Question

A rectangular beam, simply supported over a span of 4 m, is carrying uniformly distributed
load of 50 kN/m. Find the dimensions of the beam, if the depth of the beam section is 2.5 times
its width. Maximum bending stress in the beam section is 60 MPa.

Answer 1

Answer:

acha theek hai aur??

Step-by-step explanation:

ans. 53MPa.

Answer 2

Answer:

63mm,157.5mm

Step-by-step explanation:

Total load(W)=50kN/m=50*10^3N

Span:4m=4*10^3mm

Depth of beam section (d)=2.5b (2.5 times of its width)

Maximum bending stress=60MPa=60N/mm^2

section modulus of rectangular section=Z=bd^2/6

=b*(2.5b)^2/6

b*6.25b^2/6

Z=6.25b^3/6

and maximum bending moment at the centre of a simply supported beam subject to a uniformly distributed load

M=Wl/8

=(50*10^3)*(4*10^3)/8

M=25*10^6 N-mm

Maximum bending stress=

60=M/Z

60=25*10^6/6.25b^3/6

60=24*10^6/b^3

b^3=24*10^6/60

b^3=0.4*10^6

b=0.63*10^2

b=63mm

d=2.5*b =2.5*63

=157.5mm

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