Sm ch (11)-

850

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11–1. The load binder is used to support a load. If the force applied to the handle is 50 lb, determine the tensions T1 and T2 in each end of the chain and then draw the shear and moment diagrams for the arm ABC.

SOLUTION

12 in.50 lb

T2

T1

3 in.

A

B

C

851


11–2. Draw the shear and moment diagrams for the shaft The bearings at A and D exert only vertical reaction on the shaft. The loading is applied to the pulleys at B and C and E.

SOLUTION

A

B

14 in. 20 in. 15 in. 12 in.

80 lb110 lb

35 lb

CD

E

852


11–3. The engine crane is used to support the engine, which has a weight of 1200 lb. Draw the shear and moment diagrams of the boom ABC when it is in the horizontal positions shown.

5 ft3 ft

CB

4 ft

A

SOLUTION

853


*11–4. Draw the shear and moment diagrams for the cantilever beam.

2 kN/m

6 kN�m2 m

A

SOLUTION

854


11–5. Draw the shear and moment diagrams for the beam.

2 m 3 m

10 kN 8 kN

15 kN�m

SOLUTION

855


11–6. Express the internal shear and moment in terms of x and then draw the shear and moment diagrams.

SOLUTION

A B

x

L2

L2

w0

856


11–7. Draw the shear and moment diagrams for the compound beam.

SOLUTION

BA CD

2 m 1 m 1 m

5 kN/m

857


*11–8. Express the internal shear and moment in terms of x and then draw the shear and moment diagrams for the beam.

SOLUTION

AB

900 lb

400 lb/ft

6 ft 3 ft

x

858


11–9. Express the internal shear and moment in terms of x and then draw the shear and moment diagrams for the overhanging beam.

SOLUTION

AB

6 kN/m

x

4 m 2 m

859


11–10. Members ABC and BD of the counter chair are rigidly connected at B and the smooth collar at D is allowed to move freely along the vertical slot. Draw the shear and moment diagrams for member ABC.

SOLUTION

A

D

BC

P � 150 lb

1.5 ft1.5 ft1.5 ft

860


11–11. Draw the shear and moment diagrams for the pipe. The end screw is subjected to a horizontal force of 5 kN. Hint: The reactions at the pin C must be replaced by an equivalent loading at point B on the axis of the pipe.

SOLUTION

80 mm

400 mm

5 kN

A

B

C

861


*11–12. A reinforced concrete pier is used to support the stringers for a bridge deck. Draw the shear and moment diagrams for the pier when it is subjected to the stringer loads shown. Assume the columns at A and B exert only vertical reactions on the pier.

SOLUTION

1 m 1 m 1 m 1 m1.5 m60 kN 60 kN35 kN 35 kN 35 kN

1.5 m

A B

862


11–13. Draw the shear and moment diagrams for the rod. It is supported by a pin at A and a smooth plate at B. The plate slides within the groove and so it cannot support a vertical force, although it can support a moment.

SOLUTION

4 m

A

B

2 m

15 kN

863


11–14. The industrial robot is held in the stationary position shown. Draw the shear and moment diagrams of the arm ABC if it is pin connected at A and connected to a hydraulic cylinder (two-force member) BD. Assume the arm and grip have a uniform weight of 1.5 lb> in. and support the load of 40 lb at C.

SOLUTION

10 in.4 in.

50 in.A B C

D

120�

864


11–15. Draw the shear and moment diagrams for the overhang beam.

SOLUTION

4 kN/m

3 m 3 m

AB

865


*11–16. Determine the placement distance a of the roller support so that the largest absolute value of the moment is a minimum. Draw the shear and moment diagrams for this condition.

SOLUTION

A

P

a

P

B

L–2

L–2

866


11–17. Draw the shear and moment diagrams for the cantilevered beam.

SOLUTION

300 lb 200 lb/ft

A

6 ft

867


11–18. Draw the shear and moment diagrams for the beam, and determine the shear and moment throughout the beam as functions of x.

