AASHTO(MCFT)

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 strength for 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 spacing These 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 Theta These 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 5 10 15 20 30 40 60 80

-0.2 25.4 27.6 29.5 31.2 34.1 36.6 40.8 44.3

-0.1 25.5 27.6 29.5 31.2 34.1 36.6 40.8 44.3

-0.05 25.9 28.3 29.7 31.2 34.1 36.6 40.8 44.3

0 26.4 29.3 31.1 32.3 34.2 36.6 40.8 44.3

0.125 27.7 31.6 34.1 36.0 38.9 41.1 44.5 47.1

0.25 28.9 33.5 36.5 38.8 42.3 45.0 49.2 52.3

0.5 30.9 36.3 39.9 42.7 46.9 50.2 55.1 58.7

0.75 32.4 38.4 42.4 45.5 50.1 53.7 58.9 62.8

1 33.7 40.1 44.4 47.6 52.6 56.3 61.8 65.7

1.5 35.6 42.7 47.4 50.9 56.2 60.2 65.8 69.7

2 37.2 44.7 49.7 53.4 59.0 63.0 68.6 72.4

Beta

sxe \ ex 5 10 15 20 30 40 60 80

-0.2 6.362 5.776 5.337 4.988 4.456 4.062 3.496 3.099

-0.1 6.058 5.777 5.337 4.988 4.456 4.062 3.496 3.099

-0.05 5.556 5.376 5.270 4.987 4.456 4.062 3.496 3.099

0 5.152 4.892 4.728 4.608 4.434 4.062 3.496 3.099

0.125 4.414 4.053 3.821 3.647 3.389 3.197 2.915 2.706

0.25 3.905 3.524 3.275 3.089 2.817 2.616 2.323 2.110

0.5 3.260 2.882 2.639 2.458 2.193 1.999 1.721 1.522

0.75 2.862 2.498 2.265 2.093 1.841 1.657 1.396 1.210

1 2.584 2.234 2.011 1.846 1.605 1.431 1.183 1.011

1.5 2.209 1.884 1.676 1.523 1.300 1.139 0.916 0.764

2 1.961 1.654 1.458 1.313 1.103 0.954 0.750 0.616

Input Parameters Fill in each yellow cell.

Units:

u (m or u for Metric or US units) fc'

Material Properties

Geometry of section

fy-long fp0 fpy

3300 40 0 0

psi ksi ksi ksi

Concrete compressive strength Yield strength of longitudinal non-prestressed reinforcement Jacking stress in prestressing strands (0.7 fpu generally) "yield" of prestressing strands ( 0.9 fpu generall)

dv bv Ac As Aps sxe stirrups Vp

31 13 234 6.24 0 50 0 0

inch inch inch2 inch2 inch2 inch psi kips

Flexural level arm at given section Web width Concrete area of bottom half of section (for compression in bottom chord) Non prestressed longitudinal reinforcement Prestressed longitudinal reinforcement Effective crack spacing Quantity of stirrups (Av.fy/bw.s) Vertical component of prestressing force

Loading

M/V Nu

1 ft 0 kips

Moment to shear ratio at given section Applied Axial Load (tension = positive)

Moment Shear

US units 49 kip-ft 49 kips

Moment Shear

She ar (k ips )

Final Capacity SI units 66.9 kNm 220 kN

AASHTO Inte raction Diagram 70 60 50

Converted Parameters from above listing fc' Effective Crack Spacing EsAp+EpAps Fe As Aps fp0 fpy stirrups

3300 50 180960 0.19105 6.24 0 0 0 0

40

psi inch kips

dv bv M/V Asfy+Apsfpu inch2 fy-long inch2 Nu ksi phi ksi Vp psi Ac

31 13 1 249.6 40 0 1.00 0 234

inch inch ft kips ksi kips (not tested yet) kips inch2

30 20 10 0 0

100

200

300 400 Mom e nt (k ip.ft)

