Calculating the integration constants

[Waffle24]

Homework Statement

Is it even possible to solve C1 and C2?

I feel like I'm missing some information. (possible the teacher made a mistake)

Normally, a shear force or a diagram is given, but in this case, it is not known or given.

Could anyone guide me?

Relevant Equations

N/A

 

[erobz]

Homework Statement: Is it even possible to solve C1 and C2?

I feel like I'm missing some information. (possible the teacher made a mistake)

Normally, a shear force or a diagram is given, but in this case, it is not known or given.

Could anyone guide me?
Relevant Equations: N/A

View attachment 358613

I'm not sure, but lets see if you can satisfy all the conditions. $w(x)$ is given as a deflection. It's usually a distributed load in the texts I've seen but...whatever.

Can you show your work?

 

[Waffle24]

I'm not sure, but lets see if you can satisfy all the conditions. $w(x)$ is given as a deflection. It's usually a distributed load in the texts I've seen but...whatever.

Can you show your work?

I'm not quite sure what you're referring with "if I can satisfy all the conditions". Anyway, the steps to get to the deflection equation is also a little bit confusing to me, because there is a '-' sign before 1/EI.

I've tried getting the C2 by substituting the M(2) = -5 in the M equation. Is this the right approach?

 

[Mark44]

I don't see how this is connected to integration, unless somehow the integration has already been done to arrive at the equation for w(x).
From the first boundary condition, w(0) = 0, it's simple to find $c_4$.
From the other boundary condition, w(2) = 0, you get $\frac{-1}{EI}(4/3 \cdot c_1 + 2 \cdot c_2 + 2 \cdot c_3) = 0$

Your screen shot doesn't provide any information about $\phi$ or M or V, so perhaps they enter into the calculations for $c_1, c_2,$ and $c_3$.

In your work, what is $\epsilon_1$? The equation shown in the screen shows E and I, but not $\epsilon$. Also, your work shows $\theta$. Did you mean $\phi$?

 

[erobz]

I'm not quite sure what you're referring with "if I can satisfy all the conditions". Anyway, the steps to get to the deflection equation is also a little bit confusing to me, because there is a '-' sign before 1/EI.

I've tried getting the C2 by substituting the M(2) = -5 in the M equation. Is this the right approach?


View attachment 358625

Yeah, that's the right idea. You have 4 conditions and 4 constants to determine.

But instead of working "up" from the shear $V(x)$, work "down" from the equation for deflection given $w(x)$. Derive everything from the equation given (which has a negative sign out front as well as the constant $EI$).

we have $w(x)$, derive the others from it.

$\phi(x) = EI \frac{dw}{dx}$

$M(x) = EI \frac{d^2w}{dx^2}$

 

[erobz]

I don't see how this is connected to integration, unless somehow the integration has already been done to arrive at the equation for w(x).

The integration has been done, we are supposed to derive the other relations from $w(x)$.

From the first boundary condition, w(0) = 0, it's simple to find $c_4$.
From the other boundary condition, w(2) = 0, you get $\frac{-1}{EI}(4/3 \cdot c_1 + 2 \cdot c_2 + 2 \cdot c_3) = 0$

Your screen shot doesn't provide any information about $\phi$ or M or V, so perhaps they enter into the calculations for $c_1, c_2,$ and $c_3$.

In your work, what is $\epsilon_1$? The equation shown in the screen shows E and I, but not $\epsilon$. Also, your work shows $\theta$. Did you mean $\phi$?

It's an "$EI$"

And the $\phi$ is $EI\frac{dw}{dx}$.

 

[Waffle24]

Yeah, that's the right idea. You have 4 conditions and 4 constants to determine.

But instead of working "up" from the shear $V(x)$, work "down" from the equation for deflection given $w(x)$. Derive everything from the equation given (which has a negative sign out front as well as the constant $EI$).

we have $w(x)$, derive the others from it.

$\phi(x) = EI \frac{dw}{dx}$

$M(x) = EI \frac{d^2w}{dx^2}$

Ah that explains it! Thank you!