The shear capacity calculations are split into separate tables. The sample table shown in Table 5.13 displays the results that are applicable to each shear section being
analyzed. The shear capacity of the concrete, original vertical stirrup area, and shear distribution factor for each beam are displayed in this table.
Table 5.13 Sample Shear Analysis Results Table
Shear Capacity of Concrete Original Vertical Stirrup Area Shear Distribution Facor
(lbs) (in.2)
72128 1 72128 0.393 0.393 0.586 I 0.586
The ultimate shear capacity calculation of each section is computed in the table shown in Table 5.14. The program calculates the effective vertical and inclined shear reinforcement steel area then calculates its capacity and the beam's ultimate shear
capacity at each section. Once the shear capacity of each section has been calculated, the program calculates the ultimate shear capacity at each tenth point as shown in Table 5.15.
Table 5.14 Sample Section Shear Capacity Results Table
Section #
1
2
3
4
5
6
7
8
Vertical Stirrup Area in Section 1 Inclined Stirrup Area in Section 1
Shear Reinforcement Capacity in Section 1 Ultimate Shear Capacity in Section 1 Vertical Stirrup Area in Section 2 Inclined Stirrup Area in Section 2
Shear Reinforcement Capacity in Section 2 Ultimate Shear Capacity in Section 2 Vertical Stirrup Area in Section 3 Inclined Stirrup Area in Section 3
Shear Reinforcement Capacity in Section 3 Ultimate Shear Capacity in Section 3 Vertical Stirrup Area in Section 4 Inclined Stirrup Area in Section 4
Shear Reinforcement Capacity in Section 4 Ultimate Shear Capacity in Section 4 Vertical Stirrup Area in Section 5 Inclined Stirrup Area in Section 5
Shear Reinforcement Capacity in Section 5 Ultimate Shear Capacity in Section 5 Vertical Stirrup Area in Section 6 Inclined Stirrup Area in Section 6
Shear Reinforcement Capacity in Section 6 Ultimate Shear Capacity in Section 6 Vertical Stirrup Area in Section 7
Inclined Stirrup Area in Section 7
Shear Reinforcement Capacity in Section 7 Ultimate Shear Capacity in Section 7 Vertical Stirrup Area in Section 8 Inclined Stirrup Area in Section 8
Shear Reinforcement Capacity in Section 8 Ultimate Shear Capacity in Section 8
(in.*) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs) (in.14) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs) (in.2) (in.2) (lbs) (lbs)
4 • ran
0.353 0.00 120000 163000 0.353
2.81 196000 228000 0.353
2.81 196000 228000 0.353
2.81 183000 217000 0.353
0.00 40000 95000 0.353 0.00 27000 84000 0.353 0.00 20000 78000 0.000 0.00
0 61000
0.353 ; 0.00 120000 163000 0.353
2.81 196000 228000 0.353
2.81 196000 228000 0.353
2.81 183000 217000 0.353
0.00 40000 95000 0.353 0.00 27000 84000 0.353 0.00 20000 78000 0.000 0.00
0 61000
Table 5.15 Sample Tenth Point Shear Capacity Results Table
X
0 4.5
9 13.5
18 22.5
Tenth Point
1 2 3 4 5 6
In Section
# 1 3 6 6 8 8
Shear Stirrup Capacity
(ibs>
120000 196000 27000 27000
0 0
Shear Capacity
(lbs) 163000 228000 84000 84000 61000 61000
Shear
• <ằ _ • ~A- Shear In Section Sttrrup _
# Capacity C a,p K a c't y
flb* { l b S )
1 3 6 6 8 8
120000 196000 27000 27000
0 0
163000 228000 84000 84000 61000 61000
The required dead load resistance at each shear investigation point is displayed in Table 34. The results from the live load generator analysis, dead load analysis, and
ultimate shear capacity are displayed in the table shown in Table 35. This table is where the shear load rating analysis for each loading vehicle is performed. A similar table is used to calculate the shear load ratings at each tenth point.