500

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

spacing 5 10 15 20 30 40 60 80

-0.2 5 10 15 20 30 40 60 80

-0.1 5 10 15 20 30 40 60 80

-0.05 5 10 15 20 30 40 60 80

0 5 10 15 20 30 40 60 80

0.125 5 10 15 20 30 40 60 80

0.25 5 10 15 20 30 40 60 80

0.5 5 10 15 20 30 40 60 80

0.75 5 10 15 20 30 40 60 80

1 5 10 15 20 30 40 60 80

1.5 5 10 15 20 30 40 60 80

2 5 10 15 20 30 40 60 80

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

Interpolate Theta Each 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 normal 0.0 0.0 0.0 0.0 0.0 0.0 0.0

top row of table lower rows

600

700

max

0.0 0.0 0.0 0.0 38.7 0.0 0.0

0.0 0.0 0.0 0.0 38.7 0.0 0.0

0.0 0.0 0.0 0.0 38.7 0.0 0.0

0.0 0.0 0.0 0.0 38.7 0.0 0.0

0.0 0.0 0.0 0.0 42.8 0.0 0.0

0.0 0.0 0.0 0.0 47.1 0.0 0.0

0.0 0.0 0.0 0.0 52.6 0.0 0.0

0.0 0.0 0.0 0.0 56.3 0.0 0.0

0.0 0.0 0.0 0.0 59.0 0.0 0.0

0.0 0.0 0.0 0.0 63.0 0.0 0.0

0.0 0.0 0.0 0.0 65.8 0.0 0.0

final theta

38.7

38.7

38.7

38.7

42.8

47.1

52.6

56.3

59.0

63.0

65.8

bottom row

Interpolate Beta This is done the same way as the beta table above min 0.00 0.00 normal 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.78 3.78 0.00 0.00 max 0.00 0.00 final beta

0.00 0.00 0.00 0.00 0.00 0.00 3.78 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 3.78 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 3.06 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 2.47 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 1.86 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 1.53 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 1.31 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 1.03 0.00 0.00

0.00 top row of table 0.00 lower rows 0.00 0.00 0.00 0.00 0.85 0.00 0.00 bottom row

3.78

3.78

3.78

3.78

3.06

2.47

1.86

1.53

1.31

1.03

0.85

Variable Vc Vs Vc+Vs+Vp Final V

87.5 0.0 87.5 87.5

87.5 0.0 87.5 87.5

87.5 0.0 87.5 87.5

87.5 0.0 87.5 87.5

70.7 0.0 70.7 70.7

57.2 0.0 57.2 57.2

43.1 0.0 43.1 43.1

35.3 0.0 35.3 35.3

30.3 0.0 30.3 30.3

23.8 0.0 23.8 23.8

19.7 0.0 19.7 19.7

Fe Moment yield theta long yield final M M/V (ft)

0.19 -630.3 65.8 543.2 -630.3 -7.2

0.19 -385.7 65.8 543.2 -385.7 -4.4

0.19 -263.3 65.8 543.2 -263.3 -3.0

1.00 -141.0 65.8 543.2 -141.0 -1.6

1.00 -40.1 65.8 562.7 -40.1 -0.6

1.00 48.2 65.8 578.4 48.2 0.8

1.00 191.2 65.8 594.8 191.2 4.4

1.00 320.2 65.8 603.8 320.2 9.1

1.00 444.0 65.8 609.7 444.0 14.7

1.00 685.6 65.8 617.2 617.2 26.0

1.00 923.5 65.8 621.9 621.9 31.5

Final Calculations Equation 5.8.3.3-3 5.8.3.3-4 5.8.3.3-1 5.8.3.3-2

5.8.3.4.2-2 5.8.3.5-1

Max M Vs/2+Vp 19.7 0.2 0.0 0.2 19.7 0.4 19.7 0.4

65.8 621.9 621.9 31.5

65.8 644.3 644.3 1610.8

V=0 0.1 0.1 0.2 0.2

65.8 644.8 kip.feet 644.8 kip.feet 3224.0 feet

Interpolate V We 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 b moment shear

0.000 87.5 0 0

0.000 87.5 0 0

0.000 87.5 0 0

-0.166 64.1 0 0

-0.154 64.6 0 0

-0.099 61.9 56 56

-0.060 54.5 0 0

-0.041 48.5 0 0

-0.037 46.9 0 0

-0.861 #DIV/0! 555.5 #DIV/0! 0 0 0 0

-0.861 last 555.5 column 0 0 kip.feet 0 0 kips

Check Max V at M=dv*V AASHTO 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 moment shear

