In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 209

50 100 50 100

75 75

1 2 3 4 5 1 2

1 0 12 12

5 C y

C

C y

y
y

6 6

1

6 5

z

z

z

4 3

1 0 6

6 6

1400 cm 4 600 cm 4 z 1 I = I =

z z

(a) Z-section (b) Pi-section (c) Rectangular hollow section

(All dimensions in mm)

Figure 5.42 Worked examples 4, 9, 10, and 11.

I z 1 = 2 × ( 75 × 10 × 37.5 2 ) + 2 × ( 75 3 × 10 / 12 )
= 2813 × 10 3 mm 4 = 281.3 cm 4 ,
I y 1 z 1 = 75 × 10 × 37.5 × ( − 75 ) + 75 × 10 × ( − 37.5 ) × 75
=− 4219 × 10 3 mm 4 =− 421.9cm 4 .

The centre of the Mohr's circle (see Figure 5.37b) is at
I y 1 + I z 1
2

984.4 + 281.3
2

= 6328 cm 4 . =

The diameter of the circle is
√ [ ( 984.4 − 281.3 ) 2 + ( 2 × 421.9 ) 2 ]= 1098.3 cm 4

and so

I y = ( 632.8 + 1098.3 / 2 ) = 1182 cm 4 ,
I z = ( 632.8 − 1098.3 / 2 ) = 83.7 cm 4 ,
tan2 α = 2 × 421.9

( 984.4 − 281.3 ) = 1.200,
α = 25.1 ◦ .

5.12.5 Example 5 - biaxial bending of an angle
section cantilever

Problem . Determinethemaximumelasticstressanddeflectionoftheanglesection
cantilever shown in Figure 5.41 whose section properties were determined in
Section 5.12.3.