Table 5.16 Sample Dead Load Shear Results Table
Point # Distance (ft) i DeadlLoadl I Shear (kips);
1 0.00 b 8 : 4 :
2 0.33
5;:37ia-
3 2.58 [ 3*0-'
t . . . .
4 4.83
;:3(X2:
5 5.83
•2S5:: 6 8.83 i.23&
7 14.83
; rar:.-
8 16.50
; 10:2:
Table 5.17 Sample Shear Load Rating Calculation Table
By Section Break
1
2
3
4
5
6
• 7
8
MaximumtSheartin&ectionfl*DueôoiDeadi!a>aaôsằ
Max. Shear in Section 1 Due to Undist. Live Load Max5Sheanin4Sectionsi*Due(toiOist5tilveii:oada!i^a!
Ultimate&heanCapacitygoftSectlonclftg^^
SheaainvertoiytRtetlngiEactoBottSet^oRBiMWWWi SheartOpepatlnmRatinaiEactortottSectionwiWHiiiBg MaximumiSheaiSirnSectionODueitoiDeadsUoadSBsafi Max. Shear in Section 2 Due to Undist. Live Load Max"$Shear?inHSectionf25Dueito?DlstJ(llive>iroadiôBSBS iyitimate^SheanCapacityiofiâectioni2JS^^ôWôiHKi8 Sheai*nventorviRatinpAI^ctoffoBSe<^ont2ằSôH(WWB SheartOperatir^E^ino^EadotfoftSectionCBilPBBB Maximum)Shean(in!Sectionf3iDuettoiiDeadilIoadWM Max. Shear in Section 3 Due to Undist. Live Load MaxSSheartinlSectioni3*Duetto3Dist5EveiL:oadSI8SK UltimateôheaiJGapadty3of*Sectiont3Jaôeôfiôôsôasi SheartrwentoryjRatingiEaôoôoằSe(^oni3ằRBằBWB Sheart0peratinq1BatinciiactortoflSectioni3ôWSWW MaximumJSrieartiniSectionf'MDLieHoôDeadll*oadi8S8S Max. Shear in Section 4 Due to Undist. Live Load MaxgSheartinSSectionS48DueitolDistSCiveilioadSaES5 li)ltimatetSheariCapacitysoftSection<4ôôiôôiằas3iô#
Sheartliwentop^atingiEactortoftSectionWiiaaaeBI Sheariepet^ingiRatinpliacaoffof^ectionriWIWOIWIl Maximum5Sheartin(SectionSiDue^to*Deadllioadieft Max. Shear in Section 5 Due to Undist. Live Load MaxSSheaiiiniSection55f.DueltcHDistSBive3t;oadSEesô
)!lltimate)SheaiiGapacitv$o^ectiorrtSHPôiSWm^
SheaiS!nventor^Bating|l=actotK)ftSection16ôôaBSW SheariGperatinplRatingiiiaaoifo^ectonKnawWBaB Maximum8SheafliniSectionj6lDueao?DeadHioadiằô
Max. Shear in Section 6 Due to Undist. Live Load Max5Shear?in?Sectionf6!Due5to?DistSllivejiloadiWeS iyitimatejSheartGapacityJoôSectioni6iằ^S3ằ!^6K^
SheafllnventoryjRatingi(iactoaoftSectioô6Bassaaaa SheanGpei^tir^raatinflliactoiidfiSectiontSiBgSWWi MaximumsSheai5in3Sectioni7?DueitoJDeadlHoadô8 Max. Shear in Section 7 Due to Undist. Live Load MaxSSheatiinlSectronS7i!DueltolDis11t!)vellôoad^n UltimateiSheaBeapacityJofiSeôiorm7^đS6is^Sisiim SheaalrwentopflRatingiiiactosollSectioniaiBBaffia*
SheaHGpecatinglRatinp^f^rtotfoftSectionBWeweag MaximumJSheaRin;(Sectioni84DuertcHiDeadllloadằiS Max. Shear in Section 8 Due to Undist. Live Load MaxaSheaRin!Section?8lDueito3DistSiiiveilloadS8^
l^ltimate3SheamGapacityio^Sectioni8l@iim£%iii^