2.5833 feet 0 0

Extra line on plot

0 0

0 0

M V

0 49

Activate limit on the shear if necessary ratio of V/limit 1.142153 final capacity M V

0 0

0 0

127 49

0 0

0 0

0 0

0 0

49 49

AASHTO Interaction Diagram: Less than minimum stirrups She ar (k ips )

50 45 40 35 30 25 20 15 10 5 0 0

100

200

0 0

0 kip.feet 0 kips

If this is greater than 1, then we have calculated a shear higher than that from M=Vdv and should pro-rate it. 49 kip.feet 49 kips

This is the AASHTO shear-moment interaction diagram for this section. The line indicates the given moment to shear ratio. M V

0 0

127 kip.feet 49 kips

Interaction Diagram Loading Line

0 0

300 400 Mom ent (k ip.ft)

500

600

700

kips kips kips kips

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 strength for 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 reinforcement These 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 Theta These 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 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

-0.2 22.3 18.1 19.9 21.6 23.2 24.7 26.1 27.5

-0.1 20.4 20.4 21.9 23.3 24.7 26.1 27.3 28.6

-0.05 21 21.4 22.8 24.2 25.5 26.7 27.9 29.1

0 21.8 22.5 23.7 25 26.2 27.4 28.5 29.7

0.125 24.3 24.9 25.9 26.9 28 29 30 30.6

0.25 26.6 27.1 27.9 28.8 29.7 30.6 30.8 31.3

0.5 30.5 30.8 31.4 32.1 32.7 32.8 32.3 32.8

0.75 33.7 34 34.4 34.9 35.2 34.5 34 34.3

1 36.4 36.7 37 37.3 36.8 36.1 35.7 35.8

1.5 40.8 40.8 41 40.5 39.7 39.2 38.8 38.6

2 43.9 43.1 43.2 42.8 42.2 41.7 41.4 41.2

Beta

v/fc' \ ex 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

-0.2 6.32 3.79 3.18 2.88 2.73 2.63 2.53 2.39

-0.1 4.75 3.38 2.99 2.79 2.66 2.59 2.45 2.39

-0.05 4.10 3.24 2.94 2.78 2.65 2.52 2.42 2.33

0 3.75 3.14 2.87 2.72 2.60 2.51 2.40 2.33

0.125 3.24 2.91 2.74 2.60 2.52 2.43 2.34 2.12

0.25 2.94 2.75 2.62 2.52 2.44 2.37 2.14 1.93

0.5 2.59 2.50 2.42 2.36 2.28 2.14 1.86 1.70

0.75 2.38 2.32 2.26 2.21 2.14 1.94 1.73 1.58

1 2.23 2.18 2.13 2.08 1.96 1.79 1.64 1.50

1.5 1.95 1.93 1.90 1.82 1.71 1.61 1.51 1.38

2 1.67 1.69 1.67 1.61 1.54 1.47 1.39 1.29

M

V 0

Input Parameters Fill in each yellow cell.

Units: fc'

Material Properties

fy-long fp0 fpy Geometry of section 24 in 0.4 in^2 52 ksi

Loading

4000 60 0 0

psi ksi ksi ksi

Concrete compressive strength Yield strength of longitudinal non-prestressed reinforcement Jacking stress in prestressing strands (0.7 fpu generally) "yield" of prestressing strands ( 0.9 fpu generall)

dv 40.83 inch bv 14 inch Ac 0 inch2 As 6 inch2 Aps 0 inch2 stirrups 61.90476 psi Vp 0 kips M/V Nu

Flexural level arm at given section Web width Concrete area of bottom half of section (for compression in bottom chord) Non prestressed longitudinal reinforcement Prestressed longitudinal reinforcement Quantity of stirrups (Av.fy/bw.s) Vertical component of prestressing force

6 ft

Moment to shear ratio at given section

0 kips

Applied Axial Load (tension = positive)