SOLUTION

6 ft 4 ft

2 kip/ft 8 kip

x

10 kip

40 kip�ft

868



SOLUTION

A

30 kip�ft

B

5 ft 5 ft

2 kip/ ft

5 ft

869


*11–20. Draw the shear and moment diagrams for the overhanging beam.

SOLUTION BA

12 ft

3 kip/ft

6 ft

870


11–21. The 150-lb man sits in the center of the boat, which has a uniform width and a weight per linear foot of 3 lb>ft. Determine the maximum bending moment exerted on the boat. Assume that the water exerts a uniform distributed load upward on the bottom of the boat.

SOLUTION

7.5 ft 7.5 ft

871



SOLUTION

w0

A B

L3

L3

L3

872



SOLUTION

BA4.5 m 4.5 m

5 kN/m5 kN/m

873


*11–24. Draw the shear and moment diagrams for the compound beam.

SOLUTION

BA

6 ft

150 lb/ft 150 lb/ft

3 ft

C

874


11–25. Express the shear and moment in terms of x and then draw the shear and moment diagrams for the simply supported beam.

SOLUTION

A B

3 m 1.5 m

300 N/m

875


11–26. Draw the shear and moment diagrams for the beam and determine the shear and moment in the beam as functions of x, where 4 ft < x < 10 ft.

SOLUTION

200 lb�ft

B

x

4 ft 4 ft

150 lb/ft

6 ft

200 lb�ft

A

876


11–27. The ski supports the 180-lb weight of the man. If the snow loading on its bottom surface is trapezoidal as shown, determine the intensity w, and then draw the shear and moment diagrams for the ski.

SOLUTION

180 lb

w w1.5 ft 3 ft 1.5 ft

3 ft

877


*11–28. Draw the shear and moment diagrams for the compound beam.

SOLUTION

3 m 3 m1.5 m 1.5 m

5 kN3 kN/m

AB C D

878


11–29. Draw the shear and moment diagrams for the simply supported beam.

SOLUTION

AB

2 m 2 m

10 kN 10 kN

15 kN�m

2 m

879


11–30. Draw the shear and moment diagrams for the overhang beam.

SOLUTION

AB

M � 10 kN�m2 m 2 m 2 m

6 kN18 kN

880


11–31. The beam is used to support a uniform load along CD due to the 6-kN weight of the crate. If the reaction at bearing support B can be assumed uniformly distributed along its width, draw the shear and moment diagrams for the beam.

SOLUTION

2.75 m 2 m0.75 m0.5 m

C

BA

D

881


*11–32. The support at A allows the beam to slide freely along the vertical guide so that it cannot support a vertical force. Draw the shear and moment diagrams for the beam.

SOLUTION

BA

L

w

882


11–33. The shaft is supported by a smooth thrust bearing at A and a smooth journal bearing at B. Draw the shear and moment diagrams for the shaft.

SOLUTION

A B

900 N

600 N�m

0.8 m 0.8 m 0.8 m

883


11–34. The footing supports the load transmitted by the two columns. Draw the shear and moment diagrams for the footing if the reaction of soil pressure on the footing is assumed to be uniform.

SOLUTION

6 ft 12 ft 6 ft

14 kip14 kip

884


11–35. If the A-36 steel sheet roll is supported as shown and the allowable bending stress is 165 MPa, determine the smallest radius r of the spool if the steel sheet has a width of 1 m and a thickness of 1.5 mm. Also, find the corresponding maximum internal moment developed in the sheet.

SOLUTION

r

885


*11–36. Determine the moment M that will produce a maximum stress of 10 ksi on the cross section.

SOLUTION

3 in.

D

A B

0.5 in.

M

0.5 in.

3 in.

C

10 in.

0.5 in.0.5 in.

886


11–37. Determine the maximum tensile and compressive bending stress in the beam if it is subjected to a moment of M = 4 kip # ft.

SOLUTION

3 in.

D

A B

0.5 in.

M

0.5 in.

3 in.

C

10 in.

0.5 in.0.5 in.