Sheai*nventoryJBatiDgifeictoaoft!Sectiorit8ôKasafiSI SheaoQperatina^RatinoiEartoacflSectiorjl8WiằS8il
B(klps)*
(kips) (?(kipsyc W(kips)l
• M i
ô(kips)l (kips) P{kips)B
*(klps)ằ
• m M H M M fe(klps)I
(kips)
*(kips)l i(kips)l I f
ttmmm
S(kips)l (kips) f(kfps)S f(kips)ằ
WSB8BW
wmem
B(kips)ô
(kips) I(kips)f f ( k i p s ) l
xyBMBHSMB WMMWaBB
S(kips)8 (kips) B(kips)H 8f(kips)S
mmm
g H S I(kips)l
(kips)
ằ(kips)l Sf(kips)S tssssms
ms®m
H(kips)l (kips) S(kips)l
ô(kips)fc
mmm
H20 HS20 HS25
'—"'' ''['%jff%3' "• 'EZ23r "' !ES33l
38.4 37.1 J'28;*r
'163:0;
1,85
> 3.09 37.8 37.1 fc28H~
1228:0 :• 2.93 i'4:89- 34.0 34.8
t2Bằ-
?228:0 3.21
• 5.36 30.2 33.1
£ 2 5 ; *
!217:0 3.26 5.45 28.5 32.2
^24:4;- i-'95.0 1.09 1.83 23.3 29.5
^22:4::
' 8 4 . 0 1.11 1.84 13.1 24.2
$-18:4:
578.0>
1.53 2.56 10.2 22.8
m-T&.
i61.0 1.27
• 2.12 38.4 37.1
•28;1;
163:0:
1.85 3:09 37.8 37.1 - 2 8 . t;
228:0>
2.93 4.89 34.0 34.8 ::26.4
^228.0 3.21 5.36 30.2 33.1 25V1"
'217:0 3.26 5.45 28.5 32.2 - 2 4 . 4 95.0' 1.09 1.83 23.3 29.5 ' 2214,
84:0!
1.11 1.84 13.1 24.2
•i 1 8 . 4
-7810^
1.53 2.56 10.2 22.8 M 7 3 t
61.0:
1.27 2.12
38.4 52.3
^39:7' n 63.0*
1.31 2.19 37.8 56.3 M2.7-
=228:0' 1.93 3.22 34.0 52.3
^39:7?
'228:0' 2.13 3:56 30.2 49.1 S37i2^
i'217;0'' 2.20 3.67 28.5 47.5 C36-.0
^95:0 0,74
• 1.24 23.3 42.7
^ 3 2 : 4 J84.0:
Q.J-6 1.27 13.1 33.1
•v25:1--' f--78:0-
1.12 1.87 10.2 30.7
*23:3-
<--6t>0?
0,94
• 1.57 38.4 52.3 39:7 163:0
1.31 2.19 37.8 56.3 42:7
;228:0.
1.93 3.22 34.0 52.3 -39:7 - 228.0
2.13 3.56 30.2 49.1 37:2
; 217.0 2.20 3.67 28.5 47.5 36:0
"-' 95:0-- 0,74 1.24 23.3 42.7 :• 32.4':
84:0 0JS 1.27 13.1 33.1 25:1
• 78.0 1.12 1.87 10.2 30.7 23:3 - 6 1 . 0 Q..9A 1.57
38.4 70.3 53.3 -163.0
0,98 1.63 37.8 70.3 ,53.3;
E228.0 1.55 2.58 34.0 65.3
!r'49S'-
^228:0- 1.71 2.85 30.2 61.3 F46.5*
217:0 1.76 2.94 28.5 59.3 '45.0: 595.0- 0,50 0.99 23.3 53.3 i40l4
*84':0--"
0.61 1.02 13.1 41.3
;31.3:
'78.0-- 0.90
1.50"
10.2 38.3 i: 29.1- ' 6 1 . 0 0.76 1.26
38.4 70.3
• 53.3;
163.0 0.98
1.63 37.8 70.3 53.3'
;:228';0 1.55 2.58 34.0 65.3 '49:5'
•228:0 1.71 2.85 30.2 61.3
= 46.5 -2170
1.76 2.94 28.5 59.3 45.0
•:• 9 5 . 0
0.5.9 0.99 23.3 53.3
•40.4 84:0 0,51
1.02 13.1 41.3
"3 1 . f r 78.0 0.90 1.50 10.2 38.3 29:r 61:0 0.73 1.26
5.3.2.3 Dead/Live Load Generator
Though only one bridge span was investigated during this project, the same structural analysis and load rating calculations are used for any concrete T-Beam span length. The EXCEL live load generator analysis was verified by CONSYS results for multiple span lengths. CONSYS is a commercially available live load generator.