Final Capacity Moment Shear

141

u (m or u for Metric or US units) M

s Av fyv

141

481

US units 785 kip-ft 131 kips

Moment Shear

V -1462.0 -1136.6 -998.6 -866.4 -564.4 -301.8 147.7 532.7 855.1 903.1 945.8 945.8 1224.2 1224.9

239.6 222.6 215.3 208.3 190.8 176.3 153.8 139.3 128.6 111.5 97.3 97.3 18.6 0.2

AASHTO Interaction Diagram

SI units 1065.3 kNm 583 kN

180 160 140

Converted Parameters from above listing fc' stirrups EsAp+EpAps Fe As Aps fp0 fpy Ac

4000 61.90476 174000 1 6 0 0 0 0

120

psi psi kips

dv bv M/V Asfy+Apsfpu inch2 fy-long inch2 Nu ksi phi ksi Vp inch2

40.83 14 6 360 60 0 1.00 0

100

inch inch ft kips ksi kips (not tested yet) kips

80 60 40 20 0 0

200

400

Required stirrups This shows the level of stirrups (in psi) that would be required for each cell of the beta-theta chart, and the given concrete strength equation =(v_table*fcp-beta_table*SQRT(fcp))*TAN(theta_table) shear (psi) 300 400 500 600 700 800 900 1000

-0.2 -41 52 108 166 226 291 363 442

-0.1 0 69 125 182 245 312 384 463

-0.05 16 77 132 191 254 322 395 474

0 25 83 140 199 264 333 406 486

0.125 43 100 159 221 288 358 434 512

0.25 57 116 177 242 311 385 456 534

0.5 80 144 212 283 357 428 495 575

0.75 99 171 244 321 398 466 533 614

1 117 195 275 357 431 501 572 653

1.5 152 240 330 414 491 569 647 729

2 187 274 370 461 546 630 716 804

Interpolate Theta Each of these values is interpolated from the code charts based on the level of stirrups provided and the required level in the table above.

600

800

1000

1200

1400

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 30.5 33.7 normal 0.0 20.4 21.3 22.2 24.5 26.6 0.0 0.0 18.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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 18.4 20.4 21.3 22.2 24.5 26.6 30.5 33.7

36.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 36.4

40.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 40.8

43.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 43.9

top row of table lower rows

Interpolate Beta This is done the same way as the beta table above min 0.00 0.00 0.00 normal 0.00 3.52 3.44 3.69 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 final beta 3.69 3.52 3.44

0.00 3.37 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.37

0.00 3.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.13

0.00 2.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.92

2.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.59

2.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.38

2.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.23

1.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.95

1.67 top row of table 0.00 lower rows 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.67

Final Calculations Equation 5.8.3.3-3 5.8.3.3-4 5.8.3.3-1 5.8.3.3-2

5.8.3.4.2-2 5.8.3.5-1

Controlled by Yield, see notes->

Variable Vc Vs Vc+Vs+Vp Final V

133.3 106.4 239.6 239.6

Fe Moment yield theta long yield final M M/V (ft)

127.4 95.2 222.6 222.6

124.5 90.8 215.3 215.3

121.7 86.6 208.3 208.3

113.1 77.7 190.8 190.8

105.7 70.6 176.3 176.3

93.7 60.1 153.8 153.8

86.2 53.1 139.3 139.3

80.6 48.0 128.6 128.6

70.5 41.0 111.5 111.5

1.00 1.00 -1462.0 -1136.6 43.9 43.9 565.6 606.2 -1462.0 -1136.6 -6.1 -5.1

1.00 -998.6 43.9 624.0 -998.6 -4.6

1.00 -866.4 43.9 641.5 -866.4 -4.2

1.00 -564.4 43.9 687.5 -564.4 -3.0

1.00 -301.8 43.9 726.4 -301.8 -1.7

1.00 147.7 43.9 787.2 147.7 1.0

1.00 532.7 43.9 826.2 532.7 3.8

1.00 887.3 43.9 855.1 855.1 6.6

1.00 1556.3 43.9 903.1 903.1 8.1

V1 Max M Vs/2+Vp 60.5 60.5 0.1 36.8 36.8 18.5 97.3 97.3 18.6 97.3 97.3 18.6 1.00 2196.1 43.9 945.8 945.8 9.7

43.9 945.8 945.8 9.7

43.9 1224.2 1224.2 65.8

V=0 0.1 0.1 0.2 0.2

kips kips kips kips

43.9 1224.9 kip.feet 1224.9 kip.feet 6124.5 feet

Interpolate V We 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 b moment shear

