671017.pdf

0.00 1.25 2.50 3.75 5. 00 6.25 7. 50

−30. 00

−20. 00

−10. 00

0. 00


1. 00


2. 00


3. 00

0.00 1.25 2.50 3.75 5.00 6.25 7. 50

Shear

force

(kN )

Coalface distance (m)

L 1 L 2 L 3 L 4 L 5 L 6

Type 1

(a)

0.00 1.25 2.50 3.75 5. (^00) 6. 25
−30. 00
−20. 00
−10. 00

0. 00


1. 00


2. 00


3. 00

0.00 1.25 2.50 3.75 5.00 6. 25

Shear

force

(kN )

Coalface distance (m)

L 1 L 2 L 3 L 4 L 5

Type 2

(b)

Figure 10: Shear force.

(^0 1 2 3 4 5 6)
−10. 00
−8. 00
−6. 00
−4. 00
−2. 00

0. 00


1. 00

0 150 300 450 600 750 900

De ect

ion

(mm)

Points of control along the panel

0. 75 m


1. 25 m


2. 50 m

L 1 L 2 L 3 L 4 L 5 L 6

Type 1

Figure 11: Deflection versus length of spans.

Appendix

The not null elements of the matrices푀(24×24)={푚푖푗}and
퐵(24×1)={푏푖}of the problem type 1 are as follows.

Row 1.

푚1,1=푚1,3=1,

푏 1 =−푦푝1.

(A.1)

Row 2.

푚2,1=푚2,2=푚2,4=1,

푚2,3=−1.

(A.2)

0.00 1.25 2.50 3.75 5. 00 6.25 7. 50

−22. 00

−17. 00

−12. 00

−7. 00

−2. 00

3. 00

0.00 1.25 2.50 3.75 5.00 6.25 7. 50

De ect

ion

(mm)

Coalface distance (m)

500 m

1500 m

2500 m

L 1 L 2 L 3 L 4 L 5 L 6

Type 1

Figure 12: Deflection versus depth of the panel.

Row 3.

푚3,1=푒퐾^1 푥^1 ⋅cos퐾 1 푥 1 ,

푚3,2=푒퐾^1 푥^1 ⋅sin퐾 1 푥 1 ,

푚3,3=푒−퐾^1 푥^1 ⋅cos퐾 1 푥 1 ,

푚3,4=푒−퐾^1 푥^1 ⋅sin퐾 1 푥 1 ,

푚3,5=−푒퐾^2 푥^1 ⋅cos퐾 2 푥 1 ,

푚3,6=−푒퐾^2 푥^1 ⋅sin퐾 2 푥 1 ,

푚3,7=−푒−퐾^2 푥^1 ⋅cos퐾 2 푥 1 ,