Mathcad - RW_LRFD_ver11262010__RW-08-05-2_Calculation_12302010

Retaining Wall Analysis and Design

Description"RW-08-05-2"

Design Parameters

Description "RW-08-05-2" Designer "LG"

Reviewer "LDS"

CIP Precast

Concrete Footing Construction Type (affects sliding resistance)

Construction_type "CIP"

Element Height

Width Density Sound Barrier H SB 0ft 0in B SB 10in SB 150pcf Traffic Barrier H TB 2ft 8in B TBt 10.75in B TBb 1ft 4.75in

TB 150pcf Stem H Stem 9.827ft 0in B Stem 1ft 4.75in

con 150pcf

Heel H Ftg 1ft 6in B Heel 1ft 0in Toe B Toe 7ft 7.25in Key

H Key 0ft

B Key 0ft

Overall Footing Width:

B B Heel B Stem B Toe B 10.000ft

SDG Table 2.2-1

Barrier Weight

w TB 420lbf

Enter a value greater than zero to override barrier weight

32" F-Shape Index 420 = 420 plf

Density

Friction Angle

Soil Beneath Footing: soil_Ftg 105pcf Internal Friction Angle of Soil (for Sliding)Backfill:

soil_BF 105pcf

Internal Friction Angle of Soil Friction Angle between Fill and Wall

H embankment 0ft Height of embankment above Heel above Top of Wall (for sloped fill)not currently used

90deg Angle of back face of wall to the horizontal 0deg

Angle of fill to the horizontal

Toe 0deg Berm Slope B Berm 4ft Berm Width

D w 0ft Top of Berm to Water Table Elevation H Soil_Toe 24in Fill Height over Toe

H ignore 0ft Height of Soil above Toe to Ignore for Sliding Resistance (due to erosion, poor compaction, etc.)

.

Extreme Only All None

Load Combinations to include passive resistance

LC passive "All"

Live Load Surcharge offset sur_LL 0ft q sur_LL 1250 psf Dead Load Surcharge

offset sur_DL 5ft

q sur_DL 0105 psf

q n_Rpt 4625psf Nominal Bearing Resistance as specified in Geotechnical Report (allowable bearing pressure multiplied by factor of safety)

q SR 2200psf Service Level Bearing Resistance as specified in Geotechnical Report P CT 54kip Dynamic Transverse Force due to Vehicle Impact (TL-4 = 54kip)LRFD Table A13.2-1

P CT_Static_Factor 1.00 Adjust Dynamic Impact to Static Force for Stability Evaluation

L Wall 45ft

Length of wall assumed effective for Vehicle Impact for purposes of checking wall stability

Guide Specification for Structure Design of Sound Walls - Table 1-2.1.2Wind Pressure Height Application P wind_163psf H W10ft

H W10.000 P wind_250psf

H W2max H SB H TB H W1 0ft

H W2 2.667ft

Reinforcement and Concrete Properties:

SDG Table1.4.2-1

Compressive Strength of Concrete Concrete Strength - Refer to FDOT Spec 346-3

f'c5500psi

Class IV = 5500 psi

Yield Strength of Reinforcing

f y60000psi

Cover wall3in

Cover ftg_bot3in

Cover ftg_top2in

Wall Main Reinforcement (Vertical Bars U1)Bar#Wall.Vert5

S bar.Wall.Vert6in

Footing Main Reinforcement (Transverse Bars U2)Bar#Ftg.Tran5

S bar.Ftg.Tran6in

Wall Temperature Reinforcement (Horiztonal Bars B1)Bar#Wall.Horiz4

S bar.Wall.Horiz12in

Footing Temperature Reinforcement (Longitudinal Bars B2)Bar#Ftg.Long4

S bar.Ftg.Long12in

Aggregate Correction Factor K10.9

SDG1.4.1.A Exposure Factor (1.0 = Class 1 exposure condition, 0.75 = Class 2 exposure condition) e0.75

LRFD5.7.3.4-1,SDG3.10E Percent of Steel Effective (Adustment for development length):

Hooked Bar%eff_wall 1.00

%eff_wall1

%eff_heel 1.00

%eff_heel1

Straight Bar%eff_toe 1.00

%eff_toe1

Shear Reinforcement: (area of shear reinforcement within a distance s):

Resistance Factors

Calibra ng Resistance Factors in the Load and Resistance Factor Design for Florida Founda ons

(M. McVay, C. Kuo & W. Singletary; University of Florida Report for Florida Dept. of Transporta on; December 1998)

b0.55

Resistance Factor for Bearing

t 1.00

Resistance Factor for Sliding (shear resistance between soil and foundation)

ep0.50

Resistance Factor for passive resistance

Note: the resistance factors above are only applicable at the Strength Limit State.

