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

Q: The magnitude of the vertical reaction

A: Given , Length L is subjected to a varying distributed load, sin 3πx/L Nm-1Where, Distance x is…

Q: 250mm P 50mm 250mm B 50mm 2 m 2 m 50mm 400 mm

Q: Part B Perform double integration of the bending moment equations. You will obtain deflections in…

A: A simple support beam with the hinge at A, roller support at B, and an overhang portion BC. On span…

Q: A uniform elastic rod of length 4L and constant cross-section, is fixed at its left end as shown in…

A: For an uniform elastic rod of constant cross section,Length : 4LAn axial force P is acting at the…

Q: A symmetrical beam of length 300 mm is loaded with a force of 414 N downwards (positive z) and has…

A: Given: Length, L = 300 mm Force, F = 414 N Modulus of Elasticity, E = 2 x 105 N/mm2 Moment of…

Q: A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figu…

A: Given a rigid horizontal rod,

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

Q: mning Goal: use the superposition principle to find the state -tress on a beam under multiple…

A: d1= 2.15 md2 = 0.5 md3= 0.95 md4=285 mmr= 150 mmP= 4.5 kNTo find:Part A: Determine the support…

Q: Consider the frame shown in the figure: If the axial and shear deformations in different members of…

Q: C Question 3-A) vertical displacement of the point (& A) to find. Write your result in mm. Question…

A: Finding reaction and accordingly the displacement are found for rigid body

Q: The cantilever beam, whose loading condition and cross-section is given in the figure, is ideal…

Q: The cantilever beam, whose loading condition and cross-section are given in the figure, is ideal…

Q: the middle of the AB AB rigid beamWhen w = 105 kN /m is

Q: The T-beam given in the figure is made of two 250 mm x 25 mm section wooden planks. Wooden planks as…

A: Dear students here i have asnwering to this problem according to bartleby guidelines Step-1 include…

Q: The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and…

A: Given data Modulus of Elasticity (E) EAB = 70 GPA = 70 × 103 N/mm2 ECD = 200 GPA = 200 × 103…

Q: ows an elastic be igidity EI and deflection v(x) d by an equation

Q: The rectangular cross-section beam in figure 3b is subjected to a maximum bending moment of 25,000…

A: given beam section:-

Q: Figure Q2(a) shows a cantilever beam that is subjected to a pure bending moment M = 3kN.m about the…

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: A truss is subjected to different force combinations as shown in the figure below. The…

A: Here we need to find deformation in both the direction i.e. in x and y directions of point C. For…

Q: B. A beam subjected to a uniformly-distributed load has a: Choices: First-degree shear curve…

A: A) Here, there is a twist in the question, it is not asked the Representation of the change in the…

Q: L AB beam. According to this; To AB rigid beamWhen a distributed load of magnitude w = 105 kN / m is…

A: Reactions of points are calculated and rigid body displacement are found

Q: 1. The structure shown below is subjected to a total uniform load w. The flexural stress in the…

A: (a) Consider the free body diagram of beam; For CDE; Re×L+w(1)22+w(1)22=0Re=0 Calculate shear at…

Q: The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and…

Q: The cantilever beam, whose loading condition and cross-section are given in the figure, is ideal…

Q: calculate the centroid and moment of inertia

A: The given cross-section is divided into 2 rectangles and 3 triangles as shown below The areas…

Q: A symmetrical beam of length 300 mm is loaded with a force of 414 N downwards (positive z) and has…

A: Given: Length, L = 300 mm Force, F = 414 N Modulus of Elasticity, E = 2 x 105 N/mm2 Moment of…

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: Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has…

A: Derive a formula for the strain energy U of the cantilever bar shown in the figure.

Q: saw-tooth loading is applied as shown in the figure. The flexural tiffness (EI) of the beam is 1×10³…

A: Given- A propped cantilever beam carrying UVL loading. Required- To calculate support Reactions of a…

Q: A beam fixed at both the ends is subjected to a uniformly distributed load '' on its right half…

A: Beam: Fixed at both ends.Load: Uniformly distributed load (UDL) on the right half of the…

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: Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has…

A: Derive a formula for the strain energy U of the cantilever bar shown in the figure.

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

A simply supported beam AB is subjected to a concentrated bending moment, as shown in the figure below, the flexural stiffness of the beam section is constant EI:(a) Use the Moment-area Principle to find the maximum deflection on the beam and the angle of rotation at point A.(b) Same as the question above, try the Elastic Load Method to answer.
2. P Derive an equation that describes the vertical deflection of the beam, y(x), and also B calculate the maximum deflection of the beam. M = 0.5PL %3D
The cantilever beam, whose loading condition and cross-section are given in the figure, is ideal elasto-plastic and yield stressσA = 240 MPa.a) Draw the T and M diagrams.b) The PA force that will start flowing in the beam,c) Calculate the PG force that will cause collapse in the beam.
Question 2 In the below structure, the truss members stiffness matrix has been used for truss members and the beam stiffness matrix has been used for the rest. a) How many unknown displacements are in the displacement vector? b) How many displacements are in the displacement vector altogether? * J A
The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm^2; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm^2. For the 30 kN force shown, determine the deflection of B and E, respectively. 0.4 m 0.3 m B A 0.2 m OC -0.4 m 30 kN E
Help me to out
a) Find the deformation volume of the unit cube b) Find the deformation of area of OABC X3,x3 X1,x1 Function of motion: In[1]= x1 = (1+t) * X1 x2 = -X3 x3 = X2 B A X2,x2
A propped cantilever beam is loaded by a bending moment of the magnitude M3 at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight / that are constant along the length of the beam L. The beam material's Young's modulus is Q. Figure Q1 Assuming the positive deflections and positive vertical reaction forces are upward, calculate o the value of the reaction forces at points A and B o the absolute value of the reaction bending moment at point A
A simply supported beam of span L is subjected to a temperature gradient which increases linearly from zero at the left-hand support to fo at the right-hand support. If the temperature gradient also varies linearly through the depth, h, of the beam and is zero on its undersurface, calculate the deflection of the beam at its mid-span point. The coefficient of linear expansion of the material of the beam is a. Ans. -ato1?148h.
Q.3. a- A rectangular plate simply supported along its edges and subjected to a uniform of intensity po: 1. Determine the value of the maximum deflection if b 2a. Compare the result with W= 0.01013 2. Determine the expression for shear force Qx for the plate. load
The cantilever beam, whose loading condition and cross-section are given in the figure, is ideal elasto-plastic andIts stress is σA = 240 MPa.a) Draw the T and M diagrams.b) The PA force that will start flowing in the beam,c) Calculate the PG force that will cause collapse in the beam.
Non uniform beam Flexural Rigidity that is _y(x) = fixed support on left Simple support 07 right P 2.26 meters long 141702000 6441 + 100x Find the deflection of the bean if it is uniform distributed load of under a 92 N/m TPE Nm²