Page 187 - Bridge and Highway Structure Rehabilitation and Repair

162 SECTION 2 STRENGTHENING AND REPAIR WORK

Proof: Calculate the c.g. of loads where resultant is acting.
Assuming maximum BM occurs under middle heavy wheel at B.
M 3 R1 8 (L/2 6 x) 6 4k 8 14 ft
2
–
R1 3 Resultant 8 (L/2 4 x 6 x)/L
–
R1 3 36 8 (L/2 4 x 6 x)/L (4.25)
For maximum BM rate of change of moment 3 0
–
dM /dx 3 Resultant 8 (x/L 6 2x/L) 3 0
2
–
x 3 x/2
Procedure for HL-93 truck:
Replace 3 wheel loads by a single resultant of wheel loads 3 $ (16 4 16 4 4) 3 36 kip
Locate the resultant force from nearest wheel by taking moments about that wheel.
$ M 3 0 at wheel B
(36 X) 4 16 14 ft 6 4 14 ft 3 0;
Distance (to c. g. O) X 3 (12 14)/36 3 14/3 3 4.667 ft from wheel B.
Calculate reactions at supports: For a given live load, reactions will vary with span
lengths. Taking moment at about support 2,
R1 8 L 6 36 (L/2 6 2.333 ft) 3 0;
Reaction R1 3 18L – 60;
Mmax 3 18(L-1.55) (L-14)/L (Kip-ft) (4.26)
Vmax 3 24(3L-28)/L (Kips) (4.27)

Comparisons of numerical values are shown in Table 4.4.
4.11.2 Procedure for HL-93 Alternate Tandem Truckloads (Table 4.5)

Author’s BM formula for tandem loads = 12.5 (L-4) (Kip-Ft) (4.28)
Author’s shear formula for tandem loads = 50 (1-2/L) (Kips) (4.29)
Single lane moments and forces are given. For multiple lanes, live load will be increased
linearly. A multiple-lane reduction factor is allowed. A 6-foot transverse distance between tires
is assumed.
HL-93 maximum lane loads
2
Author’s use of simplifi ed formula 3 w L /8
Table 4.6 shows total HL-93 truck and lane load moment and shear $ (Lane loads of 0.64
kips/ft 4 HS-20) and $ (Lane loads of 0.64 kips/ft 4 Alternate tandem trucks)

4.11.3 Envelope of Design Moments and Shears
Design Moment 3 Total HL-93 moment 8 Impact factor 8 Applicable distribution factor
for single lane.
Dynamic load allowance (impact factors) 3 1.33 applicable to truckloads only. For reduced
posted speed, a lower factor may be used.
For multiple lane live loads, a reduction in total live load is applicable.
Fatigue dynamic load allowance (for fatigue analysis) 3 1.15 applicable to truckloads
only.
Comparison of maximum live load moments for internal beam. For truck load versus tandem
load a comparative study is shown in Table 4.5.