Please show all work!! 7) Use strain energy to calculate the strain energy of the beam in the figure in terms of the appliedforce P, applied moment M₁, the length L, modulus E, and area moment of inertia I. Then useCastigliano's theorem to calculate the deflection of the tip.MPx

Answered: Image /qna-images/answer/6694b03d-4d0a-4608-8e91-51a5fb0275b0.jpg

7) Use strain energy to calculate the strain energy of the beam in the figure in terms of the applied force P, applied moment M。, the length L, modulus E, and area moment of inertia I. Then use Castigliano's theorem to calculate the deflection of the tip. M P x

7) Use strain energy to calculate the strain energy of the beam in the figure in terms of the applied force P, applied moment M。, the length L, modulus E, and area moment of inertia I. Then use Castigliano's theorem to calculate the deflection of the tip. M P x

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.9.12P: The cross section of a sign post of constant thickness is shown in the figure. Derive the formula...

See similar textbooks

Related questions

Q: A vapor compression refrigeration cycle operates at steady flow conditions with 0.25 kg/s or R-134a.…

Q: • Determine the forces in members BE and CE of the loaded truss. A 3 m 45° 5 kN 3m B E BC=CD 3 kN 3m…

A: Determine the forces in members BE and CE of the loaded truss.

Q: A 2.0-inch diameter 4140 steel bar is austenized and tempered in oil without Agitation, determine…

A: Given:To find:Determine the hardness at 0.6 inches below the surface.

Q: A 7.9-m-long steel [E = 195 GPa] pipe column has an outside diameter of 229 mm and a wall thickness…

A: Given:The length is .The modulus of elasticity is .The outside diameter is .The thickness is .The…

Q: If a pool is irregularly shaped and a person being assessed has a weight mg= 800 N but weighs Fn=…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Gears A and B of mass 15 kg and 56 kg have radii of gyration about their respective mass centers of…

Q: 5. Air enters a compressor at a rate of 0.5 Kg of 6.4 ms', specific volume 0.85 m³Kg¹ an bar. It…

Q: Slider 1 is moving downward at a speed of 1 = 2 m/s and with a downward acceleration of a = 0,25 m/s…

A: Dear StudentsAll the solution given in below steps

Q: 1.- You have the following manufacturing system: A B с 5% 15% M M1 M2 20% 20% E G 40% D H 40% M3 I…

A: Given:

Q: Take P= 38 kN. EI is constant. (Figure 1) Figure 4 m B- 2 m- P 1 of 1 Determine the y-component of…

A: Determine the y-component of the reaction at the roller B.Determine the x component of the reaction…

Q: The pipe ABCDE is supported by ball-and-socket joints at A and D and by cable ECF that passes…

A: Pipe is supported by ball and socket joints at A and D.Since ball and socket joints only restrict…

Q: 8-7. The rigid pipe is supported by a pin at A and an A-36 steel guy wire BD. If the wire has a…

A: As per the Bartleby policy, I am solving first question only

Q: Q₁: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k-2.3 W/m °C, and…

A: Given data:- Plane wall thickness, Thermal conductivity of wall, and its surface area, The left…

Q: Problem 2 – Heat Pump Thermodynamic Analysis Refrigerant-134a enters the condenser of a residential…

A: The inlet pressure at condenser is The inlet temperature at the condenser is The volume flow rate is…

Q: A ski resort chair lift has towers spaced 38 m horizontaly appart. The upper tower is 13 m higher…

Q: Define Incompressible flow and Incompressible fluid. A fluid flow in which the density of the fluld…

A: To Define : The incompressible flow

Q: 1. Impact extrusion is carried out at than conventional extrusion. 2. Impact extrusion can be…

A: Given : 1) Impact extrusion is carried out at .........than conventional extrusions.2) Impact…

Q: A 14-kg rock Is thrown upward with a force of 280 N at a location where the local gravitational…

Q: 12-34. Design a cylindrical tank for compressed natural gas at a pres- sure of 4.20 MPa. The minimum…

A: The pressure is The minimum inside diameter is The factor safety is The cylinder material is…

Q: Determine the area moments of inertia about given x and y axes. 300 mm y 400 mm 300 mm 300 mm

A: Determine the area moments of inertia about given x and y axes.

Q: solve frist one please

A: The diametral pitch of each gear:center distance of the gears:Velocity ratio:

Q: Derive the frequency (or characteristic) equation in the form tan ( ) = ( ) for the longitudinal…

A: To Find:The equation of the frequency in the form of Tan.Given:

Q: Force F, which has a magnitude of 10 kN, acts along a line passing through points D and D'. The grid…

A: Force F, which has a magnitude of 10 kN, acts along a line passing through points D and D'.The grid…

Q: Problem: Numerical Simulation of One-Dimensional Convection-Diffusion Problem using Finite Volume…

Q: a) Name two groups of standards in addition to national, industry-wide standards and where they are…

A: "Standards play a pivotal role in shaping the quality, safety, and compatibility of products,…

Q: Determine the coordinates of the center of mass of the slender rod. The density of the rod varies…

Q: Draw the shear and bending moment diagrams for the horizontal boom of the crane as pictured here.…

Q: Calculate the stress concentration factor (kt). the small diameter is 0.88 in and the bigger one is…

A: Given:The small diameter is the bigger diameter is The radius is The moment is The torque is

Q: Titan manufactures and sells gas-powered electricity generators. It can purchase a new line of fuel…

Q: Compute the following for the given composite area. a) Locate the centroid with respect to the given…