887


11–38. A member has the triangular cross section shown. Determine the largest internal moment M that can be applied to the cross section without exceeding allowable tensile and compressive stresses of (sallow)t = 22 ksi and (sallow)c = 15 ksi, respectively.

SOLUTION

2 in.2 in.

4 in.

M4 in.

888


11–39. A member has the triangular cross section shown. If a moment of M = 800 lb # ft is applied to the cross section, determine the maximum tensile and compressive bending stresses in the member. Also, sketch a three-dimensional view of the stress distribution action over the cross section.

SOLUTION

2 in.2 in.

4 in.

M4 in.

889


*11–40. If the beam is subjected to an internal moment of M = 30 kN # m, determine the maximum bending stress in the beam. The beam is made from A992 steel. Sketch the bending stress distribution on the cross section.

SOLUTION

50 mm

150 mm

15 mm

10 mm

15 mm

A

50 mm

M

890


11–41. If the beam is subjected to an internal moment of M = 30 kN # m, determine the resultant force caused by the bending stress distribution acting on the top flange A.

SOLUTION

50 mm

150 mm

15 mm

10 mm

15 mm

A

50 mm

M

891


11–42. Two designs for a beam are to be considered. Determine which one will support a moment of M = 150 kN # m with the least amount of bending stress. What is that stress?

SOLUTION

200 mm

300 mm

(a) (b)

15 mm

30 mm

15 mm

200 mm

300 mm

30 mm

15 mm

30 mm

892


11–43. The simply supported truss is subjected to the central distributed load. Neglect the effect of the diagonal lacing and determine the absolute maximum bending stress in the truss. The top member is a pipe having an outer diameter of 1 in. and thickness of 3

16 in., and the bottom member is a solid rod having a diameter of 12 in.

SOLUTION

6 ft

5.75 in.

6 ft 6 ft

100 lb/ft

893


*11–44. A box beam is constructed from four pieces of wood, glued together as shown. If the moment acting on the cross section is 10 kN # m, determine the stress at points A and B and show the results acting on volume elements located at these points.

SOLUTION

20 mm 20 mm

250 mm

M � 10 kN�m

160 mm

25 mm

25 mm B

A

894


11–45. Determine the absolute maximum bending stress in the 1.5-in.-diameter shaft which is subjected to the concentrated forces. The sleeve bearings at A and B support only vertical forces.

SOLUTION

12 in.

18 in.

B

A

400 lb

15 in.

300 lb

895


11–46. Determine the smallest allowable diameter of the shaft which is subjected to the concentrated forces. The sleeve bearings at A and B support only vertical forces, and the allowable bending stress is sallow = 22 ksi.

SOLUTION

12 in.

18 in.

B

A

400 lb

15 in.

300 lb

896


11–47. The beam is subjected to a moment of M = 30 lb # ft. Determine the bending stress acting at point A and B. Also, stetch a three-dimensional view of the stress distribution acting over the entire cross-sectional area.

SOLUTION

3 in.

1 in.

1 in.

A

B

M � 30 lb�ft

897


*11–48. The shaft is supported by a smooth thrust bearing at A and smooth journal bearing at D. If the shaft has the cross section shown, determine the absolute maximum bending stress in the shaft.

SOLUTION

A C DB

3 kN 3 kN

0.75 m 0.75 m1.5 m

40 mm 25 mm

898


11–49. The axle of the freight car is subjected to wheel loadings of 20 kip. If it is supported by two journal bearings at C and D, determine the maximum bending stress developed at the center of the axle, where the diameter is 5.5 in.

SOLUTION

C DA B

20 kip 20 kip

10 in. 10 in.60 in.

899


11–50. If the built-up beam is subjected to an internal moment of M = 75 kN # m, determine the maximum tensile and compressive stress acting in the beam.

SOLUTION

300 mmA

M

20 mm

10 mm

10 mm

150 mm

150 mm

150 mm

900


11–51. If the built-up beam is subjected to an internal moment of M = 75 kN # m, determine the amount of this internal moment resisted by plate A.