Calculations

Geometry

Height of soil above toe at end of toe:

H at.st2ft

H Soil_Toe2ft

B Berm4ft

B Toe7.6ft

Top of Berm to bottom of Footing

D f 3.500ft

D f H at.st H Ftg

Load and Resistance Factors

Load Combinations and Load Factors

Retaining wall structures and their foundations shall be proportioned for all applicable load

combinations per 3.4.1LRFD11.5.5 Component Dead Load: DC_min0.90

DC_max 1.25

DC_max_StrIV 1.50

Earth (Vertical): Ev_min 1.00

Ev_max 1.35

Earth (Horizontal): Eh_min 1.50

* Eh_max 1.50

*1.50 used instead of 0.90 because this

combination is assumed to be more conservative

for Sliding and Eccentricity (Figure C11.5.5-2) Surcharge (Vertical): LSv_min 1.35

LSv_max 1.75

LSv_Ext0.50

Surcharge (Horizontal): LSh_min 1.35

LSh_max 1.75

LSh_Ext0.50

Wind: WS_min0.40

WS_max 1.40

Vehicle Collision: CT_Ext 1.00

Combinations:

LC

"Load Case No."

1

2

3

4

5

6

7

8

9

10

11

"Description"

"Service I"

"Strength I-min"

"Strength I-max"

"Strength III-min"

"Strength III-max"

"Strength IV-min"

"Strength IV-max"

"Strength V-min"

"Strength V-max"

"Extreme II-min"

"Extreme II-max"

"DC"

1.0

DC_min

DC_max

DC_min

DC_max

DC_min

DC_max_StrIV

DC_min

DC_max

DC_min

DC_max

"Ev"

1.0

Ev_min

Ev_max

Ev_min

Ev_max

Ev_min

Ev_max

Ev_min

Ev_max

Ev_min

Ev_max

"Eh"

1.0

Eh_min

Eh_max

Eh_min

Eh_max

Eh_min

Eh_max

Eh_min

Eh_max

Eh_min

Eh_max

"LSv"

1.0

LSv_max

LSv_max

LSv_min

LSv_min

LSv_Ext

LSv_Ext

"LSh"

1.0

LSh_max

LSh_max

LSh_min

LSh_min

LSh_Ext

LSh_Ext

"WS"

0.3

WS_max

WS_max

WS_min

WS_min

"CT"

0.0

CT_Ext

CT_Ext

Load Case for Extreme Event:

LC Ext 10

Function to find the column based on the column heading:i last rows LC ()1

i last 11

i 1i last

DC i

LC

i findCol "DC"()

Ev i LC

i findCol "Ev"() Eh i LC

i findCol "Eh"() WS i

LC

i findCol "WS"()

LSv i

LC i findCol "LSv"()

LSh i

LC i findCol "LSh"()

CT i

LC

i findCol "CT"()

All resistance factors shall be taken as 1.0 when investigating the extreme event limit state.

The resistance factors specified previously are only applicable for the strength limit state.

LRFD11.5.7 Load Case for Strength Limit States:LC Str_first2

LC Str_first2

LC Str_last LC Ext1

LC Str_last9

z STR LC Str_first LC Str_last

z1i last

T

z

if z LC Str_first

z LC Str_last

1.00

t

EP

z

if z LC Str_first

z LC Str_last

1.00

ep

LRFD10.5.5.3

B

z

if z LC Str_first

z LC Str_last

1.00

b

Forces acting on the retaining wall

Vertical Forces

L analysis 1ft

Calculation Width (use 1 ft to coincide with reinforcement design per foot)

Earth Pressure

Soil on the heel W Soil_Heel soil_BF L analysis H Stem B Heel

W Soil_Heel 1031.8lbf Soil on the toe

W Soil_Toe soil_BF L analysis max 0ft H Soil_Toe H ignore B Toe

W Soil_Toe 1596.9lbf

Retaining Wall

Sound Barrier:

H SB_eff H SB

H SB_eff 0.00 W SB SB L analysis B SB H SB_eff

W SB 0lbf

Traffic Barrier:

A T

B 3.1ft

2

W TB if w TB 0lbf w TB TB L analysis A TB

W TB 420lbf Stem:W Stem con B Stem L analysis H Stem W Stem 2057.5lbf Footing:W Ftg con B H Ftg L analysis W Ftg 2250lbf Key:W Key con B Key H Key L analysis

