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Problem: Direct Integration - Deflection Curve Statement: For the beam and loading shown, determine, as a function of $x$, the equations of the deflec- tion curve, $y(x)$, and its slope, $\theta(x)$. Use the direct integration method. Your work must show two functions with all constants solved for: y(x), $\theta(x)$ To start the integration process, you will need to develop the function: $\omega(x)$ What is the deflection at point C? Use our sign convention. Plot the deflected curve and the slope. Note that this a continuation of homework problem 15 so the determination of $\omega(x)$, $V(x)$, and $M(x)$ using integration is shown in the solutions. $\omega_A$ A C $x$ $L_C$ L $\omega_B$ B Find: The functions for the deflection and the slope in the beam. Quiz response is $y(L_C)$, in units of inches. Procedure: 1. Determine the equation $\omega(x)$ using the two known points for the distributed load. 2. Integrate $\omega(x)$ four times to get $V(x)$, $M(x)$, $\theta(x)$, and $y(x)$ with integration constants $C_1$, $C_2$, $C_3$, $C_4$. 3. Determine and apply the boundary conditions to solve for the constants of integration. 4. Write the equations $\theta(x)$ and $y(x)$. 5. Calculate the value $y(L_C)$ and plot the functions in Excel (or another plotting software). Solution: The beam is made of a W8x35 A992 steel beam. $E = 29000$ ksi, $I = 127$ in$^4$

          Problem: Direct Integration - Deflection Curve
Statement:
For the beam and loading shown, determine, as a function of $x$, the equations of the deflec-
tion curve, $y(x)$, and its slope, $\theta(x)$. Use the direct integration method. Your work
must show two functions with all constants solved for:
y(x), $\theta(x)$
To start the integration process, you will need to develop the function:
$\omega(x)$
What is the deflection at point C? Use our sign convention. Plot the deflected curve and
the slope.
Note that this a continuation of homework problem 15 so the determination of $\omega(x)$, $V(x)$,
and $M(x)$ using integration is shown in the solutions.
$\omega_A$
A
C
$x$
$L_C$
L
$\omega_B$
B
Find: The functions for the deflection and the slope in the beam. Quiz response is $y(L_C)$, in units
of inches.
Procedure:
1. Determine the equation $\omega(x)$ using the two known points for the distributed load.
2. Integrate $\omega(x)$ four times to get $V(x)$, $M(x)$, $\theta(x)$, and $y(x)$ with integration constants
$C_1$, $C_2$, $C_3$, $C_4$.
3. Determine and apply the boundary conditions to solve for the constants of integration.
4. Write the equations $\theta(x)$ and $y(x)$.
5. Calculate the value $y(L_C)$ and plot the functions in Excel (or another plotting software).
Solution:
The beam is made of a W8x35 A992 steel beam.
$E = 29000$ ksi, $I = 127$ in$^4$

Problem: Direct Integration - Deflection Curve
Statement:
For the beam and loading shown, determine, as a function of x, the equations of the deflec-
tion curve, y(x), and its slope, θ(x). Use the direct integration method. Your work
must show two functions with all constants solved for:
y(x), θ(x)
To start the integration process, you will need to develop the function:
ω(x)
What is the deflection at point C? Use our sign convention. Plot the deflected curve and
the slope.
Note that this a continuation of homework problem 15 so the determination of ω(x), V(x),
and M(x) using integration is shown in the solutions.

A
C
x
LC
L

B
Find: The functions for the deflection and the slope in the beam. Quiz response is y(LC), in units
of inches.
Procedure:
1. Determine the equation ω(x) using the two known points for the distributed load.
2. Integrate ω(x) four times to get V(x), M(x), θ(x), and y(x) with integration constants
C1, C2, C3, C4.
3. Determine and apply the boundary conditions to solve for the constants of integration.
4. Write the equations θ(x) and y(x).
5. Calculate the value y(LC) and plot the functions in Excel (or another plotting software).
Solution:
The beam is made of a W8x35 A992 steel beam.
E = 29000 ksi, I = 127 in^4

Added by Kendra L.

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