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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ Find the slenderness parameter, lambda c. [pause] In this problem, --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/1/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ Find the slenderness parameter, lambda c. [pause] In this problem, --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ an 12 foot long I beam is subjected to a compression load, P. Note that the beam is --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/2/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ an 12 foot long I beam is subjected to a compression load, P. Note that the beam is --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ supported half way along it’s length, in one direction. A cross section of the beam --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/3/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ supported half way along it’s length, in one direction. A cross section of the beam --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ is provided, and we notice the end connections are --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/4/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ is provided, and we notice the end connections are --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ fixed. The modulus of elasticity and yield stress --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/5/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ fixed. The modulus of elasticity and yield stress --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ of the steel are also given. [pause] Keep in mind, there is only 1 beam in this problem, --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/6/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ of the steel are also given. [pause] Keep in mind, there is only 1 beam in this problem, --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2
section A-A’ viewed from 2 different directions. [pause] The slenderness parameter, --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
![Find: λc P P 1[in] fixed y 8 [in] A A’ 14[in] x 1[in] L z z fixed L/2](http://slideplayer.com./slide/15497610/93/images/7/Find%3A+%CE%BBc+P+P+1%5Bin%5D+fixed+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z+fixed+L%2F2.jpg "section A-A’ viewed from 2 different directions. [pause] The slenderness parameter, --- P. P. E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) B) C) D) L = 12[ft]")
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Find: λc λc = * P P K * L fy A A’ r * π E L z z L/2 y x P P
lambda c, equals, K L, over r times Pi, multiplied by root --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = * P P slenderness parameter K * L fy A A’ r * π E L z z
x f y over E. In this equation we already know --- P P E = 2.9 * 107 [lb/in2] fy = 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = * P P slenderness parameter K * L fy A A’ r * π E L z z
x the yield stress of the steel, fy, and the modulus of elasticity, --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = * P P slenderness parameter K * L fy A A’ r * π E L z z
x E. [pause] If we simplify our equation, lamba c, equals, --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = λc = 0.01448 * * P P slenderness parameter K * L fy A A’
z z K * L λc = * L/2 r y x times K L over r. In this equation, --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = 0.01448 * P P slenderness parameter effective A A’
length factor L z z K * L λc = * L/2 r y x K represents the effective length factor, L refers to --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = 0.01448 * P P slenderness parameter effective length A
factor L z z K * L λc = * L/2 r y x the length, and r is the radius of gyration --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = 0.01448 * P P slenderness parameter effective length A
factor L z z K * L λc = * L/2 r y x radius of gyration [pause] Since the I beam can globally buckle --- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = 0.01448 * P P slenderness parameter effective length A
factor L z z K * L λc = * L/2 r y x radius of gyration about the x or y axis, our value for K L over r will be the larger between ---- P P E = 2.9 * 107 [lb/in2] fy= 60,000 [lb/in2] A) 0.24 B) 0.39 C) 0.48 D) 0.78 L = 12[ft]
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter
L = 12[ft] A A’ L z z K * L λc = * L/2 r y x radius of gyration K L over r in the x direction and K L over r in the y direction. The length in the x direction, --- K * L Kx*Lx Ky*Ly =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z Lx = L= 12 [ft] L/2 y x 12[in/ft] * equals, 12 feet, or 144 inches. [pause] And the effective length factor, K x, --- Lx=144 [in] K * L Kx*Lx Ky*Ly =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z L/2 y x Lx=144 [in] equals, 0.65, because of the fixed-fixed end connections, in the x direction. [pause] The y direction --- Kx=0.65 K * L Kx*Lx Ky*Ly =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z L/2 y x Lx=144 [in] is supported at L over 2, with a roller, or pin, connection, therefore L y, equals, --- Kx=0.65 K * L Kx*Lx Ky*Ly =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z Ly = L/2 12 [in/ft] * L/2 y x Lx=144 [in] L over 2, or 72 inches. [pause] And a fixed-pin end connections have an effective length factor of --- Ly=72 [in] Kx=0.65 K * L Kx*Lx Ky*Ly =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z Ly = L/2 12 [in/ft] * L/2 y x Lx=144 [in] 0.8. [pause] After simplifying these quotients, --- Ly=72 [in] Kx=0.65 K * L Kx*Lx Ky*Ly =max Ky=0.8 r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z L/2 y x the last variable we need to solve for is ---- K * L 93.6 [in] 57.6 [in] =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z L/2 y x the radii of gyration, r x and r y. [pause] Where the radius of gyration, equals, --- K * L 93.6 [in] 57.6 [in] =max r rx , ry
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Find: λc λc = 0.01448 , =max * x-dir y-dir slenderness parameter K * L
L = 12[ft] L z z L/2 y x the square root of the area moment of inertia, divided by the area. [pause] Next we’ll return to --- Ix Iy rx= ry= A A K * L 93.6 [in] 57.6 [in] =max r rx , ry
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Find: λc , =max x-dir y-dir 1[in] y 8 [in] A A’ 14[in] x 1[in] L z z
section A-A’ 1[in] the given cross section of the I beam, A A prime, and increase it’s size, --- Ix Iy rx= ry= A A K * L 93.6 [in] 57.6 [in] =max r rx , ry
![Find: λc , =max x-dir y-dir 1[in] y 8 [in] A A’ 14[in] x 1[in] L z z](http://slideplayer.com./slide/15497610/93/images/26/Find%3A+%CE%BBc+%2C+%3Dmax+x-dir+y-dir+1%5Bin%5D+y+8+%5Bin%5D+A+A%E2%80%99+14%5Bin%5D+x+1%5Bin%5D+L+z+z.jpg "section A-A’ 1[in] the given cross section of the I beam, A A prime, and increase it’s size, --- Ix. Iy. rx= ry= A. A. K * L [in] 57.6 [in] =max. r. rx. , ry.")
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Find: λc y-dir y 1 [in] A A’ 8 [in] 14[in] x z 1 [in] x 1 [in]
[pause] We’ll divide the cross section into 3 parts, where parts 1 and 3 --- 1 [in] section A-A’ Ix Iy rx= ry= A A
![Find: λc y-dir y 1 [in] A A’ 8 [in] 14[in] x z 1 [in] x 1 [in]](http://slideplayer.com./slide/15497610/93/images/27/Find%3A+%CE%BBc+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+x+z+1+%5Bin%5D+x+1+%5Bin%5D.jpg "[pause] We’ll divide the cross section into 3 parts, where parts 1 and [in] section A-A’ Ix. Iy. rx= ry= A. A.")
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Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] x z 1 [in] x part 3
refer to the flanges, and part 2, will refer to --- 1 [in] section A-A’ Ix Iy rx= ry= A A
![Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] x z 1 [in] x part 3](http://slideplayer.com./slide/15497610/93/images/28/Find%3A+%CE%BBc+part+1+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+x+z+1+%5Bin%5D+x+part+3.jpg "refer to the flanges, and part 2, will refer to [in] section A-A’ Ix. Iy. rx= ry= A. A.")
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Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x
the web. [pause] Now we can calculate --- 1 [in] section A-A’ Ix Iy rx= ry= A A
![Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x](http://slideplayer.com./slide/15497610/93/images/29/Find%3A+%CE%BBc+part+1+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+part+2+x+z+1+%5Bin%5D+x.jpg "the web. [pause] Now we can calculate [in] section A-A’ Ix. Iy. rx= ry= A. A.")
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Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x
the cross sectional area of the beam, A, by adding --- 1 [in] section A-A’ Ix Iy rx= ry= area A A
![Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x](http://slideplayer.com./slide/15497610/93/images/30/Find%3A+%CE%BBc+part+1+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+part+2+x+z+1+%5Bin%5D+x.jpg "the cross sectional area of the beam, A, by adding [in] section A-A’ Ix. Iy. rx= ry= area. A. A.")
