CLOSED NOTES, HANDOUTS, BOOKS AND HOMEWORKS *Read problems completely and carefully before beginning to solve.
75
Name:_______________________________________ School ID No.:_______________ Section: _________________ Name:_______________________________________ Instruction: Answer the following questions and write the corresponding letter your answer on the space provided in the separate answer sheet provided.
Refer to figure SD-07Q004. S 1 = 8.0 m; S 2 = 2.0 m; S 3 = 2.0 m; S 4 = 2.0 m Superimposed dead load = 5.0 kPa Live load = 3.6 kPa Properties of W18 x 96 section A = A = 18,193.5 mm2 tw = 13.00 mm b f = 298.45 mm I x = 699.27 x 10 6 mm4 d = = 461.26 mm S x = 3031.61 x 10 3 mm3 t f = 21.11 mm F y = 248 MPa What is the maximum bending stress (MPa) in beam BF? a. 137.6 b. 45.4 c. 148.8 d. 49.1 If lateral supports are provided determine the largest distance between lateral supports (in m) so that the maximum allowable flexural stress can be utilized. a. 5 b. 4 c. 3 d. 7 What is the permissible flexural stress (MPa)? C b = 1.0 a. 148 b. 163 c. 130 d. 141
From the figure shown in SD-07Q001, a truss is subjected to loads P 1 = 15 kN, P2 = 15 kN and P 3= 25 kN at joint C, D and E respectively. Use S 1 = 3 m; S 2 = 4 m Properties of diagonal members (2L75 x 75 x 6): Ag = 1858 mm 2 Fy = 248 MPa r x = 22.9 mm r y = 33.2 mm What is the reaction at A, in kN? a. 7.3 b. 24.2 What is the axial force in kN, in member DI? a. 7.3 b. 24.2 Calculate the allowable load in kN, in member DI. a. 42.6 b. 40.1
c. 30.8
d. 27.7
c. 30.8
d. 27.7
c. 276.5
d. 79.5
A column us built-up from 4-300 mm x 16 mm plates, welded to form a box section having a width of 300 mm along the x-axis x-axis and a depth of 332 mm along the y-axis. y-axis. The unbraced length with respect to the x-axis x-axis is 10 m. With respect to the y-axis, the column is braced at midheight so that the unbraced length is 5 m. Assume pinned-ends for both axes. Sidesway is prevented. Yield Strength: F y = 248 MPa Modulus of Elasticity: E = 200 GPa Compute the effective slenderness ratio with respect to the x-axis. x-axis. a. 126.17 b. 78.46 c. 115.47 Compute the effective slenderness ratio with respect to the y-axis. y-axis. a. 34.0 b. 42.5 c. 25.5 Compute the axial load capacity (kN) of the built-up column. a. 3212 b. 2165 c. 2054
d. 70.62 d. 126.17 d. 2304
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Refer to figure SD-07Q007. Given: Slab thickness = 150 mm Dead load = 4.8 kPa (superimposed) Live load = 3.0 kPa Longitudinal beams and girders shown are simply supported at their continuous and discontinuous ends. The plan is that of an office building, if only panel CGDH is occupied. Dimensions are: S1 = 6.0 m S2 = 6.0 m S3 = 6.0 m S4 = 2.5 m S5 = 2.5 m S6 = 2.5 m Beams: Beams: W350 x 142 Girders: Girders: W460 x 143 What is the maximum positive moment (kN.m) for beam CG? a. +74.4 b. +77.1 c. +78.2 What is the maximum negative moment (kN.m) for beam GK? a. -51.8 b. -18.0 c. -9.0 What is the maximum positive moment (kN.m) for beam KO due to live load? a. +27.4 b. +21.6 c. +4.5
d. +75.3 d. -13.5 d. +2.3
A W10 x 29 has a span of 8 m. It carries a total floor load of 6 kPa including that of the concrete slab. Neglect weight of beam. The slab serves as the lateral support of the beam thru thru vertical stud installation. installation. Properties of W10 x 29 section A = 5509.7 mm 2 tw = 7.34 mm bf = 146.79 mm Ix = 65.8 x 10 6 mm4 d = 259.59mm Sx = 504.7 x 10 3 mm3 tf = 12.70 mm Fy = 230 MPa Compute the spacing (in m) of the beam if allowable bending stress controls. a. 1.4 b. 1.6 c. 2.1 d. 0.7 Compute the spacing (in m) of the beam if allowable shear stress controls. a. 3.3 b. 3.6 c. 6.6 d. 7.3 Compute the spacing (in m) of the beam if allowable deflection of a. 0.5
b. 0.9
