###### Introduction to Engineering Mechanics A Continuum Approach

1 SOLVED PROBLEMS

72 SOLVED PROBLEMS

Question: B.1

## Calculate the divergence of F = xi + yj + zk. ...

 \nabla \cdot \underline{F}=\frac{∂}{∂x}(x)...
Question: 5.12

## A stress state is described by the tensor σi j = ( 25 15 5 15 20 -15 5 -15 -20) ksi. a. Determine the principal stresses. b. If this state of stress exists in a part made of gray cast iron (a brittle material with ultimate strength in tension of σult = 30 ksi and in compression of σult = 120 ksi), ...

a. The principal stresses may be found from the ro...
Question: 5.11

## A state of plane stress consists of a tensile stress σ0 = 8 ksi exerted on vertical surfaces and unknown shear stresses τ0. Determine (a) the magnitude of the shear stress τ0 for which the maximum normal stress is 10 ksi, and (b) the corresponding maximum shear stress. Given: Plane stress state. ...

We will assume a sense (sign) for the unknown shea...
Question: 5.10

## A compressed air tank is supported by two cradles as shown. Relative to the effects of the air pressure inside the tank, the effects of the cradle supports are negligible. The cylindrical body of the tank has a 30-in outer diameter and is fabricated from a 3/8-in steel plate by welding along a ...

First, we validate our assumption that thin-walled...
Question: 11.3

## A 3-m long fixed–fixed ended column of square cross section is to be made of wood in which the maximum allowable stress is 16 MPa and with E = 13 GPa. Using a safety factor with respect to buckling of 2.5, determine the required size of the cross section if the column is to safely support centric ...

1. Since we are asked to use a safety factor of 2....
Question: 11.2

## An 8-ft length of structural tubing has the illustrated cross section and geometric properties. Using Euler’s formula and a safety factor of 2, determine the allowable centric load for the column and the corresponding normal stress. Assuming that this allowable load is applied as shown at a point ...

Since the column has one fixed and one free end, t...
Question: 11.1

## An aluminum column of length L and rectangular cross section has a fixed end B and supports a centric axial load at A. Two smooth and rounded fixed plates restrain end A from moving in one of the vertical planes of symmetry but allow it to move in the other plane. (1) Determine the ratio a/b of the ...

Figure on next page indicates that we must conside...
Question: 9.7

## Use Castigliano’s second theorem to find the reaction force in the support at C due to the load P at B. The beam has a constant E I. Given: Statically indeterminate cantilever beam with a point load. Find: Reaction force at redundant support. Assume: Hooke’s law applies; long slender beam. ...

The work we have done in Example 9.6 allows us to ...
Question: 9.6

## Use Castigliano’s second theorem to find the deflection of the beam at points B and C due to the load P at B. The beam has a constant E I. Given: Cantilever beam with a point load. Find: Deflection at point of applied load and at the tip. Assume: Hooke’s law applies; long slender beam. ...

Castigliano’s second theorem lets us find the defl...
Question: 9.5