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Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x
the area from each of the 3 parts. If we add 8 inches squared plus --- 1 [in] A = A1+A2+A3 Ix Iy rx= ry= area A A
![Find: λc part 1 y-dir y 1 [in] A A’ 8 [in] 14[in] part 2 x z 1 [in] x](http://slideplayer.com./slide/15497610/93/images/31/Find%3A+%CE%BBc+part+1+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+part+2+x+z+1+%5Bin%5D+x.jpg "the area from each of the 3 parts. If we add 8 inches squared plus [in] A = A1+A2+A3. Ix. Iy. rx= ry= area. A. A.")
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Find: λc A1= 8 [in2] y-dir y 1 [in] A A’ 8 [in] 14[in] A2=12 [in2] x z
12 inches squared plus 8 inches squared, the total area equals, --- 1 [in] A = A1+A2+A3 Ix Iy rx= ry= area A A
![Find: λc A1= 8 [in2] y-dir y 1 [in] A A’ 8 [in] 14[in] A2=12 [in2] x z](http://slideplayer.com./slide/15497610/93/images/32/Find%3A+%CE%BBc+A1%3D+8+%5Bin2%5D+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+A2%3D12+%5Bin2%5D+x+z.jpg "12 inches squared plus 8 inches squared, the total area equals, [in] A = A1+A2+A3. Ix. Iy. rx= ry= area. A. A.")
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Find: λc A1= 8 [in2] y-dir y 1 [in] A A’ 8 [in] 14[in] A2=12 [in2] x z
28 inches squared. [pause] The area moment of inertia, --- 1 [in] A = A1+A2+A3 Ix Iy rx= ry= 28 [in2] A A
![Find: λc A1= 8 [in2] y-dir y 1 [in] A A’ 8 [in] 14[in] A2=12 [in2] x z](http://slideplayer.com./slide/15497610/93/images/33/Find%3A+%CE%BBc+A1%3D+8+%5Bin2%5D+y-dir+y+1+%5Bin%5D+A+A%E2%80%99+8+%5Bin%5D+14%5Bin%5D+A2%3D12+%5Bin2%5D+x+z.jpg "28 inches squared. [pause] The area moment of inertia, [in] A = A1+A2+A3. Ix. Iy. rx= ry= 28 [in2] A. A.")
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Find: λc part 1 y 1 [in] Ix = Σ Ic,i,x+Ai * dy,i 8 [in]
2 i n 8 [in] Iy = Σ Ic,i,y+Ai * dx,i 2 14[in] i x part 2 1 [in] part 3 I, is computed about both the x and y axis. If we write out the equation for --- area moment 1 [in] of inertia Ix Iy rx= ry= 28 [in2] A A
![Find: λc part 1 y 1 [in] Ix = Σ Ic,i,x+Ai * dy,i 8 [in]](http://slideplayer.com./slide/15497610/93/images/34/Find%3A+%CE%BBc+part+1+y+1+%5Bin%5D+Ix+%3D+%CE%A3+Ic%2Ci%2Cx%2BAi+%2A+dy%2Ci+8+%5Bin%5D.jpg "2. i. n. 8 [in] Iy = Σ Ic,i,y+Ai * dx,i [in] i. x. part 2. 1 [in] part 3. I, is computed about both the x and y axis. If we write out the equation for --- area moment. 1 [in] of inertia. Ix. Iy. rx= ry= 28 [in2] A. A.")
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Find: λc +8 [in2]*(6.5 [in])2 +1[in]*(12[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Ix = Σ Ic,i,x+Ai * dy,i 2 i Ix = 8 [in]*(1 [in])3/12 8 [in] 14[in] +8 [in2]*(6.5 [in])2 x +1[in]*(12[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +8 [in]*(1 [in])3/12 I x, we find the area moment of inertia about the x axis equals, --- +8 [in2]*(6.5 [in])2 1 [in] part 3 Ix Iy rx= ry= 28 [in2] A A
![Find: λc +8 [in2]*(6.5 [in])2 +1[in]*(12[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/35/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%286.5+%5Bin%5D%292+%2B1%5Bin%5D%2A%2812%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Ix = Σ Ic,i,x+Ai * dy,i. 2. i. Ix = 8 [in]*(1 [in])3/12. 8 [in] 14[in] +8 [in2]*(6.5 [in])2. x. +1[in]*(12[in])3/12. part [in2]*(0 [in])2. 1 [in] +8 [in]*(1 [in])3/12. I x, we find the area moment of inertia about the x axis equals, [in2]*(6.5 [in])2. 1 [in] part 3. Ix. Iy. rx= ry= 28 [in2] A. A.")