W Key 0lbf Total:

W Conc W SB W TB W Stem W Ftg W Key

W Conc 4727.5lbf

Surcharge

B sur_LL max 0ft B Heel offset sur_LL B sur_LL 1ft W sur_LL q sur_LL L analysis B sur_LL

W sur_LL 250lbf

B sur_DL max 0ft B Heel offset sur_DL B sur_DL 0ft W sur_DL q sur_DL L analysis B sur_DL

W sur_DL 0lbf

Horizontal Forces

Earth Pressure Coefficients

2.619 LRFD

3.11.5.3-2

Coefficent of active lateral earth pressure

K a 0.299 LRFD 3.11.5.3-1

Coefficent of passive lateral earth pressure

K p 3.000

Earth Pressure Functions:

LRFD 3.11.6.2-1

Lateral Forces:

Active Lateral Force:F H.soil F H_triangular H Stem H Ftg

F H.soil 2017lbf Surcharge Lateral Force:

F H.sur_LL F H_uniform H Stem H Ftg H embankment q sur_LL F H.sur_LL 847.9lbf F H.sur_DL F H_uniform H Stem H Ftg H embankment q sur_DL

F H.sur_DL 0lbf Wind:

F H.wind_1P wind_1H W1 L analysis H W10 F H.wind_10lbf F H.wind_2P wind_2H W2 L analysis H W2 2.7ft

F H.wind_2133.33lbf F H.wind_total F H.wind_1F H.wind_2

F H.wind_total 133.33lbf

Passive Lateral Force Height:

Load Combinations to include Contribution of Soil over Toe (including Passive Resistance)LC include_passive 0

LC passive "All"

H passive_toe max 0ft D f H ignore

H passive_toe 3.500ft

H passive z

H Key if z LC include_passive 0ft H passive_toe

Passive Lateral Force:

Vehicle Collision:

Vehicle Collision Force:P CT_design if H TB 0in P CT 0kip P CT_design 54kip

LRFD Table A13.2-1

Stability:

L Wall 45ft

Length of wall assumed effective for Vehicle Impact for purposes of checking wall stability:

P CT_Static_Factor 1.00 Adjust Dynamic Impact to Static Force for Stability Evaluation

F H.vehicle 1200lbf

Structure Design:

Assume vehicle impact may be near the end of wall or expansion joint y impact

32in Test Level - 4 (TL-4)

LRFD Table A13.2-1

L impact 3.5ft

L c.base 16ft

F H.vehicle_reinf 3376.3lbf

Stability Checking Moment Arm

Vertical

Sound Barrier:

arm v_SB8.02

ft

Traffic Barrier:

arm v_TB8.75ft

Stem:arm v_Stem8.30ft

Footing:arm v_Ftg 5.00ft

Soil (over Toe):

arm v_Soil_Toe 3.80ft

Soil (over Heel):arm v_Soil_Heel9.50ft

Surcharge:

arm v_sur_LL9.50ft

arm v_sur_DL10.00ft

Horizontal

Backfill:

arm h_Backfill 3.78ft

Surcharge:arm h_sur 5.66ft

Wind:

arm h_Wind_113.99ft

arm h_Wind_2

12.66ft

Vehicle Impact:arm h_Vehicle y impact H Stem

H Ftg

arm h_Vehicle13.99ft

Soil (over Toe):

Resisting Moment

Sound Barrier:M r_SB z

DC z

W SB arm v_SB

Traffic Barrier:M r_TB z

DC z

W TB arm v_TB

Stem:M r_Stem z

DC z

W Stem arm v_Stem

Footing:M r_Ftg z

DC z

W Ftg arm v_Ftg

Soil (over Heel):M r_Soil_Heel z

Ev z

W Soil_Heel arm v_Soil_Heel

Soil (over Toe):M r_Soil_Toe z

if z LC include_passive 0lbf ft Ev z

W Soil_Toe arm v_Soil_Toe

Eh z

F H.passive z

arm h_Soil_Toe

z

Surcharge (DL):M r_Sur_DL z

Ev z

W sur_DL arm v_sur_DL

Surcharge (LL):

M r_Sur_LL z

LSv z

W sur_LL arm v_sur_LL

Total (no LL surcharge*):M r_no_LL_sur z

M r_SB z

M r_TB z

M r_Stem z

M r_Ftg z

M r_Soil_Heel z

M r_Soil_Toe z

M r_Sur_DL

z

Total (with LL surcharge*):