-0.052 162.9 0 0

-0.052 162.9 0 0

-0.053 162.0 0 0

-0.058 158.2 0 0

-0.055 159.5 0 0

-0.050 161.2 0 0

-0.038 159.4 0 0

-0.033 157.0 785 131

-0.356 432.8 0 0

-0.332 #DIV/0! 411.5 #DIV/0! 0 0 0 0

-0.283 last 364.8 column 0 0 kip.feet 0 0 kips

Check Max V at M = dv*V AASHTO 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 moment shear

3.40 feet 0 0

Extra line on plot

0 0

0 0

M V

0 0

0 141

0 0

0 0

481 141

0 0

0 0

0 0

0 0

0 0

0 kip.feet 0 kips

481 kip.feet 141 kips

Activate limit on the shear if necessary ratio of V/limit 0.927 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 785 kip.feet V 131 kips

Interaction Diagram This 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 V

0 0

785 131

AASHTO Interaction Diagram 180 160 140 120 100 80 60 40 20 0 0

200

400

600

800

1000

1200

1400

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 strength for 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 reinforcement These 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, it may 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 Theta These are taken directly from the code Theta

v/fc' \ ex 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

-0.2 27 27 23.5 20 22 23.5 25 26.5 28

-0.15 27 27 23.5 21 22.5 24 25.5 27 28.5

-0.1 27 27 23.5 22 23.5 25 26.5 27.5 29

0 27 27 23.5 23.5 25 26.5 27.5 29 30

0.125 27 27 24 26 27 28 29 30.5 31

0.25 28.5 27.5 26.5 28 29 30 31 32 32

0.5 29 30 30.5 31.5 32 32.5 33 33 33

0.75 33 33.5 34 34 34 34 34 34 34

1 36 36 36 36 36 35 34.5 34.5 35.5

1.5 41 40 38 37 36.5 35.5 35 36.5 38.5

2 43 42 39 38 37 36 36 39 41.5

Beta

v/fc' \ ex 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

-0.2 6.78 6.78 6.5 2.71 2.66 2.59 2.55 2.45 2.36

-0.15 6.17 6.17 5.87 2.71 2.61 2.58 2.49 2.38 2.32

-0.1 5.63 5.63 5.31 2.71 2.61 2.54 2.48 2.43 2.36

0 4.88 4.88 3.26 2.6 2.55 2.5 2.45 2.37 2.3

0.125 3.99 3.65 2.61 2.57 2.5 2.41 2.37 2.33 2.28

0.25 3.49 3.01 2.54 2.5 2.45 2.39 2.33 2.27 2.01

0.5 2.51 2.47 2.41 2.37 2.28 2.2 2.1 1.92 1.64

0.75 2.37 2.33 2.28 2.18 2.06 1.95 1.82 1.67 1.52

1 2.23 2.16 2.09 2.01 1.93 1.74 1.58 1.43 1.4

1.5 1.95 1.9 1.72 1.6 1.5 1.35 1.21 1.18 1.3

2 1.72 1.65 1.45 1.35 1.24 1.11 1 1.14 1.25

Input Parameters

Final capacity

Fill in each yellow cell.

AASHTO-99 shear capacity:

(beam) (slab)

Flexural Tension Face of Member

Flexural Compression Face of Member

Ac1 fc' 1 Ac2 fc' 2 Aps As

Ac1 fc' 1 Ac2 fc' 2 Aps As

580 3300 735 4000 0 5

inch2 psi inch2 psi inch2 inch2

580 3300 735 4000 0 5.1

inch2 psi inch2 psi inch2 inch2

General Geometry

General Materials

Av/s dv bv

0.4 inch2/ft 69.4 inch 14 inch

fp0 fpy fy-long fy-trans

189 244 60 60

10 feet 23.9 kips

Nu phi

0 kips 1.00 (not tested yet)

US Units

M: V:

1453 kip-ft 145 kips

SI Units

M: V:

1970 kN 646 kNm

ksi ksi ksi ksi

Loading M/V Vp

Derived Numbers EsAp+EpAps 145000 kips Fe 0.031 Asfy+Apsfpy 300 kips stirrups 143 psi

