A steel cable having a diameter of 0.4 in. wraps over a drum and is used to lower an elevator having a weight of 800 lb. The elevator is 150 ft below the drum and is descending at the constant rate of 3 ft/s when the drum suddenly stops. Determine the maximum stress developed in the cable when this occurs.

$$E_{st} = 29(10^3) ksi, σ_γ = 50 ksi.$$

A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal acceleration of the car?

The cantilevered beam is subjected to a couple moment $\mathbf{M}_0$ applied at its end. Determine the slope of the beam at $B . E I$ is constant. Use the method of virtual work.

Combine like terms. Write answer in descending order :

$$\dfrac{1}{5}x^4 + 7 - 2x^2 +3 -\dfrac{2}{15}x^4 +2x^2$$

The collar has a weight of 50 lb and falls down the titanium bar. If the bar has a diameter of 0.5 in., determine the largest height $h$ at which the weight can be released and not permanently damage the bar after striking the flange at A. $E_{\mathrm{ti}}=16\left(10^3\right) \mathrm{ksi}, \sigma_Y=60 \mathrm{ksi}$.

The collar has a weight of 50 lb and falls down the titanium bar. If the bar has a diameter of $0.5 \mathrm{in}$., determine the maximum stress developed in the bar if the weight is dropped from a height of $h=1 \mathrm{ft}$.

Determine the speed v of the 50-Mg mass when it is just over the top of the steel post, if after impact, the maximum stress developed in the post is 550 MPa. The post has a length of L = 1 m and a cross-sectional area of 0.01 m².

$$E_{st} = 200 GPa, σ_γ = 600 MPa.$$

Determine the horizontal displacement of joint B. The truss is made from A992 steel rods each having a diameter of 1 in.

Determine the diameter of a red brass C83400 bar that is 8 ft long if it is to be used to absorb 800 ft · lb of energy in tension from an impact loading. No yielding occurs.

A bar is 4 m long and has a diameter of 30 mm. Determine the total amount of elastic energy that it can absorb from an impact loading if (a) it is made of steel for which

$$E_{st} = 200 GPa, σ_γ = 800 MPa,$$

and (b) it is made from an aluminium alloy for which

$$E_{al} = 70 GPa, σ_γ = 405 MPa.$$

Determine the vertical displacement of end $B$ of the frame. Consider only bending strain energy. The frame is made using two $\mathrm{A}-36$ steel $\mathrm{W} 460 \times 68$ wide-flange sections.

The rod has a circular cross section with a polar moment of inertia J and moment of inertia I. If a vertical force $\mathbf{P}$ is applied at A, determine the vertical displacement at this point. Consider the strain energy due to bending and torsion. The material constants are E and G.

The rod has a circular cross section with a moment of inertia $I$. If a vertical force $\mathbf{P}$ is applied at $A$, determine the vertical displacement at this point. Only consider the strain energy due to bending. The modulus of elasticity is $E$.

Determine the torsional strain energy in the A-36 steel shaft. The shaft has a radius of 30 mm.