4.3-10 Under cruising conditions, the distributed load aeting on the wing of a small airplane has the idealized variation shown in the figure. Calculate the shear force V and bending moment M at 4 m from the tip of the wing.

1. The figure shows a frame with negligible mass, keeping a 50-lb weight in equilibrium. The smooth pulley C has a radius of 2 in. Calculate the normal force, the shear force, and the bending moment at (a) point E and (b) point F. Note that points E and F are the midpoints of sections BA and BD, respectively. 2 in 50 lb C 2 ft + B 2 ft E F A 6 lb-ft D 1.5 ft

A fiberglass pipe is lifted by a sling, as shown in the figure. The outerdiameter of the pipe is 6,0 in., its thickness is 0.25 in,, and its weightdensity is 0,053 1b/in3 the length of the pipe is L = 36 ft and the distancebetween lifting points is s = 11 ft.a. Determine the maximum bending stress in the pipe due to its ownweight,b. Find the spacing s between lift points which minimizes thebending stress. What is the minimum bebding stress?c. What spacing s leads to maximum bending stress? What is thatstress?

The channel shape cross-section and the rectangular cross-section shown in the Figure Q4 are made of materials with elastic-perfectly plastic behaviour. The yield stress of the material used for the channel shape cross-section is oy=418 MPa, whereas that used for the rectangular cross- section is 0.70y. Compute the thickness of the web, t, of the channel shape section if the two cross sections have identical plastic bending moment about the z-axis. In Figure 4, h= 84 mm, b=46 mm, a=11 mm, H=84 mm, d= 46 mm Z || Part a) b N.mm h Z mm d 1. The numerical value of plastic section modulus of the solid rectangular section is mm ³ H 2. The numerical value of plastic moment of the solid rectangular section is Part b) calculate the value of t The numerical value of t can be calculated as

A beam ABC is simply supported at A and B and has an overhang BC( see figure).The beam is loaded by two forces P and a clockwise couple of moment Pa at D that act through the arrangement shown. a. Draw the s hear force and beanding moment diagram for the beam ABC. If moment Pa at D is replaced by moment M, Find an expression for M in terms of variables P and a so that reaction at B goes to zero. Plot the associated shear force and bending moment diagram for beam ABC.

The channel shape cross-section and the rectangular cross-section shown in the Figure Q4 are made of materials with elastic-perfectly plastic behaviour. The yield stress of the material used for the channel shape cross-section is oy = 473 MPa, whereas that used for the rectangular cross- section is 0.850y. Compute the thickness of the web, t, of the channel shape section if the two cross sections have identical plastic bending moment about the z-axis. In Figure 4, h= 77 mm, b=46 mm, a=11 mm, H=77 mm, d= 46 mm N b h a + N a | d H

A rubber cylinder Rof length L and cross-sectional area A iscompressed inside a steel cylinder S by a force Fthat applies a uniformlydistributed pressure to the rubber (see figure).(a) Derive a formula for the lateral pressure p between the rubber andthe steel. (Disregard friction between the rubber and the steel, andassume that the steel cylinder is rigid when compare d to the rubber.)(b) Derive a formula for the shortening 6 of the rubber cylinder.

Stress Example; The beam, whose loading condition is given in the figure, is connected from point A with a pin with a diameter of 20 mm and from point B with a pin with a diameter of 30 mm, and the connection figures are given next to it. Accordingly, find the average shear stress at pins A and B. 2 m- 30 kN 4 m HE 5 B 3 |4

A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude P = 177 kN, acting as shown in the figure. L 9 £a The reaction q of the ballast is assumed to be uniformly distributed over the length of the tie, which has cross-sectional dimensions b 300 mm and h = 250 mm. Calculate the maximum bending stress o (in MPa) in the tie due to the loads P, assuming the distance L = 1,500 mm and the overhang length a = 495 mm. (Enter the magnitude.) max MPa

A ladder with a length of L= 8 m and a mass of M=50 kg rests on a rough ground (providing friction) and on a roller without friction at the top of the wall at h= 5 m above the ground (see figure). The angle θin the picture is 60°, and the ladder is just about to slip. (A) Draw a force diagram whichshows all forces acting on the ladder.Take the force that the roller exerts to be perpendicular to the ladder. (B) Use a net torque equation to calculate the force that the roller exerts on the ladder. (C) Use net force equations to calculate the normal from the ground, the force of static friction, and the coefficient of static friction.