aashto-n

AASHTO Shear Calculator, No Stirrups

This will calculate the shear strength for a beam that doesn't have minimum stirrups in it. Recall that minimum stirrups in the code are one root of the concrete strength.That is, a 2500 psi concrete has a minimum stirrup level of 50 psi, but 10,000 psi concrete requires 100 psi of stirrups

Purpose: A non-iterative technique is provided that will doubly interpolate in the tables and calculate the shear strengthfor the given level crack spacing and moment to shear ratio. No macros or goal seeks are used.Stirrups may be specified and will be included.

Units US customary units or SI metric units. Internal Calculations are done in US units

Method: This spreadsheet works identically to the one with stirrups. Rather than interpolating with level of stirrups, however, it uses crack spacing.for each value of ex, the beta and theta values are interpolated at the given level of crack spacingThese values are used to calculate moment and shears, and the final answer is interpolated from that.

Usage: Fill in the yellow cells below and the shear strength will show up in the green cells to the right of the yellow ones.The spreadsheet ends with an interaction diagram

License: This spreadsheet was written by Evan Bentz, March 1999/Jan 2000. Permission is given to use, copy, duplicate and dissect this spreadsheet in any way.

Limits: This version (so far), has mistakes if phi is anything but 1.0.

Code Values of Beta and ThetaThese are taken directly from the spreadsheet used to make the code tables. They are from the 2000 revision of the shear chapter

Theta sxe \ ex -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 25 25.4 25.5 25.9 26.4 27.7 28.9 30.9 32.4 33.7 35.6 37.2

10 27.6 27.6 28.3 29.3 31.6 33.5 36.3 38.4 40.1 42.7 44.715 29.5 29.5 29.7 31.1 34.1 36.5 39.9 42.4 44.4 47.4 49.720 31.2 31.2 31.2 32.3 36.0 38.8 42.7 45.5 47.6 50.9 53.430 34.1 34.1 34.1 34.2 38.9 42.3 46.9 50.1 52.6 56.2 59.040 36.6 36.6 36.6 36.6 41.1 45.0 50.2 53.7 56.3 60.2 63.060 40.8 40.8 40.8 40.8 44.5 49.2 55.1 58.9 61.8 65.8 68.680 44.3 44.3 44.3 44.3 47.1 52.3 58.7 62.8 65.7 69.7 72.4

Beta sxe \ ex -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 25 6.362 6.058 5.556 5.152 4.414 3.905 3.260 2.862 2.584 2.209 1.961

10 5.776 5.777 5.376 4.892 4.053 3.524 2.882 2.498 2.234 1.884 1.65415 5.337 5.337 5.270 4.728 3.821 3.275 2.639 2.265 2.011 1.676 1.45820 4.988 4.988 4.987 4.608 3.647 3.089 2.458 2.093 1.846 1.523 1.31330 4.456 4.456 4.456 4.434 3.389 2.817 2.193 1.841 1.605 1.300 1.10340 4.062 4.062 4.062 4.062 3.197 2.616 1.999 1.657 1.431 1.139 0.95460 3.496 3.496 3.496 3.496 2.915 2.323 1.721 1.396 1.183 0.916 0.75080 3.099 3.099 3.099 3.099 2.706 2.110 1.522 1.210 1.011 0.764 0.616

Input ParametersFill in each yellow cell. Units: m (m or u for Metric or US units)

Material Properties 35 MPa Concrete compressive strengthfy-long 550 MPa Yield strength of longitudinal non-prestressed reinforcement

fp0 1300 MPa Jacking stress in prestressing strands (0.7 fpu generally)fpy 1675 MPa "yield" of prestressing strands ( 0.9 fpu generall)

Geometry of section dv 833 mm Flexural level arm at given sectionbv 300 mm Web width Ac 325000 mm2 Concrete area of bottom half of section (for compression in bottom chord)As 2800 mm2 Non prestressed longitudinal reinforcement

Aps 0 mm2 Prestressed longitudinal reinforcementsxe 900 mm Effective crack spacing

stirrups 0 MPa Quantity of stirrups (Av.fy/bw.s)Vp 0 kN Vertical component of prestressing force

Loading M/V 1.7 m Moment to shear ratio at given sectionNu 0 kN Applied Axial Load (tension = positive)