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Find: λc +8 [in2]*(6.5 [in])2 +1[in]*(12[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Ix = Σ Ic,i,x+Ai * dy,i 2 i Ix = 8 [in]*(1 [in])3/12 8 [in] 14[in] +8 [in2]*(6.5 [in])2 x +1[in]*(12[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +8 [in]*(1 [in])3/12 821.4 inches to the fourth power. Next, if we calculate --- +8 [in2]*(6.5 [in])2 1 [in] part 3 Ix = [in4] Ix Iy rx= ry= 28 [in2] A A
![Find: λc +8 [in2]*(6.5 [in])2 +1[in]*(12[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/36/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%286.5+%5Bin%5D%292+%2B1%5Bin%5D%2A%2812%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Ix = Σ Ic,i,x+Ai * dy,i. 2. i. Ix = 8 [in]*(1 [in])3/12. 8 [in] 14[in] +8 [in2]*(6.5 [in])2. x. +1[in]*(12[in])3/12. part [in2]*(0 [in])2. 1 [in] +8 [in]*(1 [in])3/ inches to the fourth power. Next, if we calculate [in2]*(6.5 [in])2. 1 [in] part 3. Ix = [in4] Ix. Iy. rx= ry= 28 [in2] A. A.")
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Find: λc part 1 y 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 8 [in] 14[in] x
2 i 8 [in] 14[in] x part 2 1 [in] the area moment of inertia about the y axis, --- 1 [in] part 3 Ix = [in4] Ix Iy rx= ry= 28 [in2] A A
![Find: λc part 1 y 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 8 [in] 14[in] x](http://slideplayer.com./slide/15497610/93/images/37/Find%3A+%CE%BBc+part+1+y+1+%5Bin%5D+Iy+%3D+%CE%A3+Ic%2Ci%2Cy%2BAi+%2A+dx%2Ci+8+%5Bin%5D+14%5Bin%5D+x.jpg "2. i. 8 [in] 14[in] x. part 2. 1 [in] the area moment of inertia about the y axis, [in] part 3. Ix = [in4] Ix. Iy. rx= ry= 28 [in2] A. A.")
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Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 2 i Iy = 1 [in]*(8 [in])3/12 8 [in] 14[in] +8 [in2]*(0 [in])2 x +12[in]*(1[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +1 [in]*(8 [in])3/12 we find the value of I y, equals, --- +8 [in2]*(0 [in])2 1 [in] part 3 Ix Iy rx= ry= 28 [in2] A A
![Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/38/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%280+%5Bin%5D%292+%2B12%5Bin%5D%2A%281%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Iy = Σ Ic,i,y+Ai * dx,i. 2. i. Iy = 1 [in]*(8 [in])3/12. 8 [in] 14[in] +8 [in2]*(0 [in])2. x. +12[in]*(1[in])3/12. part [in2]*(0 [in])2. 1 [in] +1 [in]*(8 [in])3/12. we find the value of I y, equals, [in2]*(0 [in])2. 1 [in] part 3. Ix. Iy. rx= ry= 28 [in2] A. A.")
39
Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 2 i Iy = 1 [in]*(8 [in])3/12 8 [in] 14[in] +8 [in2]*(0 [in])2 x +12[in]*(1[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +1 [in]*(8 [in])3/12 86.3, inches to the fourth power. [pause] Now we can --- +8 [in2]*(0 [in])2 1 [in] part 3 Iy = 86.3 [in4] Ix Iy rx= ry= 28 [in2] A A
![Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/39/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%280+%5Bin%5D%292+%2B12%5Bin%5D%2A%281%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Iy = Σ Ic,i,y+Ai * dx,i. 2. i. Iy = 1 [in]*(8 [in])3/12. 8 [in] 14[in] +8 [in2]*(0 [in])2. x. +12[in]*(1[in])3/12. part [in2]*(0 [in])2. 1 [in] +1 [in]*(8 [in])3/ , inches to the fourth power. [pause] Now we can [in2]*(0 [in])2. 1 [in] part 3. Iy = 86.3 [in4] Ix. Iy. rx= ry= 28 [in2] A. A.")
