Page 199 - Bridge and Highway Structure Rehabilitation and Repair

174 SECTION 2 STRENGTHENING AND REPAIR WORK

Yield stress in steel 3 Fy, taking moments about plastic N. A., calculate Yp

Fy 8 [b 8 t 4 t 8 (d 6 Yp 6 t )] 3 Fy [b 8 b 4 t 8 (Yp 6 t )]
f f w f b f w f
Plastic moment 3 Sum of all moments about N. A.
3 Fc 8 Yc1 4 Fwc 8 Yc2 4 Fwt 8 Yc3 4 Ft 8 Yc4 (4.37)

From the equation (4.39), the value of Yp (location of N. A.), compression, and tension
forces are known and require the following for solution:
1. Applicable I section.
2. Strength limit states I to V.
3. Construction limit state and uncured slab.
4. Reference to AASHTO Section 6.10.5.2.3.
Non-composite non-compact sections may require:

1. Strength limit states I to V.
2. Construction limit state and uncured slab.
3. Reference to Section 6.10.5.3.2 and Section 6.10.5.3.3.

4.15.2 Plastic Moment in Hybrid Girders
1. With the availability of 70W and 100W grade steel, the use of the higher-grade steel (such
as 70W for flanges and 50W for web) is becoming popular.

Moment causing initial web yielding 3 f S (d/h)
yw
Moment causing initial fl ange yielding 3 f S (d/h)
yf
Plastic bending moment M 3 b t (d 4 h) f /2 4 t h f /4 (4.38)
2
p f f yf w yw

2. Moment resisted by flanges and shear by web:
• Strength limit states I to V
• For 70W steel and construction limit state, assume non-compact
• Redistribution of moments in continuous girders permitted.

4.15.3 Plastic Moment of Composite Section
When plastic N. A. is in web:
In Figure 4.18, the sum of all horizontal forces 3 0
Fs 4 Fc 4 Fwc 3 Fwt 4 Ft (4.39)
Yield stress in steel 3 Fy, for positive moment concrete is in compression
Ultimate stress in concrete 3 0.85 fc1
0.85 fc1 8 be 8 ts 4 Fy 8 [bt 8 tf 4 tw 8 (D 6 Yp 6 tf)] 3
Fy [bb 8 bf 4 tw 8 (Yp 6 bf)]

From the above equation the value of Yp (location of N. A.), compression, and tension
forces are known.
Plastic Moment 3 Sum of all moments about N. A.
1. Strength limit states I to V.
2. Redistribution of moments in continuous girders permitted.