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"