40
Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 2 i Iy = 1 [in]*(8 [in])3/12 8 [in] 14[in] +8 [in2]*(0 [in])2 x +12[in]*(1[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +1 [in]*(8 [in])3/12 compute the radii of gyration as --- +8 [in2]*(0 [in])2 Ix = [in4] Iy = 86.3 [in4] Ix Iy rx= ry= A A A=28 [in2]
![Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/40/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%280+%5Bin%5D%292+%2B12%5Bin%5D%2A%281%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Iy = Σ Ic,i,y+Ai * dx,i. 2. i. Iy = 1 [in]*(8 [in])3/12. 8 [in] 14[in] +8 [in2]*(0 [in])2. x. +12[in]*(1[in])3/12. part [in2]*(0 [in])2. 1 [in] +1 [in]*(8 [in])3/12. compute the radii of gyration as [in2]*(0 [in])2. Ix = [in4] Iy = 86.3 [in4] Ix. Iy. rx= ry= A. A. A=28 [in2]")
41
Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/12 +12 [in2]*(0 [in])2
part 1 y n 1 [in] Iy = Σ Ic,i,y+Ai * dx,i 2 i Iy = 1 [in]*(8 [in])3/12 8 [in] 14[in] +8 [in2]*(0 [in])2 x +12[in]*(1[in])3/12 part 2 +12 [in2]*(0 [in])2 1 [in] +1 [in]*(8 [in])3/12 5.416 inches for r x, and inches for r y. [pause] Returning to ---- +8 [in2]*(0 [in])2 Ix = [in4] Iy = 86.3 [in4] Ix Iy =5.416 [in] rx= ry= =1.756 [in] A A A=28 [in2]
![Find: λc +8 [in2]*(0 [in])2 +12[in]*(1[in])3/ [in2]*(0 [in])2](http://slideplayer.com./slide/15497610/93/images/41/Find%3A+%CE%BBc+%2B8+%5Bin2%5D%2A%280+%5Bin%5D%292+%2B12%5Bin%5D%2A%281%5Bin%5D%293%2F+%5Bin2%5D%2A%280+%5Bin%5D%292.jpg "part 1. y. n. 1 [in] Iy = Σ Ic,i,y+Ai * dx,i. 2. i. Iy = 1 [in]*(8 [in])3/12. 8 [in] 14[in] +8 [in2]*(0 [in])2. x. +12[in]*(1[in])3/12. part [in2]*(0 [in])2. 1 [in] +1 [in]*(8 [in])3/ inches for r x, and inches for r y. [pause] Returning to [in2]*(0 [in])2. Ix = [in4] Iy = 86.3 [in4] Ix. Iy. =5.416 [in] rx= ry= =1.756 [in] A. A. A=28 [in2]")
42
Find: λc λc = 0.01448 , =max rx= 5.416 [in] ry=1.756 [in] * y-dir
slenderness parameter A A’ K * L λc = * r z L/2 x our equation for K L over r, K L over r equals the larger value between --- K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] ry=1.756 [in]
![Find: λc λc = , =max rx= [in] ry=1.756 [in] * y-dir](http://slideplayer.com./slide/15497610/93/images/42/Find%3A+%CE%BBc+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D+ry%3D1.756+%5Bin%5D+%2A+y-dir.jpg "slenderness. parameter. A. A’ K * L. λc = * r. z. L/2. x. our equation for K L over r, K L over r equals the larger value between --- K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] ry=1.756 [in]")
43
Find: λc λc = 0.01448 , =max rx= 5.416 [in] = max (17.28, 32.80)
y-dir slenderness parameter A A’ K * L λc = * r z L/2 x 17.28 and 32.80, which is --- K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in]
![Find: λc λc = , =max rx= [in] = max (17.28, 32.80)](http://slideplayer.com./slide/15497610/93/images/43/Find%3A+%CE%BBc+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D+%3D+max+%2817.28%2C+32.80%29.jpg "y-dir. slenderness. parameter. A. A’ K * L. λc = * r. z. L/2. x and 32.80, which is --- K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in]")
44