The live load analysis is based on the theory of superposition. The force effects from individual axle loads are calculated at each investigation point. These force effects are then superimposed together to attain the total force effect due to the loading vehicle as it crosses the bridge.
The maximum force effect results are summarized at the top of each loading vehicle analysis sheet as shown in Figure 5.6. The results include the maximum positive moment and location, and the maximum shear to the left and right of each investigation point.
HS20 Truck
9 M 92 t2 04 Jjj_ it 8,7 flằ fl.t 1.B
Tenth Point Distance (ft) Moment (klp-ft) JSằV2(Wps)Sằjaằ
??>-:&ws(kips)tằKô
Absolute Max Shear
0 0 0
$6.3 0 56.3
0.1 4.5 224 49.9
•0.8 49.9
0.2 9 384 42.7 -2.5 42.7
rem
0.3 13.5
479 35.5 -6.5 35.5
th; Point
0.4 18 512 28.4 -13.3
28.4 0.5 22.5 530 22 -20.5
2 2
t r O r C B a ' 0.6 27 53l"1 15.6 -27.7 27.7
0.7 31.5
470 9.6 -34.8
34.8 0.8
36 371 6.4 -41.2 41.2
0.9 40.5
214 3.2 -47.6
47.6 1 45
0 0
•53,3
53.3
I \
A 1
T 1 r •
V,
^ ^ ~ ^
right
Point#
Distance (ft)
'mm$(Mp*)wm
MS^ViHklpsJffi'iisaf.
Abs Max Used for Analysis
1 0.0 56.3
0 56.3
ffl^w-'TgHiBrywRTwin
2 I 3 0.3 I 2.6 56.3 52.3
0 -0.4 56.3 | 52.3
4 4.8 49.1
-0.8 49.1
5 5.8 47.5
-1 47.5
6 8.8 42.7
-2 42.7
7 14.8 33.1 -7.7 33.1
8 16.5 30.7 -10.9 30.7
9 28.5 13.5 -30.1 30.1
10 30.2 10.7 -32.5 32.5
11 36.2
6 -41.2 41.2
12 39.2
3.9 -45.5
45.5
lAjUfejSJeilSbS
13 40.2
3.2 -46.9 46.9
L i *
42.4 1.8 -49.8
49.8 15 44.7
0 -53.3
53.3 16 45.0
0 -53.3
53.3
Point # Distance (ft)
m®rswi*mm
ấ-isvB'itkips^s-sft
Abs Max Used for Analysis
^InteriorsGrrder^Sheai^aluesJtoiBeiLJsedffontAna
1 0.0 56.3
0 56.3
2 0.3 56.3
0 56.3
3 2.6 52.3 -0.4 52.3
4 4.8 49.1
-0.8 49.1
5 5.8 47.5
-1 47.5
6 8.8 42.7
-2 42.7
7 14.8 33.1 -7.7 33.1
8 16.5 30.7 -10.9 30.7
9 28.S 13.5 -30.1 30.1
10 30.2 10.7 -32.5 32.5
11 36.2
6 -41.2
41.2 12 39.2
3.9 -45.5
45.5 13 40.2
3.2 -46.9
46.9 14 42.4
1.8 -49.8
49.8
ysfsK
15 44.7
0 -53.3
53.3 16 45.0
0 -53.3
53.3
Figure 5-6 Sample Live Load Generator Results Table