Basic Loads Cases
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The document defines various types of loads that should be considered in structural analysis, including dead loads, live loads, wind loads, and earthquake loads. It provides details on how to apply these loads in both positive and negative directions of the X and Z axes. It also lists load combinations that should be analyzed according to Indian standards, including combinations for limit states of collapse and serviceability. The load combinations include factors for dead, live, wind, and earthquake loads.
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FINAL EXAM REVIEW PACKET ANSWERS
(Fall 2012)
1. (a) increasing (b) decreasing
2. (a) 2 2( 3) 25y z− + = This is a cylinder parallel to the x-axis with radius 5.
(b) 3x = , 3x = − . These are vertical planes parallel to the yz-plane.
(c) 2 2 2z x y= + . This is a cone (one opening up and one opening down) centered on the z-axis.
3. There are many possible answers.
(a) 0x = produces the curve 23y z= − .
(b) 1y = produces the curves 23 cosz x= − and 23 cosz x= − − .
(c)
2
x
π
= produces the curves 3z = and 3z = − .
4. (a) (b) (i) 1 (ii) Increase (iii) Decrease
5. (a) Paraboloids centered on the x-axis, opening up in the positive x direction. 2 2x y z c= + +
(b) Spheres centered at the origin with radius 1 ln c− for 0 c e< ≤ . 2 2 2 1 lnx y z c+ + = −
6. (a) 6 am 11:30 am
(b) Temperature as a function of time at a depth of 20 cm.
(c) Temperature as a function of depth at noon.
7. ( , ) 2 3 2z f x y x y= = − −
8. (a) II, III, IV, VI (b) I (c) I, III, VI (d) VI (e) I, V
9. (a)
12
4 12
5
z x y= − + (b) There are many possible answers.
12
4
5
i j k+ −
(c)
3 569
2
10. (a) iii, vii (b) iv (c) viii (d) ii (e) v, vi (f) i, ix
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(a) ( )5 4 3
26
i j k− +
or ( )5 4 3
26
i j k− − +
(b) 2 3i j− +
(c)
4
cos
442
θ = , 1.38θ ≈ radians (d) ( )4 4 3
26
i j k− +
(e) 4 11 17i j k− − −
12. (a)
3
5
a = − (b)
1
3
a = (c) 2( 1) ( 2) 3( 3) 0x y z− − + + − = (d)
1 2 , 2 , 3 3x t y t z t= + = − − = +
13. 6 39i
or 6 39i−
14. (a)
( )
2
23 2 2
3 2
3 1
z x y x
x x y x y
∂
= −
∂ + + +
(b)
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10 4 3
5
H
H T
f
H
+ +
=
−
(c)
2
2 2
1 1z
x y y x
∂
= − −
∂ ∂
15. (a) 2 2 24 ( 1) 3 ( 2) 2z e x e y e= − + − + (b) 4( 3) 8( 3) 6( 6) 0x y z− + − + − =
16. (a)
2sin(2 ) cos(2 )
5 5
v v
ds dv d
α α
α= +
(b) The distance s decreases if the angle α increases and the initial speed v remains constant.
(c) 0.0886α∆ ≈ − . The angle decreases by about 0.089 radians.
17. (a) The water is getting shallower.
