Abeam with a rectangular cross section is simply supported and loaded at its center with a force P. The dimensions b, h, and L are shown in the figure. b- Determine (a) the maximum bending stress ơ max a Tmax in this beam. (c) Then obtain the ratio Tmax/o occur at different locations in the beam. Be sure to s
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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 DyFind the max shear stress in bending in the cross section below if Vmax = 10 kips. 10" Flange 2" Web 2" 8" Flange 2" 10" • Identify where in the cross section the max shear will occur. Determine the thickness of the cross-section at the location you wish to find shear stress. • Calculate the Ix for the shape (assume bending in the x with most basic beams). • Calculate Q by dividing the section into two pieces at the point you want shear stress. Select one of the pieces (either will work), I picked the top piece. Use the Shear Stress equation to determine the requested stress. Compare you answer: Max shear stress = at the center of the cross section.
- wo = 9 kN/m, L = 5.5 m, E = 220 GPa, and I = 100 x 10° mm4. A Part 1 Cut a cross-section through the beam at any point and draw a free body diagram to the right of your cut. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for Mat x= 2.8 m. Wo M(x) L-x Answer: M(x = 2.8 m) = i kN-mQUESTION 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.Problem-2 beam shown here: w=300 lb/ft Draw the shear and bending moment diagrams of the 15' B 1500 lb. с x₂x₂x * 2' 3' Hint: point B is a hinge, there is only a By force when you draw the FBD, also the bending moment in B is zero.
- For 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 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=2.50 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 XProblem #5: For the 2D beam below, with F 15 kips, M, = 7 kip-ft, and shear and bending moment diagrams. Report your answer in kip and kip-ft to one decimal place. w,= 2.5 kip/ft draw the Wo F, Fo Mo Mo 2.0 ft 1.0 ft 5.0 ft 2.0 ft By uploading this work, I attest that the work contained herein is solely my own, that I only used the given equation sheet as a reference, and that I have not received any information from anyone else or source regarding this exam at any time.
- A uniform wind load of q = 0.2 kN/m? acts on the billboard with dimensions of b = 1.5 m and a = 1 m. The allowable normal stress is oalow = 140 MPa, c = 0.5 m for the circular cross section panel pole. Draw the shear force, bending moment and torsional moment diagrams for the panel pole. a) Calculate the cross-section diameter d, using the maximum shear stress (Tresca) criterion. b) Calculate the cross-section diameter d, using the maximum distortional energy (von Mises) criterion. SOLUTION kesitFor 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-ftThe Simply supported beam in Figure has a rectangular cross section 120 mm wide and 200 mm high. (1)Compute the reaction forces Ra and Point RE. (2)Compute the maximum bending stress in the beam. - --- AAIL (4)Compute the bending stress at a point on section B that is 25 mm below the top of the beam. |15 kN 6 kN/m 100 mm NA - В ID 100 mm 0.8 m 120 mm 2 m 1.0 m RA RE (a)