Deflection Given: the beam cross-section shown have the following cross-sectional properties f'c = 4000 psi n = 8 Find Instantaneous Deflection.
Deflection Given: the beam cross-section shown have the following cross-sectional properties f'c = 4000 psi n = 8 Find Instantaneous Deflection.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Deflection
Given: the beam cross-section shown have the following cross-sectional properties
f'c = 4000 psi
n = 8
Find Instantaneous Deflection.
![**McCormac Problem 6.7**
The diagram shows a beam fixed at one end and subjected to different loads.
- The fixed beam has a uniform distributed load (\(w_D\)) of 1.5 kips per foot along its length.
- Two point loads (\(P_L\)) are applied at specific positions: one \(P_L = 20\) kips at 10 feet from the fixed end, and another \(P_L = 10\) kips at the other end, 20 feet from the fixed point.
On the right side:
- There is a cross-sectional view of the beam with the following details:
- 6 #9 bars
- Total height of 34 inches
- Inner height of 31.5 inches
- Top portion of 2.5 inches
- Width of 24 inches
The formula for deflection, \( \Delta \), is given by:
\[
\Delta = \frac{Pb^2}{6EI}(3l - b)
\]
Where the problem specifically mentions calculating the deflection for \(P = 20\) kips and \(b = 10\) feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5256395-d523-408e-9a7a-e2ddecbcfab3%2F5caf62e5-2132-4002-8d22-ea95b3856607%2F451nj8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**McCormac Problem 6.7**
The diagram shows a beam fixed at one end and subjected to different loads.
- The fixed beam has a uniform distributed load (\(w_D\)) of 1.5 kips per foot along its length.
- Two point loads (\(P_L\)) are applied at specific positions: one \(P_L = 20\) kips at 10 feet from the fixed end, and another \(P_L = 10\) kips at the other end, 20 feet from the fixed point.
On the right side:
- There is a cross-sectional view of the beam with the following details:
- 6 #9 bars
- Total height of 34 inches
- Inner height of 31.5 inches
- Top portion of 2.5 inches
- Width of 24 inches
The formula for deflection, \( \Delta \), is given by:
\[
\Delta = \frac{Pb^2}{6EI}(3l - b)
\]
Where the problem specifically mentions calculating the deflection for \(P = 20\) kips and \(b = 10\) feet.
Expert Solution
Step 1: Determine the given variable
Gross moment of inertia(Ig)
Critical internal moment(Mcr)
Maximum service load(Ma)
Critical moment of inertia(Icr)
Effective moment of inertia(Ic)
b=width of beam = 24 in
h=depth of beam = 34 in
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