4
( 1, 2)
17
uh − = −
(b) There are many possible answers. 3i j+
(c) 72 ft/min
18. (a)
( )
2 2 2
22 2 22
2 2
1 1 11
yz xyz z yz
grad i j k
x x xx
= − + + + + + +
(b) ( ) ( ) ( )( )2 2 2 2curl x y z i y z j xz k i zj yk+ + − + + = + −
(c) ( ) ( ) ( )( )2 3 3cos sec 2 cos sin sec tan 3z zdiv x i x y j e k x x x y y e+ + = − + +
(d)
37
3
(e) ( , , ) sin zg x y z xy e c= + +
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- 1. Basic Loads 1) EQX (Earthquake force in X direction) a. EQX (+) (in increasing direction of X axis) b. EQX (-) (in decreasing direction of X axis) 2) EQZ (Earthquake force in Z direction) a. EQZ (+) (in increasing direction of Z axis) b. EQZ (-) (in decreasing direction of Z axis) 3) Dead Load a. Nodal Load b. Line Load c. Floor Load d. UDL/ UVL etc. 4) Live Load a. Floor Load 5) WLX (+) a. WLX (+) (in increasing direction of X axis) 6) WLX (-) a. WLX (-) (in decreasing direction of X axis) 7) WLZ (+) a. WLZ (+) (in increasing direction of Z axis) 8) WLZ (-) a. WLZ (-) (in decreasing direction of Z axis) Load Combinations: (As per IS 456:2000 Table No. 18 (pg. No. 68)) Sr. No. Load combination FOR LIMIT STATE OF COLLAPSE FOR LIMIT STATE OF SERVICEABILITY DL LL WL/EQ DL LL WL/EQ 1 DL + LL 1.5 1.5 - 1.0 1.0 - 2 DL + WL/EQ 1) DL contributing to stability 0.9 - 1.5 1.0 - 1.0 2) DL assisting over turning 1.5 - 1.5 1.0 - 1.0 3 DL + LL + WL/EQ 1.2 1.2 1.2 1.0 0.8 0.8
- 2. FOR LIMIT STATE OF SERVICEABILITY (STAAD Pro.) FOR LIMIT STATE OF COLLAPSE 1) DL + LL 2) DL + WL a. DL + WLX (+) b. DL + WLX (-) c. DL + WLZ (+) d. DL + WLZ (-) 3) DL + EQ a. DL + EQX (+) b. DL + EQX (-) c. DL + EQZ (+) d. DL + EQZ (-) 4) DL + 0.8 LL + 0.8 WL a. DL + 0.8 LL + 0.8 WLX (+) b. DL + 0.8 LL + 0.8 WLX (-) c. DL + 0.8 LL + 0.8 WLZ (+) d. DL + 0.8 LL + 0.8 WLZ (-) 5) DL + 0.8 LL + 0.8 EQ a. DL + 0.8 LL + 0.8 EQ X (+) b. DL + 0.8 LL + 0.8 EQ X (-) c. DL + 0.8 LL + 0.8 EQ Z (+) d. DL + 0.8 LL + 0.8 EQ Z (-) 1) 1.5 DL + 1.5 LL 2) 0.9 DL + 0.9 WL a. 0.9 DL + 1.5 WLX (+) b. 0.9 DL + 1.5 WLX (-) c. 0.9 DL + 1.5 WLZ (+) d. 0.9 DL + 1.5 WLZ (-) 3) 0.9 DL + 0.9 EQ a. 0.9 DL + 1.5 EQ X (+) b. 0.9 DL + 1.5 EQ X (-) c. 0.9 DL + 1.5 EQ Z (+) d. 0.9 DL + 1.5 EQ Z (-) 4) 1.5 DL + 1.5 WL a. 1.5 DL + 1.5 WLX (+) b. 1.5 DL + 1.5 WLX (-) c. 1.5 DL + 1.5 WLZ (+) d. 1.5 DL + 1.5 WLZ (-) 5) 1.5 DL + 1.5 EQ a. 1.5 DL + 1.5 EQ X (+) b. 1.5 DL + 1.5 EQ X (-) c. 1.5 DL + 1.5 EQ Z (+) d. 1.5 DL + 1.5 EQ Z (-) 6) 1.2 DL + 1.2 LL + 1.2 WL a. 1.2 DL + 1.2 LL + 1.2 WLX (+) b. 1.2 DL + 1.2 LL + 1.2 WLZ (-) c. 1.2 DL + 1.2 LL + 1.2 WLX (+) d. 1.2 DL + 1.2 LL + 1.2 WLZ (-) 7) 1.2 DL + 1.2 LL + 1.2 EQ a. 1.2 DL + 1.2 LL + 1.2 EQ X (+) b. 1.2 DL + 1.2 LL + 1.2 EQ Z (-) c. 1.2 DL + 1.2 LL + 1.2 EQ X (+) d. 1.2 DL + 1.2 LL + 1.2 EQ Z (-)