c. 2.0
L 360
controls. d. 4.5
Light-grade steel channel channel was used as a purlin of a truss. The top chord of the truss truss is inclined 1V: 3H and distance between trusses is equal to 5 m. The purlin has a weight of 79 N/m and spaced at 1.2 m. on centers. The dead load including the roof materials is 720 Pa, live load of 1000 Pa and wind load of 1440 Pa. Coefficient of pressure at leeward and windward are 0.6 and 0.2 respectively. Assume all loads passes through through the centroid of the section. Properties of C200 x 76 section Sx = 6.19 x 104 mm3 ; Sy = 1.38 x 104 mm3 w = 79 N/m ; Fbx = Fby = 207 MPa Calculate the bending stress, f bx bx (MPa), for dead load and live load combination (D + L). a. 102.6 b. 205.3 c. 97.6 d. 108.2 Calculate the bending stress, f by by (MPa), for dead load and live load combination (D + L). a. 153.5 b. 306.9 c. 256.1 d. 145.9 Calculate the maximum ratio of actual to the allowable bending stress for load combination 0.75(D+L+W) at the windward side. a. 0.99 b. 1.16 c. 1.28 d. 0.91
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Two C-channels are welded at the tip of the flanges to form a box column. Properties of each channel A = 5350 mm2 tw = 15 mm tf = = 10 mm bf = 100 mm d = 250 mm 6 4 Ix = 52 x 10 mm Iy = 5 x 106 mm4 Distance from centroidal y-axis of the channel to the outer face of the web, x x = 29 mm. Column height height = 6 m. and effective length factor K = 1.0 both axes. The major x-axis of the channel is the x-axis of the built up column. Calculate the axial compressive stress in MPa in the column due to a concentric load of 600 kN. a. 108 b. 171 c. 56 d. 112 What is maximum bending stress (MPa) in the column due to a moment of 200 kN.m about the x-axis? a. 240 b. 481 c. 391 d. 938 What is the critical slenderness ratio of the built up column? a. 102 b. 78 c. 30 d. 61
A super structure of a bridge consists of a ribbed metal deck with 50 mm concrete slab on top. The deck is supported by wide flange steel beams strengthened by cover plates 16 mm x 250 mm one at the top and one at the bottom. It is simply supported on a span of 20 m. Each of the cover c over plated steel beams is subjected to the following data: Dead load = 12 kN/m (superimposed) Live load: 17.8 kN front wheel a nd 71.2 kN rear wheel Distance between wheel loads = 4.27 m Impact on live load is
15 L 37
, with maximum of 30%
Properties of W830 x 175 175 section 2 A = 22387 mm tw = 14 mm bf = 290 mm Ix = 2500 x 10 6 mm4 d = 835 mm Fy = 248 MPa tf = = 19 mm What is the maximum flexural stress (MPa) in the cover-plated beam due to dead load? a. 72.5 b. 81.9 c. 88.7 d. 100.3 What is the maximum flexural stress (MPa) in the cover-plated beam due to live load plus impact? a. 56.6 b. 44.8 c. 69.3 d. 58.2 What is the web shear stress (MPa) in the beam due to live load? a. 8.8 b. 8.4 c. 7.6 d. 7.3
The roof beams of a warehouse are supported by pipe columns (see figure SD-07Q006) having outer diameter d 2 = 100 mm and inner diameter d 1 = 90 mm. The columns have length L length L = = 4.0 m, modulus E modulus E = = 210 GPa, and fixed supports at the base. Calculate the critical load P cr (kN) (kN) of one of the columns using the following assumptions the upper end is pinned and the beam prevents horizontal displacement. displacement. a. 55 b. 219 c. 447 d. 875 Calculate the critical load P load P cr (kN) of one of the columns using the following assumptions the upper end is cr (kN) fixed against rotation and the beam prevents horizontal displacement. a. 55 b. 219 c. 447 d. 875 Calculate the critical load P load P cr (kN) of one of the columns using the following assumptions the upper end is cr (kN) fixed against rotation but the beam is fre e to move horizontally. a. 55 b. 219 c. 447 d. 875
