Shear Strength
1. (a) A glued lap splice is to be made in a 10 × 20 mm rectangular member at α =20°, as shown in Fig.1. Assuming that, the shear strength of the glued joint controls the design, what axial force P is to be applied to the member to get separated to 2 parts? Assume the shear strength of the glued joint to be 10MPa.
Fig: 1
(b) An exploded view of a bolted connection is as shown in Fig 2(b). The width of the plate is
60mm; their thicknesses are t1 =10mm. The snugly fitting bolt is 20mm in diameter. Calculate the maximum normal stress in the plates at the critical section due to an applied tensile force P=70 kN. For the same condition calculate the bearing and shear stresses in the bolt. t1 P/2
P
P/2
Fig:2(a) Fig: 2(b)
P.T.O
1 t1 d t1 1
2. A 2‐mm‐ thick hollow circular tube of
30 mm outside diameter is subjected to a constant shear of 10 Pa in the axial direction, as shown in Fig 3. If the tube is
400 mm long what is the axial stress? Plot the variation of axial stress along the tube.
Fig: 3
3. For the given state of stress determine the normal and shear stresses exerted on the oblique face
AB of the element shown in Fig 4.
80MPa
A
40 MPa
B
Fig: 4
4. For the given state of stress as shown in Fig 5,
Find (a) principal planes and
(b) principal stresses.
48 MPa
16 MPa
60 MPa
Fig: 5
5. For the above problem (Fig 5) determine the following using Mohr’s Circle.
(a) the orientation of the planes of maximum in‐plane shearing stress
(b) the maximum in plane shearing stress,
(c) the corresponding normal stress.
2
Fig: 1
(b) An exploded view of a bolted connection is as shown in Fig 2(b). The width of the plate is
60mm; their thicknesses are t1 =10mm. The snugly fitting bolt is 20mm in diameter. Calculate the maximum normal stress in the plates at the critical section due to an applied tensile force P=70 kN. For the same condition calculate the bearing and shear stresses in the bolt. t1 P/2
P
P/2
Fig:2(a) Fig: 2(b)
P.T.O
1 t1 d t1 1
2. A 2‐mm‐ thick hollow circular tube of
30 mm outside diameter is subjected to a constant shear of 10 Pa in the axial direction, as shown in Fig 3. If the tube is
400 mm long what is the axial stress? Plot the variation of axial stress along the tube.
Fig: 3
3. For the given state of stress determine the normal and shear stresses exerted on the oblique face
AB of the element shown in Fig 4.
80MPa
A
40 MPa
B
Fig: 4
4. For the given state of stress as shown in Fig 5,
Find (a) principal planes and
(b) principal stresses.
48 MPa
16 MPa
60 MPa
Fig: 5
5. For the above problem (Fig 5) determine the following using Mohr’s Circle.
(a) the orientation of the planes of maximum in‐plane shearing stress
(b) the maximum in plane shearing stress,
(c) the corresponding normal stress.
2