Final CapacityUS units SI units

Moment 252 kip-ft Moment 341.184 kNmShear 45 kips Shear 201 kN

Converted Parameters from above listing

5075 psi dv 32.7953 inchEffective Crack Spacing 35.4331 inch bv 11.811 inch

EsAp+EpAps 125860 kips M/V 5.57743 ftFe 0.05796 Asfy+Apsfpu 346.116 kips

As 4.34001 fy-long 79.75 ksi

Aps 0 Nu 0 kipsfp0 188.5 ksi phi 1.00 (not tested yet)fpy 242.875 ksi Vp 0 kips

stirrups 0 psi Ac 503.759

Crack SpacingThis allows interpolation of beta and theta to work the same way as it does for the case with stirrups.

spacing -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 25 5 5 5 5 5 5 5 5 5 5 5

10 10 10 10 10 10 10 10 10 10 10 1015 15 15 15 15 15 15 15 15 15 15 1520 20 20 20 20 20 20 20 20 20 20 2030 30 30 30 30 30 30 30 30 30 30 3040 40 40 40 40 40 40 40 40 40 40 4060 60 60 60 60 60 60 60 60 60 60 6080 80 80 80 80 80 80 80 80 80 80 80

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AASHTO Interaction Diagram

Moment (kip.ft)

Sh

ear

(kip

s)

Interpolate ThetaEach of these values is interpolated from the code charts based on crack spacing.Take a look at the equations to see how it's done. The top row is different than all the bottom cells

min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 top row of tablenormal 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 lower rows

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.035.5 35.5 35.5 35.5 40.1 43.8 48.7 52.1 54.6 58.4 61.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

max 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 bottom row

final theta 35.5 35.5 35.5 35.5 40.1 43.8 48.7 52.1 54.6 58.4 61.2

Interpolate BetaThis is done the same way as the beta table above


0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.004.24 4.24 4.24 4.23 3.28 2.71 2.09 1.74 1.51 1.21 1.020.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

max 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 bottom row

final beta 4.24 4.24 4.24 4.23 3.28 2.71 2.09 1.74 1.51 1.21 1.02

Final Calculations

Equation Variable Max M Vs/2+Vp V=05.8.3.3-3 Vc 117.0 117.0 117.0 116.8 90.6 74.7 57.6 48.0 41.7 33.5 28.2 28.2 0.2 0.1 kips5.8.3.3-4 Vs 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.1 kips5.8.3.3-1 Vc+Vs+Vp 117.0 117.0 117.0 116.8 90.6 74.7 57.6 48.0 41.7 33.5 28.2 28.2 0.4 0.2 kips5.8.3.3-2 Final V 117.0 117.0 117.0 116.8 90.6 74.7 57.6 48.0 41.7 33.5 28.2 28.2 0.4 0.2 kips

Fe 0.06 0.06 0.06 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.005.8.3.4.2-2 Moment -1411.3 -817.9 -521.1 -223.6 -103.9 -20.5 102.8 206.8 303.5 487.8 666.7

yield theta 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.2 61.25.8.3.5-1 long yield 769.7 769.7 769.7 770.1 809.4 833.4 859.2 873.6 883.2 895.5 903.4 903.4 945.3 945.9 kip.feet

final M -1411.3 -817.9 -521.1 -223.6 -103.9 -20.5 102.8 206.8 303.5 487.8 666.7 903.4 945.3 945.9 kip.feetM/V (ft) -12.1 -7.0 -4.5 -1.9 -1.1 -0.3 1.8 4.3 7.3 14.6 23.6 32.0 2363.3 4729.6 feet

Interpolate VWe could do this with the M/V ratio as an interpolation index, but the following way is better for cases near or controlled by yield.the m and b are the shear intercept and slope of the line on the interaction diagram

m 0.000 0.000 -0.001 -0.218 -0.191 -0.139 -0.092 -0.066 -0.045 -0.029 0.000 -0.664 lastb 117.0 117.0 116.6 67.9 70.8 71.9 67.1 61.7 55.2 47.8 28.2 628.2 columnmoment 0 0 0 0 0 0 0 252 0 0 0 0 0 kip.feetshear 0 0 0 0 0 0 0 45 0 0 0 0 0 kips

Check Max V at M=dv*VAASHTO has a limit that the M in the equations not be taken as less than V*dv. To account for this, find shear at that moment and limit answer to that value.

m/v = dv 2.73 feetmoment 0 0 0 0 0 0 146 0 0 0 0 0 0 kip.feetshear 0 0 0 0 0 0 54 0 0 0 0 0 0 kips

Extra line on plot M 0 146 kip.feetV 54 54 kips

Activate limit on the shear if necessaryratio of V/limit 0.841496 If this is greater than 1, then we have calculated a shear higher than that from M=Vdv and should pro-rate it.final capacity M 252 kip.feet

V 45 kips

Interaction DiagramThis is the AASHTO shear-moment interaction diagram for this section. The line indicates the given moment to shear ratio.