SOLUTION 300 mmA

M

20 mm

10 mm

10 mm

150 mm

150 mm

150 mm

901


*11–52. If the compound beam in Prob. 11–7 has a square cross section of side length a, determine the minimum value of a if the allowable bending stress is sallow = 150 MPa.

SOLUTION

902


11–53. If the crane boom ABC in Prob. 11–3 has a rectangular cross section with a base of 2.5 in., determine its required height h to the nearest 1

4 in. if the allowable bending stress is sallow = 24 ksi.

SOLUTION

903


11–54. A shaft is made of a polymer having an elliptical cross section. If it resists an internal moment of M = 50 N # m, determine the maximum bending stress developed in the material (a) using the flexure formula, where Iz = 14p (0.08 m)(0.0 m)3, (b) using integration. Sketch a three-dimensional view of the stress distribution acting over the cross-sectional area.

SOLUTION

y

z x

M � 50 N�m

80 mm

160 mm

y———(40)

2

2

z———(80)

2

2� � 1

904


11–55. Solve Prob. 11–54 if the moment M = 50 N # m is applied about the y axis instead of the x axis. Here Iy = 14p (0.04 m)(0.08 m)3.

SOLUTION

y

z x

M � 50 N�m

80 mm

160 mm

y———(40)

2

2

z———(80)

2

2� � 1

905


*11–56. Determine the absolute maximum bending stress in the tubular shaft if di = 160 mm and do = 200 mm.

SOLUTION

A B

di do

3 m 1 m

15 kN/m

60 kN � m

906


11–57. The tubular shaft is to have a cross section such that its inner diameter and outer diameter are related by di = 0.8do. Determine these required dimensions if the allowable bending stress is sallow = 155 MPa.

SOLUTION

A B

di do

3 m 1 m

15 kN/m

60 kN � m

907


11–58. The wood beam has a rectangular cross section in the proportion shown. Determine its required dimension b if the allowable bending stress is sallow = 10 MPa.

SOLUTION

500 N/m

2 m 2 m

1.5b

bA B

908


11–59. If the beam is subjected to an internal moment of M = 100 kN # m, determine the bending stress developed at points A, B, and C. Sketch the bending stress distribution on the cross section.

SOLUTION

M300 mm

150 mm

30 mm

150 mm

C

30 mm

B

A

909


*11–60. If the beam is made of material having an allowable tensile and compressive stress of (sallow)t = 125 MPa and (sallow)c = 150 MPa, respectively, determine the maximum allowable internal moment M that can be applied to the beam.

SOLUTION

M300 mm

150 mm

30 mm

150 mm

C

30 mm

B

A

910


11–61. If the material of the beam has an allowable bending stress of sallow = 150 MPa, determine the maximum allowable intensity w0 of the uniform distributed load.

SOLUTION

6 m

150 mm

300 mm

A B

w

911


11–62. If the compound beam in Prob. 11–24 has a square cross section, determine its dimension a if the allowable bending stress is sallow = 150 MPa.

SOLUTION

912


11–63. If the beam in Prob. 11–22 has a rectangular cross section with a width b and a height h, determine the absolute maximum bending stress in the beam.

SOLUTION

913


*11–64. The shaft is supported by a smooth thrust bearing at A and smooth journal bearing at C. If d = 3 in., determine the absolute maximum bending stress in the shaft.

SOLUTION

A C Dd

B

3 ft 3 ft

3600 lb

1800 lb3 ft

914


11–65. The shaft is supported by a smooth thrust bearing at A and smooth journal bearing at C. If the material has an allowable bending stress of sallow = 24 ksi, determine the required minimum diameter d of the shaft to the nearest 1

16 in.

SOLUTION

A C Dd

B

3 ft 3 ft

3600 lb

1800 lb3 ft

915


11–66. The man has a mass of 78 kg and stands motionless at the end of the diving board. If the board has the cross section shown, determine the maximum normal strain developed in the board. The modulus of elasticity for the material is E = 125 GPa. Assume A is a pin and B is a roller.

