Department of Aerospace Engineering, IIT Kharagpur
AEROSPACE STRUCTURAL ANALYSIS (AE31009)
Tutorial Sheet No.3
SHEAR FLOW
Instructor: Prof. B.N.Singh
Email ID: bnsingh@aero.iitkgp.ernet.in
1. Fig. 1 shows a single cell rectangular beam carrying the load of 100 lb. The problem is to find the
internal resisting shear flow pattern at section abcd.
2. Fig. 2 shows a two cell cantilever beam with 10 flange stringers. The cross section is constant. Let it
be required to determine the internal shear flow in resisting the 1000 lb. load acting as shown. For
simplification, the top and bottom sheet covering and the three vertical webs will be considered
ineffective in taking bending flexural loads. Since the beam section is symmetrical about the X axis,
the beam will bend about this axis in resisting the given external load. The moment of inertia or the
section about the X axis equals 250 in.
3. Find the internal resisting shear flow pattern for the 3 flange-single cell beam of Fig. 3. Assume webs
or walls are ineffective in bending.
4. Determine the shear center location for beam of Fig. 4. Assume webs or walls are ineffective in
bending.
5. Fig. 5 shows a multiple flange-single cell beam section. Find resisting shear flow system if webs and
skin are ineffective in resisting bending stresses. All skin flange members have area of 0.1 sq. in.
each.
6. Determine the shear flow resisting system for the beam section in Fig. 6. The 6 flanges have areas of
0.2 sq. in. each. Skin is of 0.032in. thickness. Assume skins are ineffective in bending.
7. The cross-section of a high lift device is shown in Fig. 7. The aerodynamic pressure acting on the
lower panel of the device has a net resultant V3 = 100X103 N and its line of action is aligned with axis
i3 , as indicated on the figure. Material properties are: E = 73 GPa, G = 30 GPa.
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15.
(1) Find the distribution of shear stress flow associated with the shear force V3. (2) Sketch this shear
flow distribution. (3) Determine the location and magnitude of the maximum shear stress.
Fig. 8 shows the regular hexagonal cross-section of a thin-walled beam of sides ‘a’ and constant wall
thickness t. The beam is subjected to a transverse shear force S, its line of action being along a side of
the hexagon, as shown. Find the rate of twist of the beam in terms of t, a, S and the shear modulus G.
Plot the shear flow distribution around the section, with values in terms of S and a.
A uniform thin-walled beam of constant wall thickness t has a cross section in the shape of an
isosceles triangle and is loaded with a vertical shear force Sy applied at the apex. Assuming that the
distribution of shear stress is according to the basic theory of bending, calculate the distribution of
shear flow over the cross-section. Illustrate your answer with a suitable sketch, marking in carefully
with arrows the direction of the shear flows and noting the principal values. (Fig. 9)
A thin-walled closed section beam of constant wall thickness t has the cross-section shown in
Fig.10.Assuming that the direct stresses are distributed according to the basic theory of bending,
calculate and sketch the shear flow distribution for a vertical shear force Sy applied tangentially to the
curved part of the beam.
Calculate the position of the shear centre of the thin-walled section shown in Fig.11.
Find the position of the shear centre of the thin-walled beam section shown in Fig. 12.
Determine the position of the shear centre of the cold-formed, thin-walled section shown in Fig. 13.
The thickness of the section is constant throughout.
Define the term ‘shear centre’ of a thin-walled open section and determine the position of the shear
centre of the thin-walled open section shown in Fig. 14.
Show that the position of the shear centre S with respect to the intersection of the web and lower
flange of the thin-walled section shown in Fig. 15, is given by ξS = −45a/97, ηS = 46a/97.
16. A thin-walled beam has the cross-section shown in Fig.16. The thickness of each flange varies
linearly from t1 at the tip to t2 at the junction with the web. The web itself has a constant thickness t3.
Calculate the distance ξS from the web to the shear centre S.
17. Determine the position of the shear centre S for the thin-walled, open cross-section shown in Fig.17.
The thickness t is constant.
18. A beam has the singly symmetrical, thin-walled cross-section shown in Fig. 18. The thickness t of the
walls is constant throughout. Show that the distance of the shear centre from the web is given by
19. The wing box has the cross-section shown diagrammatically in Fig. 19 and supports a shear load of
100 KN in its vertical plane of symmetry. Calculate the shear stress at the mid-point of the web 3-6 if
the thickness of all walls is 2 mm.
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Figure: 9