Loading Line M 0 252V 0 45

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70AASHTO Interaction Diagram: Less than minimum stirrups

Moment (kip.ft)

Sh

ear

(kip

s)

AASHTO Calculator for cases with at least minimum reinforcement

This will calculate the shear strength for a beam that has at least minimum stirrups in it. Recall that minimum stirrups in the code are one root of the concrete strength.That is, a 2500 psi concrete has a minimum stirrup level of 50 psi, but 10,000 psi concrete requires 100 psi of stirrups

Purpose: A non-iterative technique is provided that will doubly interpolate in the tables and calculate the shear strengthfor the given level of stirrups and moment to shear ratio. No macros or goal seeking are used.

Units US customary units or SI metric units. Internal Calculations are done in US units

Method: The quantity of stirrups is calculated for each cell in the beta-theta table.for each value of ex, the beta and theta values are interpolated at the provided level of transverse reinforcementThese values are used to calculate moment and shears, and the final answer is interpolated from that.

Usage: Fill in the yellow cells below and the shear strength will show up in the green cells to the right of the yellow ones.The spreadsheet ends with an interaction diagram.

License: This spreadsheet was written by Evan Bentz, March 1999/Jan 2000. Permission is given to use, copy, duplicate and dissect this spreadsheet in any way.

Limits: This version (so far) has mistakes if phi is anything but 1.0.

Code Values of Beta and ThetaThese are taken directly from the spreadsheet used to make the code tables. They are from the 2000 revision of the shear chapter

Theta v/fc' \ ex -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 20.075 22.3 20.4 21 21.8 24.3 26.6 30.5 33.7 36.4 40.8 43.9

0.1 18.1 20.4 21.4 22.5 24.9 27.1 30.8 34 36.7 40.8 43.10.125 19.9 21.9 22.8 23.7 25.9 27.9 31.4 34.4 37 41 43.20.15 21.6 23.3 24.2 25 26.9 28.8 32.1 34.9 37.3 40.5 42.8

0.175 23.2 24.7 25.5 26.2 28 29.7 32.7 35.2 36.8 39.7 42.20.2 24.7 26.1 26.7 27.4 29 30.6 32.8 34.5 36.1 39.2 41.7

0.225 26.1 27.3 27.9 28.5 30 30.8 32.3 34 35.7 38.8 41.40.25 27.5 28.6 29.1 29.7 30.6 31.3 32.8 34.3 35.8 38.6 41.2

Beta v/fc' \ ex -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 20.075 6.32 4.75 4.10 3.75 3.24 2.94 2.59 2.38 2.23 1.95 1.67

0.1 3.79 3.38 3.24 3.14 2.91 2.75 2.50 2.32 2.18 1.93 1.690.125 3.18 2.99 2.94 2.87 2.74 2.62 2.42 2.26 2.13 1.90 1.670.15 2.88 2.79 2.78 2.72 2.60 2.52 2.36 2.21 2.08 1.82 1.61

0.175 2.73 2.66 2.65 2.60 2.52 2.44 2.28 2.14 1.96 1.71 1.540.2 2.63 2.59 2.52 2.51 2.43 2.37 2.14 1.94 1.79 1.61 1.47

0.225 2.53 2.45 2.42 2.40 2.34 2.14 1.86 1.73 1.64 1.51 1.390.25 2.39 2.39 2.33 2.33 2.12 1.93 1.70 1.58 1.50 1.38 1.29

Input ParametersFill in each yellow cell. Units: m (m or u for Metric or US units)

Material Properties 35 MPa Concrete compressive strengthfy-long 550 MPa Yield strength of longitudinal non-prestressed reinforcement

fp0 1300 MPa Jacking stress in prestressing strands (0.7 fpu generally)fpy 1675 MPa "yield" of prestressing strands ( 0.9 fpu generall)

