Chapter 2, Problem 26
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![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (2)](https://i0.wp.com/www.numerade.com/static/ace-animation-pdp/video_6.d86d01139302.gif "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (2)")
Question
Answered step-by-step
Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection $y$ (m) can be computed with
$$
y=\frac{w_0}{120 E I L}\left(-x^5+2 L^2 x^3-L^4 x\right)
$$
where $E=$ the modulus of elasticity and $I=$ the moment of inertia $\left(\mathrm{m}^4\right)$. Employ this equation and calculus to generate MATLAB plots of the following quantities
$$
\begin{aligned}
& \text { (b) }>>=4: 2: 12 ;
\end{aligned}
$$
$$
\begin{aligned}
& \gg \operatorname{sum}(q) * r(2,3)
\end{aligned}
$$
versus distance along the beam:
(a) displacement $(y)$,
(b) slope $[\theta(x)=d y / d x]$,
(c) moment $\left[M(x)=E I d^2 y / d x^2\right]$,
(d) shear $\left[V(x)=E I d^3 y / d x^3\right]$, and
(e) loading $\left[w(x)=-\right.$ EId $\left.^4 y / d x^4\right]$.
Use the following parameters for your computation: $L=600 \mathrm{~cm}, E=50,000$ $\mathrm{kN} / \mathrm{cm}^2, I=30,000 \mathrm{~cm}^4, w_0=2.5 \mathrm{kN} / \mathrm{cm}$, and $\Delta x=10 \mathrm{~cm}$. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots.
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Video Answer
![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (3)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy9hNmUyMzYwNTc1MTQ0Yjc0YTllZDY3ZWRlODAyOWY3Zi5KUEciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0= "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (3)")
![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (4)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy8yOTRkN2Y3YWM5ZWM0YmY3OGQ5NGQwOTAyMjVmZTg0Zi5KUEciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0= "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (4)")
![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (5)](https://i0.wp.com/d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy8yNTVjYmQzMWMxZTA0MDk1OTRkN2Q1NzYxMTliMTZhMy5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0= "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (5)")
![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (6)](https://i0.wp.com/www.numerade.com/static/logos/logo-full-royal-on-white.ac63bc8717eb.svg "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (6)"){kind=logo}
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![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (7)](https://i0.wp.com/www.numerade.com/static/icons/close-x.0ceebab0a1bd.svg "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (7)"){kind=icon}
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Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection $y$ (m) can be computed with$$y=\frac{w_0}{120 E I L}\left(-x^5+2 L^2 x^3-L^4 x\right)$$where $E=$ the modulus of elasticity and $I=$ the moment of inertia $\left(\mathrm{m}^4\right)$. Employ this equation and calculus to generate MATLAB plots of the following quantities$$\begin{aligned}& \text { (b) }>>=4: 2: 12 ;\end{aligned}$$$$\begin{aligned}& \gg \operatorname{sum}(q) * r(2,3)\end{aligned}$$versus distance along the beam:(a) displacement $(y)$,(b) slope $[\theta(x)=d y / d x]$,(c) moment $\left[M(x)=E I d^2 y / d x^2\right]$,(d) shear $\left[V(x)=E I d^3 y / d x^3\right]$, and(e) loading $\left[w(x)=-\right.$ EId $\left.^4 y / d x^4\right]$.Use the following parameters for your computation: $L=600 \mathrm{~cm}, E=50,000$ $\mathrm{kN} / \mathrm{cm}^2, I=30,000 \mathrm{~cm}^4, w_0=2.5 \mathrm{kN} / \mathrm{cm}$, and $\Delta x=10 \mathrm{~cm}$. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots.
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![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (8)](https://i0.wp.com/www.numerade.com/static/loading.b2df72ce9ed3.gif "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (8)")
![Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (9)](https://i0.wp.com/s3-us-west-1.amazonaws.com/com.numerade/books/fab36afb-a879-4882-b42d-c91b75b37a82.jpg "Figure P2.26a shows a uniform beam subject to a linearly increasing distributed load. As depicted in Fig. P2.26b, deflection y (m) can be computed with y=(w0)/(120 E I L)(-x^5+2 L^2 x^3-L^4 x) where E= the modulus of elasticity and I= the moment of inertia (m^4). Employ this equation and calculus to generate MATLAB plots of the following quantities (b) >>=4: 2: 12 ; ≫sum(q) * r(2,3) versus distance along the beam: (a) displacement (y), (b) slope [θ(x)=d y / d x], (c) moment [M(x)=E I d^2 y / d x^2], (d) shear [V(x)=E I d^3 y / d x^3], and (e) loading [w(x)=-. EId .^4 y / d x^4]. Use the following parameters for your computation: L=600 cm, E=50,000 kN / cm^2, I=30,000 cm^4, w0=2.5 kN / cm, and Δx=10 cm. Employ the subplot function to display all the plots vertically on the same page in the order (a) to (e). Include labels and use consistent MKS units when developing the plots. | Numerade (9)")
Applied Numerical Methods with MATLAB for Engineers and Scientists
Chapter 2
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Sections
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28