M r_with_LL_sur z

M r_no_LL_sur z

M r_Sur_LL

z

*Live Load Surcharge over the footing is:

not included for evaluation of eccentricity or sliding (except when evaluating Vehicle Impact)included over the footing for evaluation of bearing and structure design

M r_Stem 0

01234

5

670

17081.815373.621352.215373.621352.215373.625622.7lbf ft

Overturning Moment

Backfill:M o_Backfill

z

Eh

z

F H.soil

arm h_Backfill

Wind:M o_Wind

z

WS

z

F H.wind_1arm h_Wind_1

F H.wind_2arm h_Wind_2

Vehicle Impact:M o_Vehicle

z

CT

z

F H.vehicle

arm h_Vehicle

M o_no_LL_sur

z

M o_Backfill

z

M o_Wind

z

Eh

z

F H.sur_DL

arm h_sur

M o_with_LL_sur

z

M o_no_LL_sur

z

M o_Vehicle

z

LSh

z

F H.sur_LL

arm h_sur

*Live Load Surcharge over the footing is:

not included for evaluation of eccentricity or sliding (except when evaluating Vehicle Impact) included over the footing for evaluation of bearing and structure design

Stability Checking - Eccentricity

Investigate excessive loss of base contact (location of force resultant)

W no_LL_sur z

DC z

W Conc Ev z

W Soil_Heel W sur_DL if z LC include_passive 0lbf Ev z

W Soil_Toe

M net_no_LL_sur z

M r_no_LL_sur z

M o_no_LL_sur

z

W with_LL_sur

z

W no_LL_sur z

LSv z

W sur_LL

M net_with_LL_sur z

M r_with_LL_sur z

M o_with_LL_sur

z

Eccentricity (Actual):

Eccentricity (Allowable):

e allow1 2.5ft LRFD 10.6.3.3&

11.6.3.3

e allow_Ext 4ft

LRFD 10.6.4.2&11.6.5(middle 8/10ths for Extreme Event with Live Load)

e allow z

if z LC Ext e allow1 e allow_Ext

PR Eccentricity_min min submatrix PR Eccentricity 1 i last 0 0 PR Eccentricity_min 3.2

Check_Eccentricity if PR Eccentricity_min 1 "OK" "No Good" Check_Eccentricity "OK"

Stability Checking - Overturning

Checking the bearing stress and the location of the force resultant replaces the check of the ratio of the overturning moment to the stabilizing moment in AASHTO LRFD.No LL Surcharge:

PR OT_no_LL_sur_min min submatrix PR OT_no_LL_sur 1 i last 0 0 PR OT_no_LL_sur_min 3.5

Check_Overturning_no_sur if PR OT_no_LL_sur_min 1 "OK" "No Good" Check_Overturning_no_sur "OK"

With LL Surcharge:

PR OT_with_LL_sur_min min submatrix PR OT_with_LL_sur 1 i last 0 0 PR OT_with_LL_sur_min 1.6

Check_Overturning_with_sur if PR OT_with_LL_sur_min 1 "OK" "No Good" Check_Overturning_with_sur "OK"

Stability Checking - Lateral Sliding

Live Load Surcharge over the footing is not included for evaluation of eccentricity or sliding

k construction_type if Construction_type"CIP"

=1 0.8

()

k construction_type 1.0

0.8 for precast concrete footing, 1.0 for CIP concrete footing LRFD10.6.3.4-2

Nominal Sliding Resistance:R t

z

W no_LL_sur

z

k construction_type

tan Ftg

Nominal Passive Resistance:R ep

z

F H.passive

z

R R_sliding

z

T

z

R t

z

R R_passive

z

EP

z

R ep

z

Factored Sliding Resistance:R R

z

R R_sliding

z

R R_passive

z

The factored lateral loads shall not exceed R R

Backfill:F H.soil_factored z

Eh z

F H.soil

Wind:F H.wind_factored z

WS z

F H.wind_total

Vehicle Impact:F H.vehicle_factored z

CT z

F H.vehicle

Dead Load Surcharge:F H.sur_DL_factored z

Eh z

F H.sur_DL

Live Load Surcharge:F H.sur_LL_factored z

LSh z

F H.sur_LL

Total:

F H z

F H.soil_factored z

F H.wind_factored z

F H.vehicle_factored z

F H.sur_DL_factored z

F H.sur_LL_factored

z

Performance Ratio:

PR Sliding_min min submatrix PR Sliding 1 i last 0 0 PR Sliding_min 1.10 Check_Sliding if PR Sliding_min 1 "OK" "No Good"

Check_Sliding "OK"

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