Geometry of section dv 925 mm Flexural level arm at given sectionbv 300 mm Web width Ac 150000 mm2 Concrete area of bottom half of section (for compression in bottom chord)As 2100 mm2 Non prestressed longitudinal reinforcement

Aps 0 mm2 Prestressed longitudinal reinforcementstirrups 0.401 MPa Quantity of stirrups (Av.fy/bw.s)

Vp 0 kN Vertical component of prestressing force

Loading M/V 1.5 m Moment to shear ratio at given section

0 kN Applied Axial Load (tension = positive)

Final CapacityUS units SI units

Moment 467 kip-ft Moment 633.225 kNmShear 95 kips Shear 422 kN

Converted Parameters from above listing

5075 psi dv 36.4173 inchstirrups 58.145 psi bv 11.811 inch

EsAp+EpAps 94395.19 kips M/V 4.92126 ftFe 0.090895 Asfy+Apsfpu 259.587 kips

As 3.255007 fy-long 79.75 ksi

Aps 0 Nu 0 kipsfp0 188.5 ksi phi 1.00 (not tested yet)fpy 242.875 ksi Vp 0 kips

Ac 232.5041

Required stirrupsThis shows the level of stirrups (in psi) that would be required for each cell of the beta-theta chart, and the given concrete strengthequation =(v_table*fcp-beta_table*SQRT(fcp))*TAN(theta_table)

shear (psi) -0.2 -0.1 -0.05 0 0.125 0.25 0.5 0.75 1 1.5 2381 -29 16 34 45 68 86 115 141 164 209 251508 78 99 109 117 139 159 196 231 263 319 362634 148 169 179 189 213 237 282 324 364 434 484761 220 242 253 265 292 320 372 421 467 539 598888 297 321 334 346 377 407 466 519 560 636 706

1015 381 407 420 434 467 500 556 603 647 734 8111142 471 499 513 527 563 590 638 687 736 832 9191269 572 599 614 629 661 688 739 789 838 934 1030

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Interpolate ThetaEach of these values is interpolated from the code charts based on the level of stirrups provided and the required level in the table above.Take a look at the equations to see how it's done. The top row is different than all the bottom cells


0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

final theta 18.9 20.4 21.1 21.9 24.3 26.6 30.5 33.7 36.4 40.8 43.9



0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

final beta 4.25 4.05 3.82 3.64 3.24 2.94 2.59 2.38 2.23 1.95 1.67

Final Calculations Controlled by Yield, see notes->

Equation Variable V1 Max M Vs/2+Vp V=05.8.3.3-3 Vc 130.4 124.2 117.1 111.6 99.2 90.1 79.4 73.1 68.3 59.8 51.3 51.3 0.1 0.1 kips5.8.3.3-4 Vs 73.2 67.3 64.7 62.2 55.4 50.0 42.5 37.5 33.9 29.0 26.0 26.0 13.1 0.1 kips5.8.3.3-1 Vc+Vs+Vp 203.6 191.4 181.9 173.8 154.6 140.0 121.9 110.6 102.2 88.7 77.3 77.3 13.2 0.2 kips5.8.3.3-2 Final V 203.6 191.4 181.9 173.8 154.6 140.0 121.9 110.6 102.2 88.7 77.3 77.3 13.2 0.2 kips

Fe 0.09 0.09 0.09 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.005.8.3.4.2-2 Moment -2164.4 -1411.5 -1029.2 -655.1 -448.0 -281.1 -27.6 178.1 362.5 703.4 1024.0

yield theta 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.9 43.95.8.3.5-1 long yield 261.2 290.1 316.3 337.8 387.6 425.0 470.2 498.2 518.9 553.6 585.0 585.0 787.2 787.8 kip.feet

final M -2164.4 -1411.5 -1029.2 -655.1 -448.0 -281.1 -27.6 178.1 362.5 553.6 585.0 585.0 787.2 787.8 kip.feetM/V (ft) -10.6 -7.4 -5.7 -3.8 -2.9 -2.0 -0.2 1.6 3.5 6.2 7.6 7.6 59.6 3938.9 feet

Interpolate VWe could do this with the M/V ratio as an interpolation index, but the following way is better for cases near or controlled by yield.the m and b are the shear intercept and slope of the line on the interaction diagram

m -0.016 -0.025 -0.022 -0.092 -0.087 -0.071 -0.055 -0.045 -0.071 -0.365 #DIV/0! -0.317 lastb 168.7 156.1 159.6 113.2 115.5 120.0 120.4 118.7 127.8 290.6 #DIV/0! 262.8 columnmoment 0 0 0 0 0 0 0 0 467 0 0 0 0 kip.feetshear 0 0 0 0 0 0 0 0 95 0 0 0 0 kips

