Construct A and L matrices. A= 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 L= 1 , 164 , 499.387 − 4 , 660 , 600.879 4 , 182 , 158.213 1 , 164 , 499.400 − 4 , 660 , 600.884 4 , 182 , 158.214 1 , 168 , 947.849 − 4 , 650 , 766.255 4 , 191 , 851.271 1 , 168 , 947.841 − 4 , 650 , 766.249 4 , 191 , 851.263 Given that Baseline vector are given as: Explanation: Writing observation equation for X coordinate for bonnieto ray: X B − R = X B + Δ X B − R + v 1 WHERE X B = X coordinate of the station bonnie = 1 , 161 , 121.599 m ΔX B - R = X component in baseline vector = 3.377.788 m ʋ 1 = residual X B − R = 1 , 161 , 121.599 + 3.377.788 + v 1 = 1 , 164 , 499.387 + v 1 Writing observation equation for Y coordinate for Bonnie to Ray: Y B − R = Y B + Δ Y B − R + v 2 W H E R E Y B = Y c o o r d i n a t e o f t h e s t a t i o n B O N N I E = − 4 , 655 , 872.977 Δ Y B − R = Y c o m p o n e n t i n b a s e l i n e v e c t o r = − 4 , 727.902 v 2 = r e s i d u a l Y B − R = − 4 , 655 , 872.977 + − 4 , 727.902 + v 2 = − 4 , 660 , 600.879 + v 2 Writing observation equation for Z coordinate for Bonnie to Ray: Z B − R = X B + Δ Z B − R + v 3 W H E R E Z B = Z c o o r d i n a t e o f t h e s t a t i o n b o n n i e = 4 , 188 , 330.232 m Δ Z B − R = Z c o m p o n e n t i n b a s e l i n e v e c t o r = − 6 , 172.019 m v 3 = r e s i d u a l Z J − T = 4 , 188 , 330.232 − 6 , 172.019 + v 3 = 4 , 182 , 158.213 + v 3 Writing observation equation for X coordinate for tom to herb: X T − H = X T + Δ X T − H + v 4 W H E R E X T = X c o o r d i n a t e o f t h e s t a t i o n T o m = 1 , 176 , 398.558 m Δ X T − H = X c o m p o n e n t i n b a s e l i n e v e c t o r = − 7 , 450.717 m v 4 = r e s i d u a l X T − H = 1 , 176 , 398.558 − 7 , 450.717 + v 4 = 1 , 168 , 947.841 + v 4 Writing observation equation for y coordinate for tom to herb: Y T − H = Y T + Δ Y T − H + v 5 W H E R E Y T = Y c o o r d i n a t e o f t h e s t a t i o n t o m = − 4 , 653 , 039.613 m Δ Y T − H = Y c o m p o n e n t i n b a s e l i n e v e c t o r = 2 , 273.364 m v 5 = r e s i d u a l Y A − T = − 4 , 653 , 039.613 + 2 , 273.364 + v 5 = − 4 , 650 , 766.249 + v 5 Writing observation equation for Z coordinate for tom to herb Z T − H = Z T + Δ Z T − H + v 6 W H E R E Z T = Z c o o r d i n a t e o f t h e s t a t i o n t o m = 4 , 187 , 198.360 m Δ Z T − H = Z c o m p o n e n t i n b a s e l i n e v e c t o r = 4652.903 m v 6 = r e s i d u a l Z T − H = 4 , 187 , 198.360 m + 4652.903 + v 6 = 4 , 191 , 851.263 + v 6 Writing observation equations for X coordinate for bonnie to herb: X B − H = X B + Δ X B − H + v 7 W H E R E X B = X c o o r d i n a t e o f t h e s t a t i o n T o m = 1 , 161 , 121.599 m Δ X B − H = X c o m p o n e n t i n b a s e l i n e v e c t o r = 7826.248 m v 7 = r e s i d u a l X B − H = 1 , 161 , 121.599 + 7826.248 + v 7 = 1 , 168 , 947.847 + v 7 Writing observation equation for Y coordinates for bonnie to herb: Y B - H = Y B + ΔY B - H +ʋ 8 WHERE Y B = Y coordinate of the station Tom = -4,655,872.977m ΔY B - H = Y component in baseline vector = 5,106.722m ʋ 8 = residual X A - T =4,655,872.977+5,106.722+ʋ 8 = -4,650,766.255+ ʋ 8 Writing observation equation for Z coordinates for bonnie to herb: Z B − H = Z B + Δ Z B − H + v 9 W h e r e , Z B = Z c o o r d i n a t e o f t h e s t a t i o n T o m = 4 , 188 , 330.232 m Δ Z B − H = Z c o m p o n e n t i n b a s e l i n e v e c t o r = 3 , 521.039 m v 9 = r e s i d u a l Z B − H = 4 , 188 , 330.232 + 3 , 521.039 + v 9 = 4 , 191 , 851.271 + v 9 Writing observation equation for X coordinate for tom to ray: X T − R = X T + Δ X T − R + v 10 W H E R E X T = X c o o r d i n a t e o f t h e s t a t i o n T o m = 1 , 176 , 398.558 m Δ X T − R = X c o m p o n e n t i n b a s e l i n e v e c t o r = − 11 , 899.158 m v 10 = r e s i d u a l X T − R = 1 , 176 , 398.558 − 11 , 899.15 + v 10 = 1 , 164 , 499.400 + v 10 Writing observation equation for Y coordinate for tom to ray: Y T − R = Y T + Δ Y T − R + v 11 W H E R E Y T = Y c o o r d i n a t e o f t h e s t a t i o n T o m = − 4 , 653 , 039.613 m Δ Y T − R = Y c o m p o n e n t i n b a s e l i n e v e c t o r = − 7 , 561.271 m v 11 = r e s i d u a l Y T − R = 1 , 176 , 398.558 − 11 , 899.15 + v 11 = − 4 , 660 , 600.884 + v 11 Writing observation equation for Z coordinate for tom to ray: Z T − R = Z T + Δ Z T − R + v 12 W H E R E Z T = Y c o o r d i n a t e o f t h e s t a t i o n T o m = 4 , 187 , 198.360 m Δ Z T − R = Y c o m p o n e n t i n b a s e l i n e v e c t o r = − 5 , 040.146 m v 12 = r e s i d u a l Z A − T = 4 , 187 , 198.360 − 5 , 040.146 + v 12 = − 4 , 182 , 158.214 + v 12 A = X B − R 0 0 0 0 0 0 Y B − R 0 0 0 0 0 0 Z B − R 0 0 0 0 0 0 X T − R 0 0 0 0 0 0 Y T − R 0 0 0 0 0 0 Z T − R X B − H 0 0 0 0 0 0 Y B − H 0 0 0 0 0 0 Z B − H 0 0 0 0 0 0 X T − H 0 0 0 0 0 0 Y T − H 0 0 0 0 0 0 Z T − H A= 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 Construct L matrix: L = 1 , 164 , 499.387 − 4 , 660 , 600.879 4 , 182 , 158.213 1 , 164 , 499.400 − 4 , 660 , 600.884 4 , 182 , 158.214 1 , 168 , 947.849 − 4 , 650 , 766.255 4 , 191 , 851.271 1 , 168 , 947.841 − 4 , 650 , 766.249 4 , 191 , 851.263 Conclusion: A= 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 L= 1 , 164 , 499.387 − 4 , 660 , 600.879 4 , 182 , 158.213 1 , 164 , 499.400 − 4 , 660 , 600.884 4 , 182 , 158.214 1 , 168 , 947.849 − 4 , 650 , 766.255 4 , 191 , 851.271 1 , 168 , 947.841 − 4 , 650 , 766.249 4 , 191 , 851.263

