A beam with a length of 8 meters is known to carry both distributed and point loads as well as one point moment applied at the end of the beam, i.e., x = 8 m. These loads produce the shear force diagram shown in Figure 2.1: 80 {4,80} 60 60 40 40 20 20 Shear Force [kN] - {0,0} {0,-10} {2,0} -20 -40 {2,-50} {4,-40} 4 x [m] {8,40} {6,40} {8,0} 00 Figure 2.1. Shear force diagram for loaded beam. Coordinates, as in {x position, shear force} are provided for each location where a significant change in the diagram occurs. Using the information in the diagram, find the corresponding bending moment diagram and use it, along with the shear force diagram given, to deduce the loads being applied to beam and show them in a free body diagram of the beam. Show and justify your calculations to obtain the bending moment diagram and label each significant location with its corresponding value of bending moment. Furthermore, provide a brief narrative of how you used both diagrams to deduce the loads applied to the beam.

A beam with a length of 8 meters is known to carry both distributed and point loads as well as one point moment applied at the end of the beam, i.e., x = 8 m. These loads produce the shear force diagram shown in Figure 2.1: 80 {4,80} 60 60 40 40 20 20 Shear Force [kN] - {0,0} {0,-10} {2,0} -20 -40 {2,-50} {4,-40} 4 x [m] {8,40} {6,40} {8,0} 00 Figure 2.1. Shear force diagram for loaded beam. Coordinates, as in {x position, shear force} are provided for each location where a significant change in the diagram occurs. Using the information in the diagram, find the corresponding bending moment diagram and use it, along with the shear force diagram given, to deduce the loads being applied to beam and show them in a free body diagram of the beam. Show and justify your calculations to obtain the bending moment diagram and label each significant location with its corresponding value of bending moment. Furthermore, provide a brief narrative of how you used both diagrams to deduce the loads applied to the beam.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.7.12P: A bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness...

See similar textbooks

Similar questions

The dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C. What is the reaction force at A? Let a positive reaction force be to the right.
Elasticity and Stress Analysis: Torsion The three cell box girder of Figure 1 Q.1 is subjected to a clockwise torque of 10,000 kNm.Sketch the shear flow diagram for the girder.Hence, determine the shear stress set up in each member and the angle of twist of thegirder.Given: Modulus of Rigidity = 80 GN/m2 Equations: T=2Ah 2G(theta)A=(tau)L q1=q2+q3
Draw the Shear force diagram & Bending moment diagram for the cantilever beam as shown in figure, mark the salient points in the diagram. Neglect the self-weight of the beam, where F1 =30 N, F2=60N, F3 =60 N, F4 =80N, a =3 m, b=1 m, c=5 m, d=4 m The reaction at the fixed support "A" (unit in N)=_____________ Answer for part 1 (ii) Shear force at the point "A" (Unit in N) = ________ Answer for part 2 (iii) Shear force at the point "B" (Unit in N) = ________ Answer for part 3 (iv) Shear force at the point "C" (Unit in N) = ________ Answer for part 4 (v) Shear force at the point "D" (Unit in N) = ________ Answer for part 5 (vi) Shear force at the point "E" (Unit in N) = ________ Answer for part 6 (vii) Bending moment at the point "E"(unit in Nm) = ________________ Answer for part 7 (viii) Bending moment at the point "D"(unit in Nm) = ________________ Answer for part 8 (ix) Bending moment at the point "C"(unit in Nm) = ________________ Answer for part 9 (x) Bending moment…
Consider a horizontal, uniform beam that extends from x = 0 m to x = 2.5 m. The beam is supported at each end by two strings which exert forces directly upward. There is a downward force per length on the beam given by dF/dx = 488 x (2.5 - x) (N/m), which includes any weight force on the beam. Calculate the tension in the rope attached to the right end of the beam. (Please answer to the fourth decimal place - i.e 14.3225)
3. A 3-meter-long beam is used to support a heavy object. The object has a uniform distributed load of 6 kN/m on the entire beam. The Young’s modulus and moment of inertia of the beam are 200 GPa and 5×105 mm4, respectively. The beam is supported at three positions as shown below. (a) Label the element and node numbers (either on the figure or with a new simple sketch). (b) Determine the slopes at the three support positions of the beam.
For the following structure, represent Mohr's Circle at point K of the structure and pointSection P, demonstrating the following steps:a) Effort diagram;b) Calculation of the geometric properties of the section; θ= 10thq=61kN/mV= 51kNN=48kNh1 = 221 mmb1=221 mmh2=t=21 m
The section modulus for the beam of rectangular cross section of size 80 mm x 85 mm, is ______________ mm3. The section modulus (unit is in mm3)= ______________ Answer
determine the diagram of the shear forces and bending moments in the beam shown below. Data P = 20kN, M = 60kNm, q = 10kN / m, a = 5m, b = 2m, c = 3, alpha = 60.
Find the change in length between the points A and D on the bar given in the figure E= 4.10 5kN/cm2
Figure Q2(b) shows the cross-section of a cantilever beam ABC. The beam is subjected to uniformly distributed loading and a concentrated force as shown in Figure Q2(c). Determine:(i) the second moment of area or moment of inertia for the cross-section about its neutral axis (NA)(ii) the internal bending moment and bending stress at section x-x as shown in Figure Q2(c) and at points P and Q of the cross section as shown in Figure Q2(b) of the beam and state whether the bending stress is in tension or compression.
N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.6 cm from the neutral axis is
consider a beam shown in the attached figure express the internal moment in the beam as a function of x for 0 < x < L/3. express answer in terms of some or all variables x, w0 and L.