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A girder spans 12 m on simple supports. It carries two beans, each including equal concentrated load P at at third points of the span. Given: Girder Properties: A = 12500 mm 2 Ix = 446 x 10 6 mm4 d = 465 mm Iy = 23 x 106 mm4 tf = 19 mm bf = 193 mm tw = 11 mm Allowable bending stress = 148 MPa Allowable shear stress = 99 MPa Modulus of Elasticity = 200 GPa Based on the flexural capacity of the girder, what is the maximum load P (kN)? a. 71 b. 506 c. 104 d. 345 Based on the shear capacity of the girder, what is the maximum load P (kN)? a. 71 b. 506 c. 104 d. 345 To strengthen the girder, two cover plates are added, one at the top and the other at the bottom flange. The cover plates are 16 mm thick and the concentrated load P = 110 kN. Which of the following gives the required width of the cover plate ( mm) based on the bending stress? a. 200 b. 150 c. 250 d. 175
Refer to figure SD-07Q005. Given: Span , L= L= 6.0 m Slope (Top chord) = 1V:3H Dead load = 1200 Pa Wind Pressure Coefficients: Live load = 576 Pa Windward side = 0.2 pressure Wind load = 1440 Pa Leeward side = 0.6 suction Properties of C section Sx = 4.18 x 104 mm3 ; Sy = 1.18 x 104 mm3 w = 71 N/m ; Fbx =0.66Fy; Fby = 0.75F y; Fy = 250 MPa For D + L W load combination, a one third increase in the allowable stresses is allowed. Using 2 lines of sag rods, find the safe purlin spacing (m) for D + L load combination. a. 0.8 b. 1.0 c. 1.2 d. 1.4 Using 2 lines of sag rods, find the safe purlin spacing (m) for D + L + W where W is at the windward side. a. 0.8 b. 1.0 c. 1.2 d. 1.4 Using 2 lines of sag rods, find the total flexural stress (MPa) due to D + L + W load combination where W is at the leeward side. Purlins are spaced at 0.75 m on centers: a. 66.4 b. 105.1 c. 133.2 d. 118.4
Refer to figure SD-07Q007. Given: Slab thickness = 150 mm Beams: Beams: W350 x 142 Girders: Girders: W460 x 143 Dead load = 4.8 kPa (superimposed) Live load = 3.0 kPa Longitudinal beams and girders shown are simply supported at their continuous and discontinuous ends. Dimensions are: S1 = 6.0 m S2 = 6.0 m S3 = 6.0 m S4 = 2.5 m S5 = 2.5 m S6 = 2.5 m What is the maximum positive moment (kN.m) for beam CG where live load is placed on the entire plan? a. +134.5 b. +84.3 c. +86.1 d. +91.8 What is the maximum negative moment (kN.m) for beam GK due to live load? Apply possible patterns. a. -39.0 b. -27.9 c. -31.5 d. -13.5 What is the maximum positive moment (kN.m) for beam KO due to live load? Apply possible patterns. a. +45.0 b. +21.6 c. +33.8 d. +27.4
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A 5 m long W shape steel cantilever beam carries a concentrated load P = 150 kN at 3.75 m from fixed end. Properties of W24 x 94 2 A = 17870 mm tw = 13.11 mm tf = = 22.15 mm bf = 230.15 mm d = 616.97 mm Ix = 1119.7 x 10 6 mm4 What is the deflection (mm) under the load P? a. 11.77 b. 17.66 c. 27.91 d. 41.86 What is the maximum beam deflection (mm)? a. 11.77 b. 17.66 c. 27.91 d. 41.86 What force (kN) should be applied a pplied at the free end in order to prevent the beam from def lecting? a. 93.75 b. 94.92 c. 10.00 d. 60.00
Refer to figure SD-07Q002 Properties of Columns Columns AC and BD Section W 250 mm x 67 kg/m kg/m 2 A = 8580 mm Ix = 103 x 10 6 mm4 d = 255 mm Iy = 22 x 106 mm4 bf = 200 mm r x = 110 mm tw = 9 mm r y = 51 mm tf = 16 mm r z = 55 mm E = 200 GPa Fy = 230 MPa Column Loads are as follows: Total axial load (including column weight): At the base of the column: At the top: Use:
The columns are rigidly attached to the footing at the base and pin connected at the top. The weak axis of each column is braced at mid-height about the y-axis. Sidesway is uninhibited about the x-axis x-axis (K=1.2) but prevented about the y the y-axis -axis (K=1.0).
