Design Examples of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 347

We can now calculate the design plastic moment resistance as follows:
M pl , Rd ¼ 14,168 : 4 343 : 1 + 3173 : 7 118 : 1 + 3484 : 3 18 : 1 = 2

+ 3830 : 8 19 : 9 = 2 + 7585 : 6 881 : 9 + 9405 1762 : 9

¼ 28,575,456 :

5kNmm ¼ 28,575

: > :

5kNmm 26,223 26 kNm

ð Then O : K : Þ:

Design of the Intermediate Composite Plate Girder Cross Section
at Quarter-Span
Since it is decided to reduce the cross section at quarter-span, as shown in
Figure 4.106 , we should check the safety of the proposed cross section
against different stresses. Assuming the bending moment diagram is a
second-degree parabola (see Figure 4.114 ), we can determine the bending
moment at quarter-span as follows:
D
26,223

2
;

1
2

26 ¼

then D¼ 6555

:

8kNm

:

The design moment at quarter-span ( M Ed ) ¼ 26,223.26 6555.8 ¼
19,667.5 kNm. We can now repeat the previous procedures adopted for the
heavier cross section for the design of the smaller steel plate girder cross
section shown in Figure 4.115 :

14,168 : 4 + 3173 : 7+ x 500 275 = 1000

¼ 5775 + 7656 + 500 30 x ð Þ 275 = 1000

17,342 : 1 + 137 : 5 x ¼ 13,431 137 : 5 x + 4125

2 137 : 5 x ¼ 213 : 9

Then, x¼ 0.78 mm.
The design plastic moment resistance can be calculated as follows:
M pl , Rd ¼ 14,168 : 4 325 : 78 + 3173 : 7 100 : 78 + 107 : 3 0 : 78 = 2

:

8 29

: =

2 + 7656 899

:

22 + 5775 1784

:

+ 4017 22 22

¼ 22,182,667 : 7kNmm ¼ 22 182 : 7kNmm > 19,667 : 5kNm

ð Then O : K : Þ:

M 2 kN m

26,223.26 kN m

D

12 m 12 m

24 m

Figure 4.114 Calculation of bending moment acting at quarter span.