Question

Want to see the full answer?

Answer 1

Question

Chapter 16, Problem 16.25P

To determine

Construct A and L matrices.

A= 100000010000001000000100000010000001100000010000001000000100000010000001

L= 1,164,499.387−4,660,600.8794,182,158.2131,164,499.400−4,660,600.8844,182,158.2141,168,947.849−4,650,766.2554,191,851.2711,168,947.841−4,650,766.2494,191,851.263

Given that

Baseline vector are given as:

Explanation:

Writing observation equation for X coordinate for bonnieto ray:

XB−R= XB+ ΔXB−R+v1

WHERE

X_B= X coordinate of the station bonnie = 1,161,121.599m

ΔX_B_-_R= X component in baseline vector = 3.377.788m

ʋ₁= residual

XB−R=1,161,121.599+3.377.788+v1          = 1,164,499.387+ v1

Writing observation equation for Y coordinate for Bonnie to Ray:

YB−R= YB+ ΔYB−R+v2WHEREYB= Y coordinate of the station BONNIE = −4,655,872.977ΔYB−R= Y component in baseline vector = −4,727.902v2= residual YB−R=−4,655,872.977+−4,727.902+v2          = −4,660,600.879+ v2

Writing observation equation for Z coordinate for Bonnie to Ray:

ZB−R= XB+ ΔZB−R+v3WHEREZB= Z coordinate of the station bonnie = 4,188,330.232mΔZB−R= Z component in baseline vector = −6,172.019mv3= residual ZJ−T=4,188,330.232−6,172.019+v3          = 4,182,158.213+ v3

Writing observation equation for X coordinate for tom to herb:

XT−H= XT+ ΔXT−H+v4WHEREXT= X coordinate of the station Tom = 1,176,398.558mΔXT−H= X component in baseline vector = −7,450.717mv4= residual XT−H=1,176,398.558 −7,450.717+v4          = 1,168,947.841+ v4

