Answered: Determine the displacement of point B…

Determine the displacement of point B of the steel beam shown below, using Castigliano's Theorem. Take E = 200GPA, I = 500x106 mm4

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The beam is subjected to the load shown. The beam is made of material having an E = 200 GPa and I =…

Q: A built-up beam is constructed by welding two channels separated by a distance b = 1.25 in to two (5…

Q: Determine the horizontal displacement of point D in the system shown in the figure using…

A: The partial derivative of the total strain energy of a structure with respect to a specific force…

Q: A cantilevered beam of length L = 5 m is fixed at A. It has a moment of M = 35.0 kN⋅m applied at B…

Q: If the allowable bending stress is 0 = 165 MPa, find the magnitude of the maximum internal bending…

Q: The cross-sectional area of a wide-flange I-beam has the dimensions shown. Obtain a close…

A: Let us divide the given shape into three rectangles with the dimensions highlighted in below figure:

Q: A plastic beam has a cross section with dimensions of a = 4.7 in., b = 16.5 in., d = 9.4 in., and t…

Q: Diameter A da=140mm and diameter B db=140mm. What is the vertical displacement that occurs in the…

A: Given, dA=140 mmdB=140 mm Length of the beam, L=3 m

Q: The beam shown has an second moment of area of 9,500,000 mm4 and a controlling section modulus of…

Q: mm. It carries a uniformly distributed load of 550 kN/m for entire span. Determine (a) Maximum…

Q: determine the diagram of the shear forces and bending moments in the beam shown below. Data P =…

Q: 5. The rigid beam rests on two short posts AC and 80 as shown Post AC is made from steel with E-200…

Q: If the beam shown is supported by the fixed wall at B and the rod AC. if the rod has a cross…

A: The force which acts perpendicular to the cross-section of a specimen is termed as normal force and…

Q: A beam subjected to pure bending moment M = 50j + 100k kN-m has a channel section as shown below on…

Q: The cantilevered beam in Fig. a has a rectangular cross section and is subjected to a load P at its…

A: The moment of the beam about the section is, By the method of Macaulay’s double integration method.…

Q: AT-beam is subjected to bending. If a = 382 mm, b = 207 mm, and c = 12 mm, what is %3D the area…

A: Given data: - The side a is a = 382 mm. The side b is b = 207 mm. The side c is c = 12 mm. The…

Q: A simply supported beam is shown. The maximum bending moment is at B. Use the method of sections to…

A: Given Data: The allowable bending stress for the beam is, σb=24 ksi=24 ksi×144000 lb/ft2ksi=3456000…

Q: mm. Determine the second moment of area of the cross section

A: To find Second moment of inertia of cross section

Q: A uniform, rectangular beam with length 1.2 m and width 0.40 m is attached to a point (0.20, 0.20) m…

A: Given:The length of the rectangular beam is .The width of the rectangular beam is .The angle is .The…

Q: K d 2d L µ: shear modulus T a) Determine the reaction moments at both ends. b) Determine the angle…

A: Given: Total torque at the joint of the spring and tube:=T Let torque required for twisting the…

Q: 2) A rigid beam AB rests on the two short posts as shown. Post AC is made from steel and has a…

Q: If M = 9.0 kip-ft, find the magnitude of the bending stress at a point 2.72 in. above the bottom…

Q: 5. The rigid beam rests on two short posts AC and BD as shown. Post AC is made from steel with E =…

A: GivenEs=200GPaEal=70GPadst=25mmdal=40mm

Q: find the vertical displacement at Point B of the built-in entry in the figure by Castigliano's…

A: For the given beam E = 200 GPa I = 30*106 mm4 To determine vertical displacement at point B by…

Q: A beam cross section is shown. The dimensions are d - 10.2 in. and t= 0.46 in. The centroid of the…

Q: A composite beam is made of two brass [E = 98 GPa] plates bonded to an aluminum [E = 64 GPa] bar, as…

A: To find: The maximum bending stress in the aluminium bar. Given: The modulus of elasticity of brass…

Q: If the internal moment function for the shown beam is 20Lx M = What is the value of W ?

Q: Determine the vertical displacement, in mm, of point C of the beam shown in the figure below. The…

Q: If the following structural beam has a rectangular cross-section and is subjected to the loadings as…

Q: For the beam shown, a. Determine the maximum moment b. Determine the section modulus of its…

Q: 40 mm The beam shown in the figure is 15 mm made of material with a tensile d = 30 mm strength of 24…

Q: The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment…

Q: bie tee croSs section Is used for the beam snown beloW. Assume the following lengths and loads! a =…

Q: Find the maximum shear stress. Assume that c1 = 8.273 in, c2 = 3.723 in, and I =

A: From the given shear force diagram of the loaded overhang beam, maximum shear force occurs at roller…

Q: If the allowable bending stress is a = 247 MPa, find the magnitude of the maximum internal bending…

Q: For the beam cross-section shown, (a) find the maximum bending stresses of the beam if the bending…

Q: Consider the joint steel bars below. If 50,000 lb force is applied at point A, determine the…

