P8.20 A W360 x 72 standard steel shape is used to support the loads shown on the beam in Figure P8.20a. The shape is oriented so that bending occurs about the weak axis as shown in Figure PS.20b. Consider the entire 6 m length of the beam and determine: (a) the maximum tensile bending stress at any location along the beam, and (b) the maximum compressive bending stress at any location along the beam. |6 kN 15 kN/m В ' 45 kN-m 1.5 m 1.5 m I 3 m W360 x 72 FIGURE P8.20a FIGURE P8.20b
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- A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in, torque at both ends, calculate the maximum shear stress and the angle of twist between the ends. Use G = 11,600 ksi.For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg - 35kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. A Ay- 58.66 - Dy- Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x DyFor the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg = 35kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay= Dy = a M. B a PB Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB Pc a Pc kN b KN D b D X D X
- For the beam shown, (1) derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) (2) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Specify the values for key points on the diagrams. Let a = 5.9 ft, b = 7.5 ft, wa = 13 kips/ft, and w, = 5 kips/ft. Derive the equations and construct the shear-force and bending- moment diagrams on paper and use the results to answer the questions. Y || A Wa a (a) at x = 4.9 ft (b) at x = 7.9 ft B V = M = V = M = Wb b (c) Maximum bending moment Mmax = i i с ·X kips kip-ft kips kip-ft kip-ftFor the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= Mi i B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB a PB B a Pc a Pc C kN b KN b D X D₂ XFor the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.75 m, b=5.00 m, PB = 60KN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= tel tel a i B a Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB B a PB Pc a C Pc C KN b KN D b D X D₂ X
- For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.75 m, b=5.00 m, PB = 60kN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = a Dy= a B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) 36.66 BO 103.33 PB a PB Pc a Pc KN b KN b D D x P XFor the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=6.5 ft, b=24.0 ft, P = 32 kips and w = 9.5 kips/ft. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. 1. Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) 2.Determine the shear force acting at each of the following locations: (in kips)(a) x = 6.5- ft (i.e., just to the left of point B)(b) x = 6.5+ ft (i.e., just to the right of point B)(c) x = 28.5 ft 3.Determine the bending moment acting at each of the following locations: (in kips-ft)(a) x = 6.5 ft (i.e., at point B)(b) x = 28.5 ft 4.Use your…QUESTION 3 If the allowable bending stresses for a beam in one application is 6 kip/in2 in tension. The cross-section of the beam is W8 x 40. If the beam is 10 foot long and simply supported and has a concentrated load applied at x = 3 ft as shown below. • Generate the shear force and bending moment diagram in terms of P; • Based on the allowable maximum bending moment you just obtained above, calculate/ input the mazimm allowable value of the load P: please, pay attention to units, and calculate your answer to 1 decimal place.. 3 ft 7 ft kip.
- For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=11.5 ft, b=19.0 ft, P = 50 kips and w = 8.5 kips/ft. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. A Answers: Ay= Cy= Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Answers: (a) V= (b) V= (c) V= Answers: (a) M= a (b) M= B a Answers: Mmax = B Xmax= kips W kips Determine the shear force acting at each of the following locations: (a) x = 11.5-ft (i.e., just to the left of point B) (b)x= 11.5+ ft (i.e., just to the right of point B) (c) x = 28.5 ft Note that x = 0 at support A. When entering…P8.5 A beam is subjected to equal bending moments of M₂ = 45 kip-ft, as shown in Figure P8.5a. The cross-sectional dimensions (Figure P8.5b) are b₁ = 7.5 in., d₁ = 1.5 in., b2 = 0.75 in., d2 = 6.0 in., b3 = 3.0 in., and d3 = 2.0 in. Determine: (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. State whether the normal stress at H is tension or compression. (c) the bending stress at point K. State whether the normal stress at K is tension or compression. (d) the maximum bending stress produced in the cross section. State whether the stress is tension or compression. K M₂ M₂ x H b₂ y b₁ b3 d₂ dFor the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=8.5 ft, b=24.0 ft, P = 30 kips and w = 5.5 kips/ft. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise.Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Determine the shear force acting at each of the following locations:(a) x = 8.5- ft (i.e., just to the left of point B)(b) x = 8.5+ ft (i.e., just to the right of point B)(c) x = 30.5 ftNote that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. Determine the bending moment acting at each of…