고체역학 (연습문제)

- 2010 여름 계절학기 -

박성훈 교수님

4장 연습문제 : 11 , 13 , 21 , 27 , 28

4-11 . The cutter is subjected to a horizontal force of 580 lb and normal force of 350 lb. Determine the horizontal and vertical components of force acting on the pin A and the force along the hydraulic cylinder BC (a two-force member)

4-13 . The sports car has a mass of 1.5 Mg and mass center at G.If the front two springs each have a stiffness of and the rear two springs each have a stiffness of determine their compression when the car is parked on the incline. Also, what friction force must be applied to each of the rear wheels to hold the car in equilibrium? Hint : First determine the normal force at A and B, then determine the compression in the springs.

mkNkA /58=mkNkB /58=

4-21 . The mobile crane has a weight of 120,000 lb and center of gravity at the boom has a weight of 30,000 lb and center of gravity at Determine the smallest angle of tilt of the boom, without causing the crame to overturn if the suspended load is W=40,000lb. Neglect the thickness of the tracks at A and B

.2

G

;1

G

θ

4-27 . Three uniform books, each having a weight W and length a, are stacked as shown. Determine the maximum distance d that the top book can extend out from the bottom one so the stack does not topple over.

4-28 . The toggle switch consists of a cocking lever that is pinned to a fixed frame at A and held in place by the spring which has an unstretched length of 200 mm. Determine the magnitude of the resultant force at A and the normal force on the peg at B when the lever is in the position shown.

5장 연습문제 : 13 , 23 , 27 , 29 , 32

5-13 . Determine the force in each member of the truss and state if the members are in tension or compression. Set kNPP 202,01 ==

5-23 . Determine the force in members CD, CF, and FG of the Warren truss, Indicate if the members are in tension or compression

5-27 . Determine the force in members JE and GF of the truss and state if these members are in tension or compression. Also, indicate all zero-force members.

5-29 . Determine the force in members CD, CF, and CG and state if these members are in tension or compression.

5-32 . Determine the force in member GC of the truss and state if this member is in tension or compression.

6장 연습문제 : 20 , 22 , 67 , 72 , 78

6-20 . Locate the centroid of the channel’s cross-sectional area. y

6-22 . Locate the centroid of the member’s cross-sectional area. ),( yx

6-67 . Determine the moments of inertia of the shaded area about the x and y axes.

6-72 . Locate the centroid of the cross section and determine the moment of inertia of the section about the axis.

y'x

6-78 . Locate the centroid of the channel’s cross-sectional area, and then determine the moment of inertia with respect to the axis passing through the centroid.

y'x

7장 연습문제 : 26 , 59 , 61 , 63 , 65

7-26 . Determine the normal force, shear force, and moment in the beam at sections passing through points D and E. Point E is just to the right of the 3-kip load.

7-59 . Draw the shear and moment diagrams for the beam

7-61 . Draw the shear and moment diagrams for the beam.

7-63 . Draw the shear and moment diagrams for the beam.

7-65 . The beam consists of two segments pin connected at B. Draw the shear and moment diagrams for the beam.

8장 연습문제 : 31 , 34 , 53 , 67 , 68 , 71 , 74

8-31 . The bar has a cross-sectional area of If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads as shown, determine the average normal stress in the bar as a function of x for 0 < x < 0.5m

26 )10(400 m−

8-34 . Road AB and BC each have a diameter of 4mm. If a load of 6 kN is applied to the ring at B, determine the smallest angle of rod BC so that the average normal stress in each rod is equivalent. θ

8-53 . The compound wooden beam is connected together by a bolt at B. Assuming that the connections at A,B,C, and D exert only vertical forces on the beam, determine the required diameter of the bolt at B and the required outer diameter of its washers if the allowable tensile stress for the bolt is

and the allowable bearing stress for the wood is. Assume that the hole in the washers has the same

diameter as the bolt.

MPaallowb 150)( =σMPaallowb 150)( =σ

8-67 . The rectangular plate is subjected to the deformation shown by the dashed line. Determine the normal strains

.,,, '' yxyx εεεε

8-68 . The rectangular plate is subjected to the deformation shown by the dashed line. Determine the shear strains and developed at point A.

yxγ'' yx

γ

8-71 . The piece of plastic is originally rectangular. Determine the average normal strain that occurs along the diagonals AC and DB.

8-74 . A square piece of material is deformed into the dashed position. Determine the shear strain at C. yxγ

9장 연습문제 : 8 , 9 , 10 , 12 , 13

9-8 . The stress-strain diagram for a steel alloy having an original diameter of 0.5 in. and a gauge length of 2in. Is given in the figure. Determine approximately the modulus of elasticity for the material, the load on the specimen that causes yielding, and the ultimate load the specimen will support.

9-9 . The stress-strain diagram for a steel alloy having an original diameter of 0.5 in. and a gauge length of 2 in. is given in the figure. Determine approximately the modulus of resilience and the modulus of toughness for the material.

9-10 . The stress-strain diagram for a bar of steel alloy is shown in the figure. Determine approximately the modulus of elasticity, the proportional limit, the ultimate stress, and the modulus of resilience. If the bar is loaded until it is stressed to 360 Mpa, determine the elastic strain recovery and the permanent set or strain in the bar when it is unloaded.

9-12 . The stress-strain diagram for polyethylene, which is used to sheath coaxial cables, is determined from testing a specimen that has a gauge length of 10 in. If a load P on the specimen develops a strain of determine the approximate length of the specimen, measured between the gauge points, when the load is removed. Assume the specimen recovers elastically.

.,/.0024,0 inin=ε

9-13 . The change in weight of an airplane is determined from reading the strain gauge A mounted in the plane’s aluminum wheel strut. Before the plane is loaded, the strain-gauge reading in a strut is whereas after loadingDetermine the change in the force on the strut if the cross-sectional area of the strut is

.,/.00100.01 inin=ε ./.00243.02 inin=ε

.)10(10.5.3 32 ksiEin al =