Mechanics of Materials 3rd. Edition by E.J. Hearn | 9780750632669 | 750632666 | Holooly

Mechanics of Materials

Mechanics of Materials

58 SOLVED PROBLEMS

Question: 9.4

The vehicle engine mounting bracket shown in Fig. 9.39 is made from uniform steel channel section for which Young’s modulus, E = 200 GN/m². It can be assumed for both.channels that the relevant second moment of area, I = 2 × 10^-8 m^4 and cross-sectional area, A = 4× 10^-4m². The bracket can be idealised ...

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a) Figure 9.40 shows suitable node, dof. and eleme...

Question: 9.6

(a) Evaluate the element stiffness matrix, in global coordinates, for the three-node triangular membrane element, labelled a in Fig. 9.43. Assume plane stress conditions, Young’s modulus, E = 200 GN/m², Poisson’s ratio, ν = 0.3, thickness, t = 1 mm, and the same displacement functions as Example9.5 ...

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(a) Figure 9.44 shows suitable node labelling for ...

Question: 9.7

Figure 9.47 shows a 1 mm thick sheet of steel, one edge of which is fully restrained whilst the opposite edge is subjected to a uniformly distributed tension of total value 40 kN. For the material Young’s modulus, E = 200 GN/m² and Poisson’s ratio, ν = 0.3, and plane stress condition can be assumed ...

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(a) Advantage can be taken of the single symmetry ...

Question: 9.5

Derive the stiffness matrix in global coordinates for a three-node triangular membrane element for plane stress analysis. Assume that the elastic modulus, E, and thickness, t, are constant throughout, and that the displacement functions are u(x, y) =α1 + α2x + α3y υ(x, y) = α4 + α5x + α6y ...

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With reference to §9.9 and with respect to the nod...

Question: 9.3

A steel beam is supported and loaded as shown in Fig. 9.36. The relevant second moments of area are such that I^(a) = 2I^(a) = 2 × 10^-5 m^4 and Young’s modulus E for the beam material = 200 GN/m². Using the displacement based finite element method and representing each member by a simple beam ...

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(a) Figure 9.37 shows suitable node, dof. and elem...

Question: 9.2

Figure 9.34 shows the members and idealised support conditions for a roof truss. All three members of which are steel and have the same cross-sectional area such that AE = 12 MN throughout. Using the displacement based finite element method, treating the truss as a pin-jointed plane frame and each ...

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(a) Figure 9.35 shows suitable node, dof. and elem...

Question: 9.1

Figure 9.31 shows a planar steel support structure, all three members of which have the same axial stiffness, such that AE/L = 20 MN/m throughout. Using the displacement based finite element method and treating each member as a rod: (a) assemble the necessary terms in the structural stiffness ...

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(a) Figure 9.32 shows suitable node, dof. and elem...

Question: 3.2

(a) Determine the “shape factor” of a T-section beam of dimensions 100 mm × 150 mm x 12 mm as shown in Fig. 3.38. (b) A cantilever is to be constructed from a beam with the above section and is designed to carry a uniformly distributed load over its complete length of 2 m. Determine the maximum u.d ...

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(a)

\text { Shape...

Question: 4.5

An initially unstressed short steel cylinder, internal radius 0.2 m and external radius 0.3 m, is subjected to a temperature distribution of the form T =a + b loge r to ensure constant heat flow through the cylinder walls. With this form of distribution the radial and circumferential stresses at ...

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T=a+b\log _{e}r

200=a+b\log ...

Question: 12.2

A constant time section of 1000 h taken through a series of strain-time creep curves obtained for a particular polymer at various stress levels yields the following isochronous stress-strain data. σ(kN/m²) 1.0 2.25 3.75 5.25 6.54 7.85 9.0 ε(%) 0.23 0.52 0.85 1.24 1.68 2.17 2.7 The polymer is now ...

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(a) From eqn. (4.11) the maximum stress at the cen...

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