Check Max V at M = dv*VAASHTO has a limit that the M in the equations not be taken as less than V*dv. To account for this, find shear at that moment and limit answer to that value.

m/v = dv 3.03 feetmoment 0 0 0 0 0 0 0 317 0 0 0 0 0 kip.feetshear 0 0 0 0 0 0 0 104 0 0 0 0 0 kips

Extra line on plot M 0 317 kip.feetV 104 104 kips

Activate limit on the shear if necessaryratio of V/limit 0.909 If this is greater than 1, then we have calculated a shear higher than that from M=Vdv and should pro-rate it.final capacity M 467 kip.feet

V 95 kips

Interaction DiagramThis is the AASHTO shear-moment interaction diagram for this section with at least minimum stirrups. The line indicates the given moment to shear ratio.

Loading Line M 0 467V 0 95

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AASHTO-99 Calculator

This will calculate the shear strength of a beam with stirrups for a given M:V ratio using

Purpose: A non-iterative technique is provided that will doubly interpolate in the tables and calculate the shear strengthfor the given level of stirrups and moment to shear ratio. No macros or goal seeking are used.

Units US customary units

Method: The quantity of stirrups is calculated for each cell in the beta-theta table.for each value of ex, the beta and theta values are interpolated at the provided level of transverse reinforcementThese values are used to calculate moment and shears, and the final answer is interpolated from that.

Usage: Fill in the yellow cells below and the shear strength will show up in the green cells to the right of the yellow ones.The spreadsheet ends with an interaction diagram as well as the input for the example in the State of the art report (ASCE Dec 1998)

License: This spreadsheet was written by Evan Bentz, March 1999. Permission is given to use, copy, duplicate and dissect this spreadsheet in any way.

Limits: This version (so far), has mistakes if phi is anything but 1.0.

Notes: Recall that, in general, the dv for the top and bottom of a section are different. Using the smaller in conservative, but in some cases, itmay be worthwhile to use this spreadsheet once with the positive dv, then again with the negative and hand stitch them together.

Code Values of Beta and ThetaThese are taken directly from the code

Theta v/fc' \ ex -0.2 -0.15 -0.1 0 0.125 0.25 0.5 0.75 1 1.5 20.05 27 27 27 27 27 28.5 29 33 36 41 430.075 27 27 27 27 27 27.5 30 33.5 36 40 420.1 23.5 23.5 23.5 23.5 24 26.5 30.5 34 36 38 390.125 20 21 22 23.5 26 28 31.5 34 36 37 380.15 22 22.5 23.5 25 27 29 32 34 36 36.5 370.175 23.5 24 25 26.5 28 30 32.5 34 35 35.5 360.2 25 25.5 26.5 27.5 29 31 33 34 34.5 35 360.225 26.5 27 27.5 29 30.5 32 33 34 34.5 36.5 390.25 28 28.5 29 30 31 32 33 34 35.5 38.5 41.5

Beta v/fc' \ ex -0.2 -0.15 -0.1 0 0.125 0.25 0.5 0.75 1 1.5 20.05 6.78 6.17 5.63 4.88 3.99 3.49 2.51 2.37 2.23 1.95 1.720.075 6.78 6.17 5.63 4.88 3.65 3.01 2.47 2.33 2.16 1.9 1.650.1 6.5 5.87 5.31 3.26 2.61 2.54 2.41 2.28 2.09 1.72 1.450.125 2.71 2.71 2.71 2.6 2.57 2.5 2.37 2.18 2.01 1.6 1.350.15 2.66 2.61 2.61 2.55 2.5 2.45 2.28 2.06 1.93 1.5 1.240.175 2.59 2.58 2.54 2.5 2.41 2.39 2.2 1.95 1.74 1.35 1.110.2 2.55 2.49 2.48 2.45 2.37 2.33 2.1 1.82 1.58 1.21 10.225 2.45 2.38 2.43 2.37 2.33 2.27 1.92 1.67 1.43 1.18 1.140.25 2.36 2.32 2.36 2.3 2.28 2.01 1.64 1.52 1.4 1.3 1.25

Input Parameters Final capacityFill in each yellow cell. AASHTO-99 shear capacity:

Flexural Tension Face of Member Flexural Compression Face of Member

(beam) Ac1 580 Ac1 357 US Units M: 5034 kip-ftfc' 1 8000 psi fc' 1 8000 psi V: 503 kips

(slab) Ac2 0 Ac2 735fc' 2 4000 psi fc' 2 4000 psi SI Units M: 6828 kN

Aps 8.262 Aps 0 V: 2240 kNm

As 0 As 17.8

General Geometry General Materials

Av/s 0.4 fp0 189 ksidv 69.4 inch fpy 244 ksibv 8 inch fy-long 60 ksi

fy-trans 60 ksiLoading

M/V 10 feet Nu 0 kipsVp 23.9 kips phi 1.00 (not tested yet)

Derived NumbersEsAp+EpAps 236293.2 kips EsAp+EpAps 516200 kips

Fe 0.074 Fe 0.104Asfy+Apsfpy 2015.928 kips Asfy+Apsfpy 1068.0 kips

stirrups 250 psi

Required stirrupsThis shows the level of stirrups (in psi) that would be required for each cell of the beta-theta chart, and the given concrete strengthequation =(v_table*fcp-beta_table*SQRT(fcp))*TAN(theta_table)

shear (psi) -0.2 -0.15 -0.1 0 0.125 0.25 0.5 0.75 1 1.5 2 > 2 > 2 > 2400 -105 -77 -53 -19 22 48 97 122 146 196 230600 -3 25 49 83 139 172 219 259 296 361 407800 95 120 141 221 252 286 344 402 445 505 543

1000 276 291 306 334 376 413 483 543 596 646 6871200 389 400 420 453 497 544 622 685 746 789 8211400 508 521 547 586 630 685 766 827 871 912 9451600 640 657 687 719 769 836 917 969 1002 1044 10971800 788 809 824 880 937 998 1057 1113 1149 1254 13752000 951 973 992 1036 1079 1137 1203 1257 1337 1498 1670

Interpolate ThetaEach of these values is interpolated from the code charts based on the level of stirrups provided and the required level in the table above.Take a look at the equations to see how it's done. The top row is different than all the bottom cells


0.0 0.0 0.0 0.0 24.1 26.8 30.1 0.0 0.0 0.0 0.020.5 21.6 22.5 23.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

inch2 inch2

inch2 inch2

inch2 inch2

inch2 inch2

inch2/ft

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

final theta 20.5 21.6 22.5 23.5 24.1 26.8 30.1 33.5 36.0 40.7 42.9



0.00 0.00 0.00 0.00 2.63 2.69 2.46 0.00 0.00 0.00 0.003.25 3.46 3.59 3.09 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 yield

final beta 3.25 3.46 3.59 3.09 2.63 2.69 2.46 2.33 2.18 1.93 1.71 1.71 1.71 1.71

Final Calculations: Shear Controlled by Yield, see notes->

Equation Variable V1 Max M Vs/2+Vp V=05.8.3.3-3 Vc 161.4 172.0 178.5 153.5 130.6 133.5 121.9 115.8 108.3 96.0 85.0 85.0 0.0 0.1 kips5.8.3.3-4 Vs 371.4 350.8 335.1 319.4 311.0 274.7 239.3 210.1 191.1 161.6 149.5 149.5 74.8 0.1 kips5.8.3.3-1 Vc+Vs+Vp 556.7 546.7 537.5 496.7 465.6 432.1 385.1 349.8 323.4 281.5 258.5 258.5 98.7 0.2 kips5.8.3.3-2 Final V 556.7 546.7 537.5 496.7 465.6 432.1 385.1 349.8 323.4 281.5 258.5 258.5 98.7 0.2 kips

Final Calculations: MomentA Fe- ten + 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00B Fe- ten - 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07C Fe-comp + 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00D Fe-comp - 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

P-ten -848.9 -901.1 -941.8 -1017.8 -1066.9 -1157.7 -1250.2 -1315.0 -1355.4 -1411.6 -1435.25.8.3.4.2-2 P-comp 712.7 660.4 619.7 543.8 494.7 403.8 311.3 246.5 206.1 149.9 126.3Moment M - A-C 4566.1 5630.9 6515.6 8200.1 9593.6 11635.6 14334.4 16601.6 18490.3 21883.9 24771.7 tension and compresssion crackedpossibilities M - A-D 4374.6 4850.5 5252.7 6022.4 6693.3 7629.4 8935.0 10064.2 11038.5 12830.3 14415.2 tension cracked, compression uncracked