SOLUTION

B CA1.5 m 2.5 m

350 mm

20 mm30 mm

10 mm 10 mm 10 mm

916


11–67. The two solid steel rods are bolted together along their length and support the loading shown. Assume the support at A is a pin and B is a roller. Determine the required diameter d of each of the rods if the allowable bending stress is sallow = 130 MPa.

SOLUTION

B

A

2 m

80 kN20 kN/m

2 m

917


*11–68. Solve Prob. 11–67 if the rods are rotated 90� so that both rods rest on the supports at A (pin) and B (roller).

SOLUTION

B

A

2 m

80 kN20 kN/m

2 m

918


11–69. The beam is subjected to a bending moment of M = 20 kip # ft directed as shown. Determine the maximum bending stress in the beam and the orientation of the neutral axis.

SOLUTION

16 in.

10 in.

8 in.

14 in.

y

z

M

B C

A D

45�

919


11–70. Determine the maximum magnitude of the bending moment M that can be applied to the beam so that the bending stress in the member does not exceed 12 ksi.

SOLUTION

16 in.

10 in.

8 in.

14 in.

y

z

M

B C

A D

45�

920


11–71. If the resultant internal moment acting on the cross section of the aluminum strut has a magnitude of M = 520 N # m and is directed as shown, determine the bending stress at points A and B. The location y of the centroid C of the strut’s cross-sectional area must be determined. Also, specify the orientation of the neutral axis.

SOLUTION

20 mm20 mm

z BC

–y

200 mm

y

M � 520 N�m

125 13

200 mm 200 mmA

20 mm

921


*11–72. The resultant internal moment acting on the cross section of the aluminum strut has a magnitude of M = 520 N # m and is directed as shown. Determine maximum bending stress in the strut. The location y of the centroid C of the strut’s cross-sectional area must be determined. Also, specify the orientation of the neutral axis.

SOLUTION

20 mm20 mm

z BC

–y

200 mm

y

M � 520 N�m

125 13

200 mm 200 mmA

20 mm

922


11–73. Consider the general case of a prismatic beam subjected to bending-moment components My and Mz , as shown, when the x, y, z axes pass through the centroid of the cross section. If the material is linear-elastic, the normal stress in the beam is a linear function of position such that s = a + by + cz. Using the equilibrium conditions 0 = 1As dA , My = 1Azs dA , Mz =1A - ys dA , determine the constants a, b, and c, and show that the normal stress can be determined from the equation s = [- (MzIy + MyIyz)y + (MyIz + MzIyz)z]>(IyIz - Iyz

2), where the moments and products of inertia are defined in Appendix B.

SOLUTION

y

y

z x

z

dAMy

C

Mz

s

923


11–74. The box beam is subjected to the internal moment of M = 4 kN # m, which is directed as shown. Determine the maximum bending stress developed in the beam and the orientation of the neutral axis.

SOLUTION

z

y

x

150 mm

150 mm

25 mm50 mm

50 mm

50 mm

50 mm

45�

25 mm

M

924


11–75. If the wood used for the box beam has an allowable bending stress of (sallow) = 6 MPa, determine the maximum allowable internal moment M that can be applied to the beam.

SOLUTIONz

y

x

150 mm

150 mm

25 mm50 mm

50 mm

50 mm

50 mm

45�

25 mm

M

925


*11–76. For the section, Iy� = 31.7(10-6) m4, Iz� = 114(10-6) m4, Iy�z� = 15.1(10-6) m4. Using the techniques outlined in Appendix A, the member’s cross-sectional area has principal moments of inertia of Iy = 29.0(10-6) m4 and Iz = 117(10-6) m4, computed about the principal axes of inertia y and z, respectively. If the section is subjected to a moment of M = 2500 N # m directed as shown, determine the stress produced at point A, using Eq. 11–17.

SOLUTION

60 mm

60 mm

60 mm 60 mm

140 mm

80 mm

z¿

y¿

10.10�

M � 2500 N�mC

A

z

y

926


11–77. Solve Prob. 11–76 using the equation developed in Prob. 11–73.

