FAKULTI KEJURUTERAAN MEKANIKALUNIVERSITI TEKNIKAL MALAYSIA MELAKA

TUTORIAL 5SOLID MECHANICS 2 (BMCS 2333)

SEMESTER 1 SESSI 2007/2008Plastic Deformation (Solution)

1. A member of uniform rectangular cross-section 50 mm by 120 mm is subjected to a bending moment.

. Assuming that the member is made of an elastoplastic material with a yield strength of 240 MPa and a modulus elasticity of 200 GPa, determine (a) the thickness of the elastic core, (b) the radius of curvature of the neutral surface.

Solutiona) Thickness of elastic

core, ,

From equation ,

b) Radius of curvature

2. Determine the plastic moment of a steel beam of the cross section shown in right figure, assuming the steel to be elastoplastic with a yield strength of 330 MPa.

Solution

Centroid position,

= 11.92kNm

3. For beam of cross section shown in right figure which is assumed to be elastoplastic with , determine (a) the plastic moment

, (b) the shape factor of the cross-section.

Solutiona) Plastic moment,

b) Shape factor, -

50b mm

60c mm

60c mm

Yy

Figure 1

12.5mm

50mm

75mm

25mm

Figure 2

25mm 25mm

25mm

50mmC

y

z

25mm

Figure 3

12.5mm

50mm

75mm

25mm

43.75mm

1A

2A

3A

100 50

25

2

75

4. A solid circular shaft, 1.2 m long and 50 mm in diameter is subjected to a 4.6 kNm torque at each end (right figure). Assuming the shaft to be made of an elastoplastic material with yield strength in shear of 150 MPa and a modulus of rigidity of 80 GPa, determine (a) the radius of the elastic core, (b) the angle of twist of the shaft

Solutiona) Radius of elastic core

, ,

From equation

b) Angle of twist

5. The solid shaft shown in right figure is made of a mild steel which is assumed to be elastoplastic with

and . Determine

(a) the magnitude of the torque for which the radius of elastic core is 12.5 mm, (b) the corresponding maximum shearing stress, (c) the corresponding angle of twist.

Solution

, ,

a) Torque,

b) Corresponding maximum shearing stress

c) Angle of twist

6. The hollow shaft shown is made of a steel which is assumed to be elastoplastic with and

. Determine the magnitude of the torque and the

corresponding angle of twist (a) at the onset of yield, (b) when the plastic zone is 10 mm deep.

Solution

50mm

1.2m

4.60kNm4.60kNm

Figure 4

60mm

T

T

25mm5m

Figure 6

2m

20mm

T

A

B

Figure 5

FAKULTI KEJURUTERAAN MEKANIKALUNIVERSITI TEKNIKAL MALAYSIA MELAKA

TUTORIAL 5SOLID MECHANICS 2 (BMCS 2333)

SEMESTER 1 SESSI 2007/2008Plastic Deformation (Solution)

,

a) Onset of yield

b) Plastic zone=10mm

Using equation,