Strength of Materials and Structures 4th. Edition by John Case, Carl T. E Ross, Lord Chılver | 9780080518008 | 0080518001

Mechanics of Materials

Strength of Materials and Structures

140 SOLVED PROBLEMS

10 SOLVED PROBLEMS

Question: 12.1

Find the maximum stress on the section AB of the clamp when a pressure of 2500 N is exerted by the screw. The section is rectangular 2.5 cm by 1 cm. (Cambridge) ...

Verified Answer:

The section AB is subjected to a tension of 2500 N...

Question: 11.7

A reinforced concrete T-beam contains 1.25 × 10^-3 m² of steel reinforcement on the tension side. If the steel stress is limited to 115 MN/m² and the concrete stress to 6.5 MN/m², estimate the permissible bending moment. The modular ratio is 15. ...

Verified Answer:

Suppose the neutral axis falls below the underside...

Question: 25.8

If the beam of Problem 25.7 has a mass of 1 kg, with a mass moment of inertia of 0.1 kg m² added to node 2, determine the resonant frequencies of the beam. ...

Verified Answer:

From equation (25.105) (25.105) ...

Question: 25.7

Determine the resonant frequencies for the beam of the figure in Problem 23.4, assuming that the 4 kN load is not present, and that E = 2 × 10 ^11 N/m², ρ = 7860 kg/m³ A = 1 -× 10 ^-4 m², I = 1 × 10 ^-7 m ^4 ...

Verified Answer:

Element 1-2

l=3 m

Substituting the...

Question: 25.6

Determine the resonant frequencies for the tripod of Problem 25.5, if this tripod has a mass of 10 kg added to node 4. ...

Verified Answer:

From equation (25.79), (25.79) (25...

Question: 25.5

Determine the resonant frequencies and eigenmodes for the pin-jointed space truss of Problem 23.3, given that, A = 2 × 10^-4 m² E = 2 × 10^11 N/m² ρ = 7860 kg/m³ ...

Verified Answer:

Element 1-4 From Problem 25.3,

l = 10 m[/l...

Question: 25.4

If the pin-jointed truss of Problem 25.3 had an additional mass of 0.75 kg attached to node 3, what would be the values of the resulting resonant frequencies? ...

Verified Answer:

From equation (25.58): (25.58) ...

Question: 25.3

Determine the resonant frequencies and eigenmodes for the plane pin-jointed truss, below. It may be assumed that the following apply: A = 1 × 10^-4 m² ρ = 7860 kg/m³ E = 2 × 10^11 N/m² ...

Verified Answer:

Element 1-3

\alpha=60°, c = 0.5, s...

Question: 25.2

If the steel beam of the Problem 25.1 has a mass of 15 kg per metre run, estimate the lowest natural frequency of vibrations of the beam itself. ...

Verified Answer:

The lowest natural frequency of vibrations is [lat...

Question: 25.1

A steel I-beam, simply supported at each end of a span of 10 m, has a second moment of area of 10^-4 m^4. It carries a concentrated mass of 500 kg at the mid-pan. Estimate the natural frequency of lateral vibrations. ...

Verified Answer:

In this case

EI= (200 \times 10^{9})(10^{ -...

Question: 13.P.6

A uniform, simply-supported beam carries a distributed lateral load varying in intensity from w0 at one end to 2w0 at the other. Calculate the greatest lateral deflection in the beam. ...

Verified Answer:

The vertical reactions at O and A are

\frac...

Question: 13.P.4

A uniform, simply-supported beam of span L carries a uniformly distributed lateral load of w per unit length. It is propped on a knife-edge support at a distance a from one end. Estimate the vertical force on the prop. ...

Verified Answer:

If the beam is unpropped, then, from equation (13....

Question: 12.P.2

A masonry pier has a cross-section 3 m by 2 m, and is subjected to a load of 1000 kN, the line of the resultant being 1.80 m from one of the shorter sides, and 0.85 m from one of the longer sides. Find the maximum tensile and compressive stresses produced. (Cambridge) ...

Verified Answer:

P represents the line of action of the thrust. The...

Question: 11.P.7

A reinforced concrete T-beam contains 1.25 × 10^-3 m² of steel reinforcement on the tension side. If the steel stress is limited to 115 MN/m² and the concrete stress to 6.5 MN/m², estimate the permissible bending moment. The modular ratio is 15. ...

Verified Answer:

Suppose the neutral axis falls below the underside...

Question: 9.P.9

An unequal angle section of uniform thickness 0.5 cm has legs of lengths 6 cm and 4 cm. Estimate the positions of the principal axes, and the principal second moments of area. ...

Verified Answer:

Firstly, find the position of the centroid of the ...

Question: 9.P.7

A 4 m length of the I-beam of Problem 9.2 is simply-supported at each end. What maximum central lateral load may be applied if the bending stresses are not to exceed 150 MN/m²? ...

Verified Answer:

Suppose W is the central load. If this is applied ...

Question: 18.P.6

A thin circular ring of radius r and uniform flexural stiffness carries two radial loads W applied along a diameter. Estimate the maximum bending moment in the ring. ...

Verified Answer:

By symmetry the loading actions on a half-ring are...

Question: 16.P.5

A steel shaft, 20 cm external diameter and 7.5 cm internal, is subjected to a twisting moment of 30 kNm, and a thrust of 50 kN. Find the shearing stress due to the torque alone and the percentage increase when the thrust is taken into account. (RNC) ...

Verified Answer:

For this case, we have

r_1 = 0.100 m, ...

Question: 6.P.5

A long steel tube, 7.5 cm internal diameter and 0.15 cm thick, has closed ends, and is subjected to an internal fluid pressure of 3 MN/m². If E = 200 GN/m², and v = 0.3, estimate the percentage increase in internal volume of the tube. ...

Verified Answer:

The circumferential tensile stress is

\sigm...

Question: 1.P.13

A uniform beam weighing 500 N is held in a horizontal position by three vertical wires, one attached to each end of the beam, and one at the mid-length. The outer wires are brass of diameter 0.125 cm, and the central wire is of steel of diameter 0.0625 cm. If the beam is rigid and the wires are of ...

Verified Answer:

On considering the two outer brass wires together,...