre working governs% distance from endmin momentmax momente000-19-2122110.163.3683.52-557-560-813-8240.2115.2149.76-998-1000-1476-148757.60.3155.52198.72-1341-1343-1965-197676.80.4184.32230.4-1585-1588-2282-22930.5201.6244.8-1732-1735-2426-24370.6207.36241.92-1781-1784-2397-24080.7201.6221.76-1732-1735-2196-22070.8184.32184.32-1585-1588-1821-18320.9155.52129.6-1341-1343-1274-12851115.257.6-998-1000-554-565

This is a moment due to a dead load that is applied after the prestressing of the concrete.This is the moment due to self weight and occurs before the concrete is stressedThis is the moment due to the imposed load and occurs after the stressing of the concreteThis is the strength of the concrete when the beam is stressed. Usually stressing occurs at about 10 days and so the transfer strength will be approximately 60% of the cube strength, however it is possible to stress after 28 days and then the transfer strength will equal the cube strengthYou specify the concrete strength that you wish to use. Usually for pre-stressed concrete, good quality concrete is specified (say 30 MPa and above)This is the distance from the centroid of the concrete cross section to the centroid of the prestressingPre-stress has both initial losses (such as elastic shortening due to the pre-stress) and time dependant losses (such as shrinkage of concrete). These losses reduce the initial value of pre-stress to effective values. Losses are usually in the order of 15%-25%This is the force in the pre-stress when the concrete is first stressed (ie. before losses hae occurred). Too little pre-stressing force and the beam will not be able to resist the applied moments, too much pre-stressing and the beam will fail in the opposite direction (i.e there is not enough applied load to hold the beam down.Class 1 pre-stress is very high quality and will have no tensile stresses in it. It is more expensive, but ensures that no cracking can possibly occur as the whole section is in compression. Typical uses of class 1 pre-stress are bridges and water retaining structures.

Class 2 pre-stress allows small tensile stresses in the concrete. These stresses are less than the tensile strength of the concrete and therefore cracking should still not occur. This is the most common form of pre-stress, although class 3 (which is not covered in this course) is becoming increasingly popular.A balance must be struck between the stresses due to the applied loads and the stresses dut to the pre-stress. If the section modulus of the beams is not greater than Zmin then there is no possible amount of pre-stressing that can satisfy these competing conditions.

Zmin > (Mmax-Mmin)/(ftw-fcw)This is the force in the pre-stress when the concrete is in the 'in-service' condition(i.e. after the losses have occurred). Too little pre-stressing force and the beam will not be able to resist the applied moments, too much pre-stressing and the beam will fail in the opposite direction (i.e there is not enough applied load to hold the beam down.There are 3 main types of prestressing steel.1 Strand fpu = 1770 Mpa E = 195 000 MPa2 wire fpu = 1570 Mpa E = 205 000 MPa3 bars fpu = 1030 Mpa E=206 000 MPaeffective depth is the distance from the extreme compressive fibre to the pre-stressThis is the moment when the beam is stressed. It is usually equal to the moment due to dead.This is the maximum moment (without load factors) that will be applied to the beam.Msmax = Md + Msi + MiThis is the moment that will cause the beam to fail in its ultimate limit state (i.e. Break ) and includes load factorsMu = 1.4 (Md + Msi) + 1.6 Mifcs = allowable compressive stress for the in service condition it is given in Cl 4.3.4.2 for simply supported members fcs = 0.33 fcufcs = allowable tensile stress for the in service condition it is given in Cl 4.3.4.3 Class 1 fts = 0 - i.e. No tensile stressesClass 2 fts = 0.45 fcu - pre-tensioned = 0.36 fcu - post-tensionedfct = allowable compressive stress at transfer and is given in Cl 4.3.5.1 fct = 0.5 fci at the extreme fibre fct = 0.4fci for near uniform stress distributionsftt = allowable tensile stress at transfer and is given in Cl 4.3.5.2 Class 1 ftw = 1 MPaClass 2 ftw = 0.45 fci - pre-tensioned = 0.36 fci - post-tensionedA= B * DZ= BD2/6Z= BD2/6=-Peff/A + Peff e/Z - M/Z=-Peff/A - Peff e/Z + M/Z=-Pt/A + Pt e/Z - M/Z=-Pt/A -Pt e/Z + M/ZIg = BD3/12This should be approximately 75% of fpu/gmPre-stressed concrete can be either pre-tensioned or post tensioned.

Pre-tensioned means that the pre-stressing is tensioned before the concrete is poured. This is usually done at a pre-casting yard. Pre-tensioned concrete usually has better quality control and therefore superior properties, but is only suitable for members that can be transported to site.

Post-tensioned concrete is tensioned after the concrete is poured and is the more flexible method of construction as any size member can be made, but the properties are generally not as good and construction times are longer.StrandWireBarsThere are 3 main types of prestressing steel.

1 Strand (normally used for post-tensioned)fpu = 1770 Mpa E = 195 000 MPa

2 wire (normally used for pre-tensioned)fpu = 1570 Mpa E = 205 000 Mpa

3 bars fpu = 1030 Mpa E=206 000 MPaDistance from neutral axis to extreme fibre of beamDistance from neutral axis to bottom fibre of beamThe spreadsheet assumes a rectangular cross section, but you can enter any section properties you like, just remember that the formulas will be overwritten if you do.

profile

Top Fibre Failure - In Service (e>)Bottom Fibre Failure - In Service (e>)Bottom Fibre Failure - Transfer (e