Use the method of virtual work and determine the displacement of point C of the beam made from steel. E=29$(10^3)$ ksi, I=245 ${in}^4$

A glass slab surrounded by air causes a sideways displacement in a beam of light. If the slab is now placed in water, does the displacement it causes increase, decrease, or stay the same?

Choose the best explanation from among the following:

I. The displacement of the beam increases because of the increased refraction due to the water. II. The displacement of the beam is decreased because with water surrounding the slab there is a smaller difference in index of refraction between the slab and its surroundings. III. The displacement stays the same because it is determined only by the properties of the slab; in particular, the material it is made of and its thickness.

A simply supported beam with a cruciform cross section is loaded as shown. Calculate the maximum horizontal shear stress. Neglect the weight of the beam. (Hint: Check two planes in the cross section.)

Determine the reactions at A and B for the simply supported beam shown.

The bridge is constructed as a three-hinged trussed arch. Determine the horizontal and vertical components of reaction at the hinges (pins) at A, B, and C. The dashed member D E is intended to carry no force.

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.When the charges in the rod are in equilibrium, which point, $a$ or $b$, has an excess of positive charge?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.When the charges in the rod are in equilibrium, what are the magnitude and direction of the electric field within the rod?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.What is the potential difference across the rod if it moves (i) parallel to $a b$ and (ii) directly out of the page?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.What is the potential difference between the ends of the rod?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.Which point, $a$ or $b$, is at higher potential?

The forked rod is supported by a collar at $A$, a thrust bearing at $B$, and a cable $C D$. Determine the tension within cable $C D$, and the $x, y, z$ components of reaction at supports $A$ and $B$. The supports at $A$ and $B$ are in proper alignment and exert only force reactions on the rod.

The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall at $C$ and three torques are applied to it as shown, determine the shear stress developed at points $A$ and $B$. These points lie on the pipe's outer surface. Sketch the shear stress on volume elements located at $A$ and $B$.

Compute the design moment strengths $\phi M_n$ of the beams shown if $f_y=60,000 \mathrm{psi}$ and $f_c^{\prime}=4000 \mathrm{psi}$. Check the maximum permissible $A_s$ in each case to ensure ductile behavior.

Determine the magnitude and direction of the force that must be applied to the bottom of the gate shown to keep the gate closed.