1. Derivation of the stresses and sectional forces in biaxially bended beam. a) Make a graphs of the following functions: Ty, Tz, My i Mz. b) In cross section C derive and plot -components of the sectional forces and neutral axis, -graph of the normal stresses with its extreme values. c) In points K and L of the above cross section derive values of the effective stresses according to the Coulomb-Tresca/Huber-Mises hypothesis. Remark: For determination of the stresses take into account only the influence of the sectional forces Ty, Tz, My i Mz. 45/P1

1. Derivation of the stresses and sectional forces in biaxially bended beam. a) Make a graphs of the following functions: Ty, Tz, My i Mz. b) In cross section C derive and plot -components of the sectional forces and neutral axis, -graph of the normal stresses with its extreme values. c) In points K and L of the above cross section derive values of the effective stresses according to the Coulomb-Tresca/Huber-Mises hypothesis. Remark: For determination of the stresses take into account only the influence of the sectional forces Ty, Tz, My i Mz. 45/P1

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.5.9P: A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure)....

See similar textbooks

Similar questions

1. A beam of length L is simply supported shown as follows. A concentrated force F is applied at point A. The cross section of the beam is a rectangular with sides a and b. Please determine: 1) The shear force diagram and the bending moment diagram of the beam. 2) Determine the normal stress distribution on cross section B. Specify the locations and magnitudes of the max. tensile/compressive stress on cross section B. 3) Find the location and the magnitude of the max. bending stress ON THE BEAM. For simplicity, transverse shear stress is neglected. 4) Find the location and magnitude of the max. transverse shear stress on cross section B. F A В
Figure shows a beam made from bronze subjected to a 3.5kN.m bending couple and its respective tensile properties. i) With aid of illustration, draw the deformation of the bean and locate the position where the beam experience maximum tensile stress (αmax)t and maximum compressive stress (αmax)c. Accordingly. Determine the magnitude of these two stresses. ii) Sketch the two-dimensional stress distribution acting on point A and point B over the cross-sectional area of the beam as observed from side view. Estimate the magnitude of the stresses at those two points.
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. 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 given fig find the correct representation of the longitudinal variation of the bending stress
a) Calculate the reaction forces in terms of F andtheta.b) Calculate the internal shear force and moment as a function of x using cuts and summingforces and moments in terms of F, L, andtheta.c) Calculate the shear force and moments by integration in terms of x, L, F andtheta.d) Assuming a rectangular cross section compute the average normal stress for the case F =10kNat 30° where b =0.04 m, h = 0.08 m, at the point x = L/4, L = 1 m at the centroid.e) With the cross section given above compute the average normal stress for the case F =10kN at30° at the point x = L/4, L = 1 m at each surface of the beam.f) Calculate the shear stress at the top and bottom surface, at the neutral axis and at x = 0.25 mand y = 0.02 m above the neutral axis.
For the steel beam is used to support the loads shown below: a) Draw shear force diagram and bending moment diagram. b) Determine the magnitude and location maximum moment. c) Calculate the maximum stress. Modulus of elasticity (E) = 400 MP , Modulus of rigidity (G) = 78 GPa
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 Dy
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 X
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=2.50 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 X
Figure Q1 b) State if the cantilever beam is in plain stress or plain strain and explain briefly your reasoning. Refer to the differences between the two systems with regards to stresses and strains. Use sketches as part of your answer where appropriate.
Task 1 (a) A steel cantilever beam with a 1-in-diameter round cross section and length of 10 in is loaded at the tip with a transverse force of 1000 lbf and an axial force of 5000 lbf, as shown in the figure. Study the significance of the transverse shear stress in combination with tension and bending by calculating magnitudes of the stresses. Explain and comment on the stresses and strains generated. 1000 Ibf 1 in dia. Cross section at the wall 5000 Ibf (b) Consider a square element in the x-y plane with side length of 3 cm. The thickness of the element is 7 mm. The element has modulus of elasticity of 200 GPa and Poison's ratio of 0.33. If the element is subjected to forces in the x and y directions of 3 KN and 1.5 KN, respectively, find the dimensions of the loaded element. (c) Consider a cubic element with side length of 4 cm. The element has modulus of elasticity of 80 GPa and Poison's ratio of 0.3. If the element is subjected to equal forces in the x, y and z direction of 3 KN.…
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 X