A: Given DataP=50000 lbθ=50°E=29×106psiA=2.5 in2

Q: A plastic beam has a cross section with dimensions of a = 2.3 in., b = 8.1 in., d = 4.6 in., and t =…

Q: A built-up beam is constructed by welding two channels separated by a distance b = 1.25 in to two (5…

Q: The beam shown has an second moment of area of 9,500,000 mm and a controlling section modulus of…

A: Maximum flexural stress due to bending is given by the following realation, Sigma,b=Mmax*Ymax/INA…

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

MTN
O ".l| 20.ll 98 20:31
Vodafone GH|Stay Safe
DCV 203 - Lectures 7-9.pdf
aM \ dx
M
ƏM' ) EI
27
Example 4
Determine the displacement of point B of the steel
beam shown below, using Castigliano's Theorem.
Take E = 200GPA, I = 500x106 mm4
1 kN
12 kN/m
B
-10 m
10 m
28
Solution
Sum of moment about A
ΣΜΑ0
12
De
...

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

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 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-sectional area of a wide-flange I-beam has the dimensions shown. Obtain a close approximation to the handbook value of Ix = 654 in.4 by treating the section as being composed of three rectangles. 0.380" 7.073" ·x 16.25" Answer: I = i k 10.628" in.4
* For the cross section shown in the figure. Given the value of Y= 172 mm. Find the :value of total moment of Inertia 250 mm A1 Neutral Axis (N.A) A2 Ý Reference Line 50 mm 40 mm 220 mm 145.2 x 10^6 mm^4 119.7 x 10^6 mm^4 169.4 x 10^6 mm^4 129.5 x 10^6 mm^4 O 119.7 x 10^6 mm^3 O 119.7 x 10^6 mm^2 119.7 x 10^6 mm 134.2 x 10^6 mm^4 O 47.57 x 10^6 mm^4 O 193.1 x 10^6 mm^4 86.65 x 10^6 mm^4
Need correct solution. If C is the mid-point of PQ; What is the magnitude of bending moment at fixed end O?
481 A Find the shear force and bending moment at points C and D. 300 lb/ft Answer: Vc = -2.11 kip Mc = -3.72 kip ft VD = 900 lbf Mp = -7.35 kip ft D 12 ft 15 ft C weights Lea... B D 3 ft 6 ft I Centroids -... 6000 lb-ft G4.4.1 Weight...
A simply supported beam of dimension 11.5 m x 45 mm x 75 mm. It carries a uniformly distributed load of 450 kN/m for entire span. Determine (a) Maximum stress due to bending and (b) Young's modulus of the material used for the beam, if it deflects 125 mm maximum at the mid of the span. Also find the maximum slope in the beam. Moment of inertia of the cross section of the beam in m4 = Young's modulus of the beam material in MPa is = Maximum bending stress due to bending in MPa is = The slope at the supports of beam in radians is =
Answer the following:
Determine the displacement of point B of the steel beam shown in the figure
41. The wide-flange I beam as shown is 20 ft. long. It is fixed at one end and free at the other. A twisting moment of 30,000 lb-in. is applied at the free end. If E=30×10° psi and G =12x10° psi, compute the maximum normal and shearing stresses due to bending and the maximum shearing stress due to twist. What is the angle of twist of the beam at the free end? 10.5" 1.368" 0.845" 10" prob 41
A beam is subjected to equal bending moments of M, = 3000 N-m. The cross-sectional dimensions areb = 190 mm, c = 30 mm, d = 73 mm, and t = 7 mm. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. M, M2 H d (typ) K b Answer: (a) y= mm 1z = i mm4 S= i mm3 (b) ƠH = MPа ( c) σκ-1 MPа (d) Omax= MPa
A beam is subjected to equal 21.7 kip-ft bending moments. Assume t₁ =t₂ = tw- 3 in., d = 15 in., b₁ = 6 in., and b₂ =8 in. The cross- sectional dimensions of the beam are illustrated. Determine: (a) the distance y to the centroid (measured from the bottom), the moment of inertial₂ about the z axis, and the controlling section modulus S₂ about the z axis. (b) the bending stress at point H (positive if tension, negative if compression). (c) the bending stress ok at point K(positive if tension, negative if compression). (d) the maximum bending stress max produced in the cross section (positive if tension, negative if compression). M Answers: (a) y = (b) 6μ = 6.978 (c) OK (c) omax = = i M in., I₂ = X i psi. psi. psi. 41 1₂ 2886.59 b₁ b₂ Cross section H K in.4, S₂ = i in.³.
A beam of circular cross-section has a length of 5m and is simply supported at its ends. It is required to carry a total load of 57 kN uniformly distributed over the whole length. If the maximum bending stress is not to exceed 13 MPa and the maximum deflection is limited to 4 cm, the diameter of shaft in mm is given by : (take E= 18 GPa.)
Q4: 125 mm 25 mm 25 mm 12 kN 8 kN/m 75 mm B 75 mm 4 m 2 m a) If d = 420mm, determine the absolute maximum bending stress in the beam.