Find: λc λc = 0.01448 , =max rx= 5.416 [in] = max (17.28, 32.80)
y-dir slenderness parameter A A’ K * L λc = * r z L/2 x [pause] Lastly, we can solve for lambda c by --- K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in] = 32.80
![Find: λc λc = , =max rx= [in] = max (17.28, 32.80)](http://slideplayer.com./slide/15497610/93/images/44/Find%3A+%CE%BBc+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D+%3D+max+%2817.28%2C+32.80%29.jpg "y-dir. slenderness. parameter. A. A’ K * L. λc = * r. z. L/2. x [pause] Lastly, we can solve for lambda c by --- K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in] =")
45
Find: λc λc = 0.01448 , =max rx= 5.416 [in] = max (17.28, 32.80)
y-dir slenderness parameter A A’ K * L λc = * r z L/2 x plugging in for K L over r, and lambda c, --- K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in] = 32.80
![Find: λc λc = , =max rx= [in] = max (17.28, 32.80)](http://slideplayer.com./slide/15497610/93/images/45/Find%3A+%CE%BBc+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D+%3D+max+%2817.28%2C+32.80%29.jpg "y-dir. slenderness. parameter. A. A’ K * L. λc = * r. z. L/2. x. plugging in for K L over r, and lambda c, --- K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in] =")
46
Find: λc λc = 0.01448 λc = 0.475 , =max rx= 5.416 [in]
y-dir slenderness parameter A A’ K * L λc = * r z λc = 0.475 L/2 x equals, [pause] K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in] = 32.80
![Find: λc λc = λc = , =max rx= [in]](http://slideplayer.com./slide/15497610/93/images/46/Find%3A+%CE%BBc+%CE%BBc+%3D+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D.jpg "y-dir. slenderness. parameter. A. A’ K * L. λc = * r. z. λc = L/2. x. equals, [pause] K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in] =")
47
Find: λc λc = 0.01448 λc = 0.475 , =max rx= 5.416 [in]
y-dir slenderness A) 0.24 B) 0.39 C) 0.48 D) 0.74 parameter A A’ K * L λc = * r z λc = 0.475 L/2 x When looking over the possible solutions, --- K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in] = 32.80
![Find: λc λc = λc = , =max rx= [in]](http://slideplayer.com./slide/15497610/93/images/47/Find%3A+%CE%BBc+%CE%BBc+%3D+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D.jpg "y-dir. slenderness. A) B) C) D) parameter. A. A’ K * L. λc = * r. z. λc = L/2. x. When looking over the possible solutions, --- K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in] =")
48
Find: λc λc = 0.01448 λc = 0.475 , =max rx= 5.416 [in]
y-dir slenderness A) 0.24 B) 0.39 C) 0.48 D) 0.74 parameter A A’ K * L λc = * r z λc = 0.475 L/2 x answerC the answer is C. K * L 93.6 [in] 57.6 [in] =max r rx , ry rx= [in] = max (17.28, 32.80) ry=1.756 [in] = 32.80
![Find: λc λc = λc = , =max rx= [in]](http://slideplayer.com./slide/15497610/93/images/48/Find%3A+%CE%BBc+%CE%BBc+%3D+%CE%BBc+%3D+%2C+%3Dmax+rx%3D+%5Bin%5D.jpg "y-dir. slenderness. A) B) C) D) parameter. A. A’ K * L. λc = * r. z. λc = L/2. x. answerC. the answer is C. K * L [in] 57.6 [in] =max. r. rx. , ry. rx= [in] = max (17.28, 32.80) ry=1.756 [in] =")
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