SOLUTION

60 mm

60 mm

60 mm 60 mm

140 mm

80 mm

z¿

y¿

10.10�

M � 2500 N�mC

A

z

y

927


11–78. If the beam is subjected to the internal moment of, M = 1200 kN # m, determine the maximum bending stress acting on the beam and the orientation of the neutral axis.

SOLUTION

150 mm

150 mm

150 mm

150 mm

300 mm

150 mm

y

xz

M

30�

928


11–79. If the beam is made from a material having an allowable tensile and compressive stress of (sallow)t = 125 MPa and (sallow)C = 150 MPa, respectively, determine the maximum allowable internal moment M that can be applied to the beam.

SOLUTION

150 mm

150 mm

150 mm

150 mm

300 mm

150 mm

y

xz

M

30�

929


*11–80. The stepped bar has a thickness of 15 mm. Determine the maximum moment that can be applied to its ends if it is made of a material having an allowable bending stress of sallow = 200 MPa.

SOLUTION

M

10 mm

M

30 mm45 mm

3 mm6 mm

Stress Concentration Factor:

For the smaller section with and , we have

obtained from the graph in the text.

For the larger section with and , we have

obtained from the graph in the text.

Allowable Bending Stress:

For the smaller section

Ans.

For the larger section

M = 257 N # m

200 A106 B = 1.75B M(0.015)112 (0.015)(0.033)

R

smax = sallow = K Mc

I ;

M = 41.7 N # m (Controls !)

200 A106 B = 1.2B M(0.005)112 (0.015)(0.013)

R

smax = sallow = K Mc

I ;

K = 1.75r

h=

330

= 0.1wh

=4530

= 1.5

K = 1.2r

h=

610

= 0.6wh

=3010

= 3

930


11–81. If the radius of each notch on the plate is r = 0.5 in., determine the largest moment that can be applied. The allowable bending stress for the material is sallow = 18 ksi.

SOLUTION

12.5 in.

14.5 in.1 in.

MM

931


11–82. The symmetric notched plate is subjected to bending. If the radius of each notch is r = 0.5 in. and the applied moment is M = 10 kip # ft, determine the maximum bending stress in the plate.

SOLUTION

12.5 in.

14.5 in.1 in.

MM

932


11–83. The bar is subjected to a moment of M = 40 N # m. Determine the smallest radius r of the fillets so that an allowable bending stress of sallow = 124 MPa is not exceeded.

SOLUTION

80 mm

20 mm 7 mm

M Mr

r

933


*11–84. The bar is subjected to a moment of M = 17.5 N # m If r = 5 mm, determine the maximum bending stress in the material.

SOLUTION

80 mm

20 mm 7 mm

M Mr

r

934


11–85. The simply supported notched bar is subjected to two forces P. Determine the largest magnitude of P that can be applied without causing the material to yield. The material is A-36 steel. Each notch has a radius of r = 0.125 in.

SOLUTION

20 in. 20 in.

1.75 in.

0.5 in.

P P

1.25 in.

20 in. 20 in.

935


11–86. The simply supported notched bar is subjected to the two loads, each having a magnitude of P = 100 lb. Determine the maximum bending stress developed in the bar, and sketch the bending-stress distribution acting over the cross section at the center of the bar. Each notch has a radius of r = 0.125 in.

SOLUTION

20 in. 20 in.

1.75 in.

0.5 in.

P P

1.25 in.

20 in. 20 in.

936


11–87. The bar is subjected to a moment of M = 153 N # m. Determine the smallest radius r of the fillets so that an allowable bending stress of sallow = 120 MPa is not exceeded.

SOLUTION

60 mm40 mm 7 mm

M M

r

r

937


*11–88. The bar is subjected to a moment of M = 17.5 N # m. If r = 6 mm determine the maximum bending stress in the material.

SOLUTION

60 mm40 mm 7 mm

M M

r

r

938


11–89. The beam is made from three boards nailed together as shown. If the moment acting on the cross section is M = 650 N # m, determine the resultant force the bending stress produces on the top board.