M - B-C 5394.0 4619.1 3936.9 2616.2 1332.4 -285.5 -2807.6 -5107.1 -7211.6 -11222.9 -14973.3 tension uncracked, compression crackedM - B-D -14233.3 -7717.6 -1507.4 10769.0 24905.7 40143.0 68266.7 95658.0 122406.9 175253.4 227241.5 compression and tension uncracked

et A-C -0.3 0.3 0.8 1.7 2.5 3.6 5.2 6.6 7.8 10.0 12.1ec A-C -0.33 -1.33 -2.15 -3.70 -4.93 -6.81 -9.17 -11.11 -12.66 -15.38 -17.59et A-D -0.4 -0.3 -0.1 0.1 0.4 0.7 1.2 1.8 2.3 3.4 4.5ec A-D -0.02 -0.08 -0.13 -0.22 -0.29 -0.40 -0.54 -0.65 -0.75 -0.91 -1.04et B-C 0.0 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.7 -0.8 -1.0 -1.3ec B-C -0.93 -0.59 -0.26 0.39 1.12 1.92 3.37 4.78 6.15 8.85 11.49et B-D -1.0 -0.7 -0.4 0.3 1.0 1.8 3.3 4.8 6.2 9.0 11.9ec B-D 1.39 0.87 0.39 -0.58 -1.67 -2.86 -5.04 -7.14 -9.18 -13.21 -17.16

Select M - A-C - - - - - - - - - - -M - A-D - - - 6022.4 6693.3 7629.4 8935.0 10064.2 11038.5 12830.3 14415.2M - B-C - - - 2616.2 1332.4 -285.5 -2807.6 -5107.1 -7211.6 -11222.9 -14973.3M - B-D - - - - - - - - - - -

(large values located here >Mmax)max = 0.0 0.0 0.0 6022.4 6693.3 7629.4 8935.0 10064.2 11038.5 12830.3 14415.2 ### ### ###min 0.0 0.0 0.0 2616.2 1332.4 -285.5 -2807.6 -5107.1 -7211.6 -11222.9 -14973.3 ### ### ###

yield theta 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.95.8.3.5-1 yield - pos 9497.2 9495.5 9503.7 9708.6 9876.8 9972.2 10154.3 10283.2 10389.0 10557.5 10663.7 10663.7 11658.8 11658.8 kip.feet

Positive M 0.0 0.0 0.0 6022.4 6693.3 7629.4 8935.0 10064.2 10389.0 10557.5 10663.7 10663.7 11658.8 11658.8 kip.feet

yield theta 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9yiled - neg -4015.0 -4013.4 -4021.5 -4226.4 -4394.6 -4490.0 -4672.1 -4801.1 -4906.8 -5075.4 -5181.5 -5181.5 -6176.6 -6176.6Negative M 0.0 0.0 0.0 2616.2 1332.4 -285.5 -2807.6 -4801.1 -4906.8 -5075.4 -5181.5 -5181.5 -6176.6 -6176.6

Positive agai final M 0.0 0.0 0.0 6022.4 6693.3 7629.4 8935.0 10064.2 10389.0 10557.5 10663.7 10663.7 11658.8 11658.8 kip.feetM/V (ft) 0.0 0.0 0.0 12.1 14.4 17.7 23.2 28.8 32.1 37.5 41.3 41.3 118.2 58293.9 feet

Interpolate VWe could do this with the M/V ratio as the m and b are the shear intercept and slope of the line on the interaction diagram

m #DIV/0! #DIV/0! -0.007 -0.046 -0.036 -0.036 -0.031 -0.081 -0.248 -0.217 #DIV/0! -0.161 lastb #DIV/0! #DIV/0! 537.5 776.5 704.8 706.5 664.7 1169.4 2901.7 2577.5 #DIV/0! 1970.8 columnmoment 0 0 5034 0 0 0 0 0 0 0 0 0 0 kip.feetshear 0 0 503 0 0 0 0 0 0 0 0 0 0 kips

Interaction DiagramThis is the AASHTO shear-moment interaction diagram for this section. The line indicates the given moment to shear ratio.

-10000 -5000 0 5000 10000 150000.0

100.0

200.0

300.0

400.0

500.0

600.0

AASHTO-99 Interaction Diagram

aashto-n

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