rectanular section , triangular section, symmetric I section , unsymmetrical I section, T section, circular section

1. Shear stresses in beams
Venkata Sushma Chinta
Assistant Professor, MED

2. Shear stress in Beams:
The bending stress act longitudinally and its intensity is directly proportional to
its distance from neutral axis.
A typical beam
section is subjected to shear
force in addition to bending
moment. The variation of
shearing stress, which is due
to the presence of shear
force, is studied in this
chapter.

6. Note :The above expression is for horizontal shear
stress. From The principle of complementary
shear, this horizontal shear stress Is accompanied
by a vertical shear stress of the same intensity.

7. The integral represents the moment of the area
A’ about the neutral axis. We will denote this by
symbol Q. Since the location of the centroid A’ is
determined from 𝑦̅’.

11. Q1. A wooden beam 100 mm wide and 150 mm deep is simply
supported over a span of 4 meters. If shear force at a section of
the beam is 4500 N, i)find the shear stress at a distance of 25 mm
above the N.A.ii) Shear stress at neutral axis iii) mean shear stress

13. Q2. A timber beam of rectangular section is simply supported at
the ends and carries a point load at the center of the beam. The
maximum bending stress is 12 N/mm2 and maximum shearing
stress is 1 N/mm2, find the ratio of the span to the depth.

14. Q3. A simply supported wooden beam of span 1.3 m having a cross-
section 150 mm wide by 250 mm deep carries a point load W at the
center. The permissible stress are 7N/mm2 in bending and 1 N/mm2
in shearing. Calculate the safe load W.

24. A 100 mm X 40 mm I-beam is subjected to a shear force of 15 kN. Find the
transverse shear stress at the neutral axis and at the top of the web. Compare
it with the mean stress on the assumption of uniform distribution over the
web. What is the percentage of shear force carried by the web? Moment of
inertia of the section is 1.1 X 106 mm4, web thickness is 3 mm and flange
thickness is 4 mm.

25. A 100 mm X 40 mm I-beam is subjected to a shear force of 15 kN. Find the
transverse shear stress at the neutral axis and at the top of the web. Compare
it with the mean stress on the assumption of uniform distribution over the
web. What is the percentage of shear force carried by the web? Moment of
inertia of the section is 1.1 X 106 mm4, web thickness is 3 mm and flange
thickness is 4 mm.

29. A simply supported beam of 2-m span carries a uniformly distributed load of
140 kN per m over the whole span. The cross-section of the beam is a T-section
with a flange width of 120 mm, web and flange thickness of 20 mm and overall
depth of 160 mm. Determine the maximum shear stress in the beam and draw
the shear stress distribution for the section.