5 A beam is subjected to maximum bending moment of 15 kNm a

5. A beam is subjected to maximum bending moment of 15 kNm.

a) Calculate the maximum bending stress if the beam profile is IPE 240.

b) Choose an appropriate IPE profile if the maximum allowable normal stress is 170 MPa.

6. A rectangular beam with cross section 120 × 40 mm (upright) is subjected to a bending

moment of 20 kNms and an axial pull of 100 kN.

Calculate the largest composite normal stress in the element. Sketch the stress distribu-tion.

Solution

The formula for the bending stress is Mc/I where Mis the bending moment, c is the distance from the neutral axis and I is the geometric moment of Inertia.

The IPE 240 section has the dimensions b=120mm, h = 240mm, t1= 6.2 mm, t2 =9.8mm

h/2 = 120mm,= c

Iy = 277.7 cm^4

M = 15000 Nm

Stress of bending = 15000*100* 12/177.7 N/cm^2 =8438 N/cm^2 =84.38 MPa

If max allowable stress is 170 which is 2 times the calculated, the flange ht canbe increased. New I has to be calculated and the calculations redone.