SOLUTION

M � 650 N�m

250 mm

15 mm

125 mm 20 mm

20 mm

939


11–90. The beam is made from three boards nailed together as shown. Determine the maximum tensile and compressive stresses in the beam.

SOLUTION

M � 650 N�m

250 mm

15 mm

125 mm 20 mm

20 mm

940


11–91. Draw the shear and moment diagrams for the shaft if it is subjected to the vertical loadings of the belt, gear, and flywheel. The bearings at A and B exert only vertical reactions on the shaft.

SOLUTION

A B

200 mm

450 N

150 N

300 N

200 mm400 mm 300 mm

941


*11–92. The beam is subjected to a moment M. Determine the percentage of this moment that is resisted by the stresses acting on both the top and bottom boards, A and B, of the beam.

SOLUTION

150 mm

25 mm

25 mm

150 mm

M

25 mm

25 mm

B

A

D

Section Property:

Bending Stress: Applying the flexure formula

Resultant Force and Moment: For board A or B

Ans.scaM¿Mb = 0.8457(100%) = 84.6 %

M¿ = F(0.17619) = 4.80M(0.17619) = 0.8457 M

= 4.800 M

F = 822.857M(0.025)(0.2) +12

(1097.143M - 822.857M)(0.025)(0.2)

sD =M(0.075)

91.14583(10-6)= 822.857 M

sE =M(0.1)

91.14583(10-6)= 1097.143 M

s =My

I

I =112

(0.2) A0.23 B -1

12 (0.15) A0.153 B = 91.14583 A10-6 B m4

942


11–93. Determine the moment M that should be applied to the beam in order to create a compressive stress at point D of sD = 30 MPa. Also sketch the stress distribution acting over the cross section and compute the maximum stress developed in the beam.

SOLUTION

150 mm

25 mm

25 mm

150 mm

M

25 mm

25 mm

B

A

D

Section Property:

Bending Stress: Applying the flexure formula

Ans.

Ans.smax =Mc

I=

36458(0.1)

91.14583(10-6)= 40.0 MPa

M = 36458 N # m = 36.5 kN # m

30 A106 B =M(0.075)

91.14583(10-6)

s =My

I

I =112

(0.2) A0.23 B -1

12 (0.15) A0.153 B = 91.14583 A10-6 B m4

943


11–94. A shaft is made of a polymer having a parabolic cross section. If it resists an internal moment of M = 125 N # m, determine the maximum bending stress developed in the material (a) using the flexure formula and (b) using integration. Sketch a three-dimensional view of the stress distribution acting over the cross-sectional area.

SOLUTION

y

z

x

M � 125 N· m

50 mm

100 mm

50 mm

y � 100 – z

2/ 25

944


11–95. Determine the maximum bending stress in the handle of the cable cutter at section a–a. A force of 45 lb is applied to the handles. The cross-sectional area is shown in the figure.

SOLUTION

4 in.

45 lb20�

a

a

3 in.

5 in.

A

45 lb

0.75 in.

0.50 in.

945


*11–96. The chair is supported by an arm that is hinged so it rotates about the vertical axis at A. If the load on the chair is 180 lb and the arm is a hollow tube section having the dimensions shown, determine the maximum bending stress at section a–a.

SOLUTION

1 in.

3 in.

a

a

A

180 lb

2.5 in.

0.5 in.8 in.

946


11–97. Draw the shear and moment diagrams for the beam and determine the shear and moment in the beam as functions of x, where 0 … x 6 6 ft .

SOLUTION

6 ft 4 ft

2 kip/ ft

50 kip�ft

8 kip

x

947


11–98. The wing spar ABD of a light plane is made from 2014–T6 aluminum and has a cross-sectional area of 1.27 in.2, a depth of 3 in., and a moment of inertia about its neutral axis of 2.68 in4. Determine the absolute maximum bending stress in the spar if the anticipated loading is to be as shown. Assume A, B, and C are pins. Connection is made along the central longitudinal axis of the spar.

SOLUTION

2 ft DBA

C3 ft 6 ft

80 lb/in.

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