## Solution to Problem 222 Poisson's Ratio

**Problem 222**

A solid cylinder of diameter d carries an axial load *P*. Show that its change in diameter is 4*P*ν / π*Ed*.

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**Problem 222**

A solid cylinder of diameter d carries an axial load *P*. Show that its change in diameter is 4*P*ν / π*Ed*.

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**Problem 131**

Repeat Problem 130 if the rivet diameter is 22 mm and all other data remain unchanged.

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**Problem 130**

Figure P-130 shows a roof truss and the detail of the riveted connection at joint *B*. Using allowable stresses of τ = 70 MPa and σ_{b}= 140 MPa, how many 19-mm-diameter rivets are required to fasten member *BC* to the gusset plate? Member *BE*? What is the largest average tensile or compressive stress in *BC* and *BE*?

**Problem 123**

A rectangular piece of wood, 50 mm by 100 mm in cross section, is used as a compression block shown in Fig. P-123. Determine the axial force P that can be safely applied to the block if the compressive stress in wood is limited to 20 MN/m^{2} and the shearing stress parallel to the grain is limited to 5MN/m^{2}. The grain makes an angle of 20° with the horizontal, as shown. (Hint: Use the results in Problem 122.)

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Stress is defined as the strength of a material per unit area or unit strength. It is the force on a member divided by area, which carries the force, formerly express in psi, now in N/mm^{2} or MPa.

$\sigma = \dfrac{P}{A}$

where P is the applied normal load in Newton and A is the area in mm^{2}. The maximum stress in tension or compression occurs over a section normal to the load.

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**Problem 114**

The homogeneous bar ABCD shown in Fig. P-114 is supported by a cable that runs from A to B around the smooth peg at E, a vertical cable at C, and a smooth inclined surface at D. Determine the mass of the heaviest bar that can be supported if the stress in each cable is limited to 100 MPa. The area of the cable AB is 250 mm^{2} and that of the cable at C is 300 mm^{2}.

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**Problem 113**

Find the stresses in members BC, BD, and CF for the truss shown in Fig. P-113. Indicate the tension or compression. The cross sectional area of each member is 1600 mm^{2}.

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