For the beam in Figure 1 1. Derive the differential equations describing the buckled shape for spans AB and BC, and state their general solutions in terms only of the variables α = √P/EI, x, L, where x is measured from point B, as defined in Figure 1. Assume the flexural rigidity is EI, and is the same for both spans of the beam. Write the general solutions in its simplest form in the space provided below. 2. State boundary conditions for relevant slopes and deflections that will be sufficient to determine the buckling load, and use these and results of step 1 to derive a single simplified equations for the bulkling load in terms only of the variable ô aL. Write the boundary conditions and expression for = op in the space provided below in simplified form. 3. Solve the equation for Ø, hence determine the buckling load P in terms of only the variable EI and L. Write the expression for the buckling load in the space provided below. A Ат L ΕΙ (x=-L) P 4/2 EI (x = 1/2) Х Figure 1: (NOTE: In the left span (AB), −L ≤x≤ 0, distance from A = x+L, and distance from B = −x. In the right span (BC), 0 ≤x≤L/2, distance from B = x, and distance from C = L/2—x.) Write answers in the space provided below and submit this page, along with a cover page and all workings attached. Quantity General solutions for buckled shape in each span Boundary conditions sufficient to solve the problem Simplified equation from which the constant Q = αL: = P/EI × L, can be determined. Buckling load P (in terms of only variables El and L) Answer
For the beam in Figure 1 1. Derive the differential equations describing the buckled shape for spans AB and BC, and state their general solutions in terms only of the variables α = √P/EI, x, L, where x is measured from point B, as defined in Figure 1. Assume the flexural rigidity is EI, and is the same for both spans of the beam. Write the general solutions in its simplest form in the space provided below. 2. State boundary conditions for relevant slopes and deflections that will be sufficient to determine the buckling load, and use these and results of step 1 to derive a single simplified equations for the bulkling load in terms only of the variable ô aL. Write the boundary conditions and expression for = op in the space provided below in simplified form. 3. Solve the equation for Ø, hence determine the buckling load P in terms of only the variable EI and L. Write the expression for the buckling load in the space provided below. A Ат L ΕΙ (x=-L) P 4/2 EI (x = 1/2) Х Figure 1: (NOTE: In the left span (AB), −L ≤x≤ 0, distance from A = x+L, and distance from B = −x. In the right span (BC), 0 ≤x≤L/2, distance from B = x, and distance from C = L/2—x.) Write answers in the space provided below and submit this page, along with a cover page and all workings attached. Quantity General solutions for buckled shape in each span Boundary conditions sufficient to solve the problem Simplified equation from which the constant Q = αL: = P/EI × L, can be determined. Buckling load P (in terms of only variables El and L) Answer
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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--- Please answer the attached question ---
Transcribed Image Text:For the beam in Figure 1
1. Derive the differential equations describing the buckled shape for spans AB and BC, and state their
general solutions in terms only of the variables α = √P/EI, x, L, where x is measured from point B,
as defined in Figure 1. Assume the flexural rigidity is EI, and is the same for both spans of the beam.
Write the general solutions in its simplest form in the space provided below.
2. State boundary conditions for relevant slopes and deflections that will be sufficient to determine the
buckling load, and use these and results of step 1 to derive a single simplified equations for the
bulkling load in terms only of the variable ô aL. Write the boundary conditions and expression for
=
op in the space provided below in simplified form.
3. Solve the equation for Ø, hence determine the buckling load P in terms of only the variable EI and L.
Write the expression for the buckling load in the space provided below.
A
Ат
L
ΕΙ
(x=-L)
P
4/2
EI
(x = 1/2)
Х
Figure 1: (NOTE: In the left span (AB), −L ≤x≤ 0, distance from A = x+L, and distance from B = −x.
In the right span (BC), 0 ≤x≤L/2, distance from B = x, and distance from C = L/2—x.)
Write answers in the space provided below and submit this page, along with a cover page and all
workings attached.
Quantity
General solutions for buckled
shape in each span
Boundary conditions sufficient to
solve the problem
Simplified equation from which
the constant Q = αL: =
P/EI × L, can be determined.
Buckling load P (in terms of only
variables El and L)
Answer
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