EsAp+EpAps Fe Asfy+Apsfpy

147900 kips 0.031 306.0 kips

Required stirrups This shows the level of stirrups (in psi) that would be required for each cell of the beta-theta chart, and the given concrete strength equation =(v_table*fcp-beta_table*SQRT(fcp))*TAN(theta_table) shear (psi) 165 248 330 413 495 578 660 743 825

-0.2 -114 -72 -19 93 138 186 239 300 367

-0.15 -97 -54 -3 99 143 191 247 309 376

-0.1 -81 -39 11 104 150 201 258 314 382

0 -59 -17 62 114 163 216 270 336 400

0.125 -33 19 80 129 179 233 290 358 417

0.25 -19 39 92 143 196 254 316 382 443

0.5 12 61 113 169 227 287 350 411 475

0.75 19 75 134 194 254 314 375 436 498

1 27 90 153 216 279 334 391 454 531

1.5 46 116 181 242 302 357 413 499 597

2 62 137 200 262 319 373 438 548 666

Each 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 min 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 normal 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 36.0 39.2 0.0 0.0 0.0 0.0 0.0 28.0 31.0 34.0 0.0 0.0 0.0 22.5 23.3 24.4 26.3 0.0 0.0 0.0 0.0 0.0 22.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 41.7 0.0 0.0 0.0 0.0 0.0 0.0

>2

>2

Interpolate Theta

final theta

22.1

22.5

Interpolate Beta This is done the same way as the beta table above

23.3

24.4

26.3

28.0

31.0

34.0

36.0

39.2

41.7

top row of table lower rows

>2

min normal

0.00 0.00 0.00 0.00 0.00 2.65 0.00 0.00 0.00

0.00 0.00 0.00 0.00 2.61 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 2.63 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 2.57 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 2.55 0.00 0.00 0.00 0.00

0.00 0.00 0.00 2.50 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 2.39 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 2.27 0.00 0.00 0.00 0.00 0.00

0.00 0.00 2.10 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 1.83 0.00 0.00 0.00 0.00 0.00 0.00

0.00 top row of table 0.00 lower rows 1.63 0.00 0.00 0.00 0.00 0.00 0.00 yield

final beta

2.65

2.61

2.63

2.57

2.55

2.50

2.39

2.27

2.10

1.83

1.63

Final Calculations: Shear Equation 5.8.3.3-3 5.8.3.3-4 5.8.3.3-1 5.8.3.3-2

Variable Vc Vs Vc+Vs+Vp Final V

1.63

1.63

1.63

Controlled by Yield, see notes->

139.5 261.2 424.6 424.6

133.3 230.8 388.1 388.1

126.4 205.9 356.2 356.2

117.3 191.1 332.3 332.3

101.9 170.5 296.2 296.2

V1 91.1 155.7 270.7 270.7

Fe- ten + 1.00 1.00 1.00 1.00 1.00 1.00 Fe- ten 0.03 0.03 0.03 0.03 0.03 0.03 Fe-comp + 1.00 1.00 1.00 1.00 1.00 1.00 Fe-comp 0.03 0.03 0.03 0.03 0.03 0.03 P-ten 601.3 580.7 546.0 496.1 429.1 376.9 5.8.3.4.2-2 P-comp 601.3 580.7 546.0 496.1 429.1 376.9 Moment M - A-C -368317.6 -352019.8 -327458.7 -289777.6 -239967.1 -198785.2 possibilities M - A-D -4045.0 -3831.9 -3531.7 -3051.9 -2423.6 -1886.1 M - B-C 4056.9 3841.8 3539.6 3055.8 2422.5 1880.1 M - B-D ### ### ### ### 2954846.8 ###

