The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam (Fig. P24.16) is given as EI dx? dy wLx_ wx 2 2 where E = the modulus of elasticity and I = the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using (a) the finite-differ- %3D %3D %3D ence approach (Ax = 0.6 m) and (b) the shooting method. The following parameter values apply: E = 200 GPa, I = 30,000 cm“, w = numerical results to the analytical solution: %3D 15 kN/m, and L = 3 m. Compare your wLx³ y = 12 EI wx4 24 EI wL'x 24 EI

The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam (Fig. P24.16) is given as EI dx? dy wLx_ wx 2 2 where E = the modulus of elasticity and I = the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using (a) the finite-differ- %3D %3D %3D ence approach (Ax = 0.6 m) and (b) the shooting method. The following parameter values apply: E = 200 GPa, I = 30,000 cm“, w = numerical results to the analytical solution: %3D 15 kN/m, and L = 3 m. Compare your wLx³ y = 12 EI wx4 24 EI wL'x 24 EI

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: A circular shaft AB of radius Ras shown in the figure below is subjected to torsion T at the free…

Q: - A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform…

Q: Question #3 For the beam shown in Figure 3, a) Determine the maximum compressive bending stress in…

Q: Using the "Effects Overlay" of the original beam, using isostatic sub-beams and simulating them…

A: Given that :- Modulus of Elasticity (E) = 200 GPa = 200,000 MPaWeight of the beam (W) = 2.5 Applied…

Q: Suppose we have a uniform beam that is 3.73 metres long has a flexural rigidity of 34301 Nm². N Find…

Q: If the deflection at the free end of a uniformly loaded cantilever beam is 15 mm and the slope of…

Q: b) In Figure Q1, an axial load P is applied at point D that is 5 mm from the geometric axis of the…

A: Iy = π/64(1204 - 1124) = 2.455 x 106 mm4 L = 2.8 m = 2800 mm

Q: simply supported beam 10 m long carries a uniform load of 24 kN/m. Using E = 200 GPa, I = 240 x 10 6…

A: 62mm

Q: Calculate the maximum deflection of a uniformly loaded simple beam having a span length L = 2 m, the…

A: Given data:

Q: Determine the maximum deflection for the beam shown in figure below by the conjugate-beam method.

Q: Consider an elastic straight beam of length L= 10t m, with square cross-section of side a = 5 mm,…

A: To find the maximum bending stress-

Q: Displacement components at a point in a solid u(x, y, t) = 2y²x + 2t v(x, y, t) = 8y³x³ + 5t? w(x,…

Q: 6. A cantilever beam subjected to uniform variable load, if the beam is made of I Beam having a…

A: In cantilever beam, maximum deflection will occur at free end (point B). By using virtual work…

Q: Problem (8.2): Calculate the maximum deflection 8max of a uniformly loaded simple beam as shown in…

Q: A W = 500 N R = 150 mm 250 mm Figure Q3

A: from the figure,using equilibrium conditionmoment at the supportMA=w150 N-mmtotal strain…

Q: 7. The uniform beam shown carries a triangular load from zero at A to a maximum "w" at C. It is…

Q: The 16 x 22 x 25-mm rubber blocks shown are used in a double U shear mount to isolate the vibration…

Q: The cantilever beam is a carbon steel bar of length 10 in and diameter 1 in. And it is loaded by a…

Q: 4. The supported beam in Figure 4 is being tested for a bridge design. Knowing that the beam AB…

A: Simply Supported Beam: A beam that consists of two supports at each end of the beam and which is…

Q: The plastic block shown is bonded to a fixed base and to a horizontal rigid plate to which a force P…

A: Therefore, the deflection of the plate is 0.0709 inches.

Q: Compute/Derived the following: a. wall shear b. wall moment c. Reaction

A: As per bartleby guidelines, only 1st 3 parts among multiple parts questions need to be solved.…

Q: A simply supported beam AB is subjected to a concentrated bending moment, as shown in the figure…

Q: For the plane frame with an overhang as shown in the figure, assuming negligible axial deformation,…

Q: A propped cantilever beam is loaded by a bending moment of the magnitude M3 at the point B as shown…

Q: PROBLEM 03: Determine the shear modulus of the body shown in the figure if the top and bottom…

A: Given data Width (B) = 150mm Length (L) = 400 mm Height (H) = 200 mm Displacement (∆h) = 2.5mm…

Q: A simply supported beam of span L is subjected to a temperature gradient which increases linearly…

A: Data Given: Length of the beam = L Temperature gradient increases linearly from zero at the…

Q: A tapered circular varying from 20 mm to 10 mm is

Concept explainers

British Gravitational Bg System Of Units

Measuring is the comparison of a particular physical quantity with its reference value. A unit is a fixed physical quantity. The length is a physical quantity. A physical quantity is the product of a unit and the numerical value we need to compare with. 