Writing observation equation for y coordinate for tom to herb:

YT−H= YT+ ΔYT−H+v5WHEREYT= Y coordinate of the station tom = −4,653,039.613mΔYT−H= Y component in baseline vector = 2,273.364mv5= residual YA−T=−4,653,039.613+2,273.364+ v5          = −4,650,766.249+ v5

Writing observation equation for Z coordinate for tom to herb

ZT−H= ZT+ ΔZT−H+v6WHEREZT= Z coordinate of the station tom = 4,187,198.360mΔZT−H= Z component in baseline vector = 4652.903mv6= residual ZT−H=4,187,198.360m +4652.903+v6          = 4,191,851.263+ v6

Writing observation equations for X coordinate for bonnie to herb:

XB−H= XB+ ΔXB−H+v7WHEREXB= X coordinate of the station Tom = 1,161,121.599mΔXB−H= X component in baseline vector = 7826.248mv7= residual XB−H=1,161,121.599+7826.248+v7          = 1,168,947.847+ v7

Writing observation equation for Y coordinates for bonnie to herb:

Y_B_-_H= Y_B+ ΔY_B_-_H+ʋ₈WHERE

Y_B= Y coordinate of the station Tom = -4,655,872.977m

ΔY_B_-_H= Y component in baseline vector = 5,106.722m

ʋ₈= residual

X_A_-_T=4,655,872.977+5,106.722+ʋ₈ = -4,650,766.255+ ʋ₈

Writing observation equation for Z coordinates for bonnie to herb:

ZB−H= ZB+ ΔZB−H+v9Where,ZB= Z coordinate of the station Tom = 4,188,330.232mΔZB−H= Z component in baseline vector = 3,521.039m v9= residual ZB−H=4,188,330.232+3,521.039+v9          = 4,191,851.271+ v9

Writing observation equation for X coordinate for tom to ray:

XT−R= XT+ ΔXT−R+v10WHEREXT= X coordinate of the station Tom = 1,176,398.558mΔXT−R= X component in baseline vector = −11,899.158mv10= residual XT−R=1,176,398.558 −11,899.15+v10          = 1,164,499.400+ v10

Writing observation equation for Y coordinate for tom to ray:

YT−R= YT+ ΔYT−R+v11WHEREYT= Y coordinate of the station Tom = −4,653,039.613mΔYT−R= Y component in baseline vector = −7,561.271mv11= residualYT−R=1,176,398.558 −11,899.15+v11          = −4,660,600.884+ v11

Writing observation equation for Z coordinate for tom to ray:

ZT−R= ZT+ ΔZT−R+v12WHEREZT= Y coordinate of the station Tom = 4,187,198.360mΔZT−R= Y component in baseline vector = −5,040.146mv12= residualZA−T=4,187,198.360−5,040.146+v12= −4,182,158.214+ v12

A = XB−R000000YB−R000000ZB−R000000XT−R000000YT−R000000ZT−RXB−H000000YB−H000000ZB−H000000XT−H000000YT−H000000ZT−H

A= 100000010000001000000100000010000001100000010000001000000100000010000001

Construct L matrix:

L = 1,164,499.387−4,660,600.8794,182,158.2131,164,499.400−4,660,600.8844,182,158.2141,168,947.849−4,650,766.2554,191,851.2711,168,947.841−4,650,766.2494,191,851.263

Conclusion:

A= 100000010000001000000100000010000001100000010000001000000100000010000001

L= 1,164,499.387−4,660,600.8794,182,158.2131,164,499.400−4,660,600.8844,182,158.2141,168,947.849−4,650,766.2554,191,851.2711,168,947.841−4,650,766.2494,191,851.263

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

The tension in cable BA is 10 kN. The questions will lead you toward determining the moment of the force acting from B to A about the x-axis. Hints: Pay attention to the orientation of the XYZ coordinate axes. 1000 mm A (400, 300, 0) mm 600 mm x

The beam shown in the figure below is typical for a floor system in an existing building.It needs to carry a uniform live load of 260 lb/ft and a uniform dead weight of 400 lb/ft,including its own weight. The owner wants to add a partition weighing 7 kip (live load) asshown. Assuming the added partition as live load, is the beam section adequate to safelycarry the extra live load?PartitionStirrups15 ft 3 in.14 in.a. Determine the d e s i g n m o m e n t c a p a c i t y .b. D e t e r m i n e t h e f a c t o r e d a p p l i e d b e n d i n g m o m e n t .c. Is the beam safe and adequate for bending? Please explain your response.

4. Use the influence function method to draw the influence line for the shear just to the right of A. Assume C is fixed, A is a roller, and B is a pin. 8 ft A 16 ft B 10 ft-