1.00 0.03 1.00 0.03 302.7 302.7 -134034.5 -996.7 981.2 ###

1.00 0.03 1.00 0.03 246.4 246.4 -79762.5 -217.7 192.8 ###

1.00 0.03 1.00 0.03 212.3 212.3 -38448.5 424.8 -458.9 ###

1.00 0.03 1.00 0.03 167.2 167.2 30662.5 1567.6 -1619.9 ###

1.00 0.03 1.00 0.03 138.3 138.3 90283.4 2610.4 -2680.8 ###

-157.7 161.92 0.9 0.10 0.1 0.92 1410.8 -1438.01

-93.4 96.81 1.4 0.06 0.1 1.47 2259.4 -2303.08

-44.4 47.31 2.0 0.03 0.0 2.01 3092.7 -3152.55

37.7 -35.41 3.0 -0.02 0.0 3.08 4743.4 -4835.21

108.6 -106.71 4.1 -0.07 -0.1 4.15 6382.9 -6506.43

1567.6 -1619.9 -

2610.4 -2680.8 -

148.1 341.2 513.2 513.2

145.7 335.3 504.9 504.9

146.5 322.9 493.4 493.4

143.5 306.3 473.7 473.7

142.4 281.3 447.6 447.6

Max M Vs/2+Vp 91.1 0.0 155.7 77.8 270.7 101.7 270.7 101.7

V=0 0.1 0.1 0.2 0.2

kips kips kips kips

Final Calculations: Moment A B C D

et A-C ec A-C et A-D ec A-D et B-C ec B-C et B-D ec B-D Select

M - A-C M - A-D M - B-C M - B-D max = min

5.8.3.5-1

-435.1 443.36 -0.7 0.28 0.3 -0.69 -1062.5 1083.33 -

-415.8 423.78 -0.6 0.27 0.3 -0.58 -886.3 903.76 -

-386.7 394.26 -0.4 0.25 0.2 -0.46 -700.4 714.24

-342.1 348.98 -0.2 0.22 0.2 -0.22 -342.1 348.98

-

-

-283.2 289.12 0.1 0.18 0.2 0.07 108.9 -110.87

-234.4 239.65 0.4 0.15 0.1 0.36 549.8 -560.32

-

-

-

-

-

tension and compresssion cracked tension cracked, compression uncracked tension uncracked, compression cracked compression and tension uncracked

(large values located here >Mmax) ### ### ### ### ### ###

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

1567.6 -1619.9

2610.4 -2680.8

yield theta yield - pos Positive M

41.7 -331.0 -331.0

41.7 -296.1 -296.1

41.7 -261.6 -261.6

41.7 -187.8 -187.8

41.7 -99.6 -99.6

41.7 -16.2 -16.2

41.7 122.6 0.0

41.7 248.0 0.0

41.7 355.4 0.0

41.7 522.1 522.1

41.7 639.8 639.8

41.7 639.8 639.8

41.7 1735.0 1735.0

yield theta yiled - neg Negative M

41.7 296.3 296.3

41.7 261.4 261.4

41.7 226.9 226.9

41.7 153.1 153.1

41.7 64.9 64.9

41.7 -18.5 0.0

41.7 -157.3 0.0

41.7 -282.7 0.0

41.7 -390.1 0.0

41.7 -556.8 -556.8

41.7 -674.5 -674.5

41.7 -674.5 -674.5

41.7 -1769.7 -1769.7

-331.0 -0.6

-296.1 -0.6

-261.6 -0.5

-187.8 -0.4

-99.6 -0.2

-16.2 0.0

0.0 0.0

0.0 0.0

0.0 0.0

522.1 1.8

639.8 2.4

639.8 2.4

1735.0 17.1

-2.264 388.1 0 0

#DIV/0! #DIV/0! 0 0

#DIV/0! #DIV/0! 0 0

-0.069 332.3 0 0

-0.217 409.6 0 0

#DIV/0! #DIV/0! 0 0

Positive agai final M M/V (ft)

41.7 1735.0 kip.feet 1735.0 kip.feet 41.7 -1769.7 -1769.7

1735.0 kip.feet 8675.0 feet

Interpolate V We 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 b moment shear

-0.240 434.0 0 0

-0.333 406.2 0 0

-0.267 423.6 0 0

-0.296 418.1 0 0

-0.275 420.2 0 0

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

AASHTO-99 Interaction Diagram 600.0 500.0 400.0 300.0 200.0 100.0 0.0 -2000.0

-1500.0

-1000.0

-500.0

0.0

500.0

1000.0

1500.0

2000.0

-0.154 last 369.4 column 1453 0 kip.feet 145 0 kips