Question

The basic differential equation of the elastic curve for
a simply supported, uniformly loaded beam (Fig. P24.16) is
given as
d'y
EI
wLx_ wx
2
dx?
2
where E = the modulus of elasticity and I = the moment of
inertia. The boundary conditions are y(0) = y(L) = 0. Solve
for the deflection of the beam using (a) the finite-differ-
%3D
%3D
ence approach (Ax = 0.6 m) and (b) the shooting method.
The following parameter values apply: E
30,000 cm", w = 15 kN/m, and L = 3 m. Compare your
numerical results to the analytical solution:
= 200 GPa, I
%3D
wLx?
wxt
.3
wL'x
y =
12 EI
-
24 EI
24 EI

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 3 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, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Figure 4–5a shows a cantilever beam with an end load. Normally we model thisproblem by considering the left support as rigid. After testing the rigidity of thewall it was found that the translational stiffness of the wall was kt force per unitvertical deflection, and the rotational stiffness was kr moment per unit angular(radian) deflection (see Fig. 4–5b). Determine the deflection equation for the beamunder the load F.
The simply supported beam shown in Fig. P-610 carries a uniform load of intensity w symmetrically distributed over part of its length. Determine the maximum deflection ô and check your result by letting a = 0 and comparing with the answer to Problem 3. Wo 2b a R1 R2
Problem Solving. 1. The maximum bending moment for a 4 meters freely supported beam has been found to be 15 kN-m. If the allowable bending stress is 9 MPa, design the beam with respect to bending. Use E = 12,000 MPa a. a. Investigate if the computed dimensions will not exceed the allowable shearing stress of 0.90 MPa. b. Investigate if the computed dimensions will not exceed the allowable deflection of L/360. w (kN/m) 4m
2. A uniform, simply supported beam, is loaded as shown in Figure 2. Using singularity functions, determine an expression for the bending moment at any point along the beam. Hence, determine the slope of the beam at point, A, and the deflection of the beam at point, B. The bending stiffness of the beam is 3200 Nm². 320 N 200 N/m 1.2m 0.6m Figure 2 2 A 0.4m X * B D
Problem 1) A simply supported beam is loaded as shown in Figure 1-A. Use E = 40 MPa and I = 5 x 10⁶ mm⁴. c) Determine the deflection at midspan of the beam
A cantilever of length I, and flexural rigidity El, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown. 1,EI mm The transverse deflection under the load is
For the beam shown in Figure 3, a) Determine the maximum compressive bending stress in the beam. State exactly what location on the beam and where on the cross-section this maximum compressive bending stress occurs. b) Use the double integration method to calculate the deflection at point A, located at the end of the cantilever Given: E = 200 GPa A 5 kN/m 2 m BA 3 m 44 2 kN.m 75 mm 150 mm
The uniform forces U and P are applied to a plate with dimensions of 500mm x 400mm and a thickness of 10 mm as illustrated. Consider the linear elastic behavior, 200GPa Young's modulus, and 78GPa shear modulus. The plate is subjected to a uniform force U with an undetermined magnitude and direction and a uniform tensile force P=50KN. X 500 mm 400 mm A. What is force U, in kN, if deformation along y is zero? Is it a compressive or tensile force? B. What is the x-axis deformation, in mm? Is the dimension growing or shrinking?
SHOW COMPLETE AND CLEAN SOLUTION and DRAW ILLUSTRATION SOLVE THE PROBLEMS USING THE DOUBLE INTEGRATION METHOD
NOTE: PLEASE SOLVE THIS QUESTION WİTH FINITE ELEMENT METHOD...solve 20 mins asap hand written
Calculate the maximum deflection of a uniformly loaded simple beam having a span length L=2m, the intensity of uniform load q=2KN/m and the maximum bending stress is 60mpa.The cross section of beam is square,and the material is aluminum having modulus of elasticity E=70Gpa
Please solve