A: Compute the following for the given composite area.a) Locate the centroid with respect to the given…

Q: A flywheel is mounted with a fixed axis of rotation through 0, a constant as shown. It starts at…

Q: Two steels are being considered for manufacture of as-forged connecting rods. One is AISI 4340…

A: We need to find out the advantages of using these two materials.4340 Steel.Uncorrected endurance…

Q: There are variety of errors that might affect the attitude motion of a spacecraft. Discuss what type…

A: Errors in spacecraft attitude control systems can arise from various sources, impacting the…

Q: Many new factory stacks were built in Birmgham, uk. The Stacks Jare sources of pollutant emissión…

Q: A shaft with a diameter of D = 80 mm and a length of L = 385 mm, shown in the figure below, is…

A: The diameter of the shaft is D = 80 mm = 0.08 mThe length of the shaft is L =385 mm = 0.385 m.The…

Q: You are given a set slip gauge containing 46 pieces of 2mm base (M46/2). Show how you would build…

Q: A bucket of height H is filled to height H and has two holes A (H/2 from the ground) and B (3H/4…

A: The cross sectional area for hole A is aAnd the cross sectional area for hole B is a/100Heights of…

Q: The state of stress at a point in a structural member may be represented by a two-dimensional stress…

A: Given:To find:Direct stress at the required plane and the principal stresses.

Q: E Problem Number A 3.5 in 4.25 in 6 in TI 8 in 10 1500 psi Bolt grade B C D E F N Pr Bolt spec. 8-34…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Given the multiview projection of the solid, draw the isometric view. HRP FRP F DA FRP PRP

A: Given the multiview projection of the solid, draw the isometric view.

Q: 7-63. The cotter is used to hold the two rods together. Determine the smallest thickness t of the…

Q: You have writtern Nc = (mp/mo)^3/2 (kT/Eg)^3/2 x 2.51x10^19 Then, for your final answer you…

A: Here you are asking why in the final answer, mn is used instead of mp.

Q: A bar of steel has the minimum properties Se= 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is…

A: Given:The endurance stress is The yield stress is The ultimate stress is The steady torsion stress…

Q: Strut System Real Engineering Product (Motorcycle) C04 mvehicle rider 4ka 2k Simplified model and…

Q: Compute the torque to be applied by the servo motor fixed to the pin at point

A: Torque applied by servo motor is required

Q: For the beam shown, EI is constant. (Figure 1) Figure 4 1 of 1 ▼ Y Determine the vertical reaction…

A: The load at the end of the cantilever beam is the length of AB is the length of the cantilever beam…

Q: 3. A main supply line in which water flows at 320°C, 150 MPa, is connected through a valve to an…

A: Given:The initial temperature is the initial pressure is the mass of water enters is The final…

Q: Question 3 a. b. Calculate the second moment area of the section shown about an axis Y - Y through…

Q: Draw the shear diagram for the beam. Click on "add vertical line off" to add discontinuity lines.…

A: Draw the shear diagram for the beam.

Q: 1. Fig. 1 Shows an aerofoil cutting mechanism which has a laser cutting device located at point E -…

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

Please show all work!!

7) Use strain energy to calculate the strain energy of the beam in the figure in terms of the applied
force P, applied moment M₁, the length L, modulus E, and area moment of inertia I. Then use
Castigliano's theorem to calculate the deflection of the tip.
M
P
x

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given and required

VIEW

Step 2: Determination of strain energy

VIEW

Step 3: Determination of deflection

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 10 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The cross section of a sign post of constant thickness is shown in the figure. Derive the formula for the distance e from the cent crime of the wall of the post to the shear center S: where I2. = moment of inertia about the z axis. Also, compare this formula with that given in Problem 6.9-11 for the special case of ß = 0 here and a = h/2 in both formulas.
The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?
The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.
A cantilever beam is subjected to a concentrated moment at B, The length of the beam L = 3 m and the height h = 600 mm. The longitudinal strain at the top of the beam is 0,0005 and the distance from the neutral surface to the bottom surface of the Iva m is 300 nun. Find the radius of curvature, the curvature, and the deflection of the beam at B.
-6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)
A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.
A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.6 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 0.5 cm from the neutral axis (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.5 cm from the neutral axis is
A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.7 cm and internal diameter 2.2 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 (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 Answer and unit for part 4
Given the beam shown below (E=200GPa, I=180x106 mm4, 80mmx300mm), do the following: a. Draw the shear force and bending moment diagrams b. Find the magnitude and location of the maximum tensile bending stress c. Using superposition, find the elastic curve and then the deflection of the beam at B, C, and D 8kN 4kN A B 4m 3m 3m
3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam shown in the following figure. Also determine the reaction forces and moments. Each element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105 mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for each element, assembly of k matrices to get global stiffness matrix (K) and application of boundary conditions. Then solve the reduced K matrix to get displacements and reactions 3000 N 150 mm 75 mm 125 mm
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 in (N/mm^2) Answer and unit for part 3 iv) The bending stress at the point 0.6 cm from the neutral axis is in(N/mm^2) Answer and unit for part 4
For the beam illustrated in the figure, find the locations and magnitudes of the maximum tensile bending stress due to M and the maximum shear stress due to V. Parameters are a = 290 mm, b= 135 mm, c = 20 mm, h = 39 mm, and F = 4300 N. a mm FN bmm C mm hmm The moment of inertia is 6.673x105 mm4 The maximum tensile bending stress due to Mis The maximum shear stress due to Vis 0 MPa. * MPa.