P = 140 kN M x = 21 kN.m. kN.m. ; M y = 0. M x = M y = 0
H 1 = 6 m; H 2 = 4 m F bx = 0.60 F y F by = 0.75 Fy Moment Magnification factor =1.0 Calculate the allowable axial compression stress F a in column BD in MPa. a. 109.49 b. 116.41 c. 123.62 d. 138.0 If the moment on top and at the base both x and y and y axes axes are neglected, determine the interaction value. a. 0.149 b. 0.068 c. 0.175 d. 0.159 Considering the moment on top and at the base both x and y and y axes, axes, determine the interaction value. a. 0.256 b. 0.320 c. 0.239 d. 0.337
Refer to figure SD-07Q003. A C375 x 50.5 (channel) is used as purlins of a roof truss having a pitch of ⅓. There are 8 purlins on each side of the top chord spaced at 2.0 m on centers. The spacing between trusses is 6 m. The trusses are subjected to the f ollowing loads: Given: Given: wt (tangential uniform load) = 1.3 kN/m Use A36 Steel : Fy = 248 MPa; Fu = 400 MPa Allowable tensile strength of sag rods and tie rods = 0.33Fu Determine the tension at the most critical sag rods are placed at midspan in kN. a. 39.00 b. 34.13 c. 22.88 Determine the diameter of the sag rods are placed at midspan in mm. a. 12 b. 16 c. 20
d. 35.44 d. 22
Determine the diameter of the tie rods if of the sag rods are placed at midspan in mm. Use T h a. 12
b. 16
c. 20
T total cos
d. 22
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Light-grade steel channel channel was used as a purlin of a truss. The top chord of the truss truss is inclined 1V: 3H and distance between trusses is equal to 3 m. The purlin has a weight of 71 N/m and spaced at 1.2 m. on centers. The dead load including the roof materials is 1200 Pa, live load of 1000 Pa and wind load of 1440 Pa. Coefficient of pressure at leeward and windward are 0.6 and 0.2 respectively. Sag rods are placed at the middle thirds. Properties of C-section C-section 4 3 Sx = 4.18 x 10 mm ; Sy = 1.18 x 104 mm3 w = 71 N/m ; Fbx = Fby = 138 MPa Calculate the maximum ratio of actual to the allowable bending stress for D+L load combination. a. 0.529 b. 0.554 c. 0.634 d. 1.108 Calculate the maximum ratio of actual to the allowable bending stress for load combination 0.75(D+L+W) at the windward side. a. 0.466 b. 0.619 c. 0.526 d. 0.438 Calculate the maximum ratio of actual to the allowable bending stress for load combination 0.75(D+L+W) at the leeward side. Sag rods are omitted. a. 0.616 b. 0.899 c. 0.770 d. 0.997
A 5 m long W shape steel cantilever beam carries a total uniformly distributed load of 10 kN/m. Properties of W24 x 94 2 A = 17870 mm tw = 13.11 mm tf = = 22.15 mm bf = 230.15 mm d = 616.97 mm Ix = 1119.7 x 10 6 mm4 What is the maximum beam deflection (mm)? a. 2.91 b. 3.49 c. 27.91 d. 9.30 What is the force (kN) should be applied at the free end of the beam to prevent its deflection? a. 150.00 b. 133.33 c. 18.75 d. 6.25 What force (kN) should be applied a pplied at mid length of the beam in order to balance its deflection at the free end? a. 6.25 b. 18.75 c. 10.00 d. 60.00
Refer to figure SD-07Q007. Given: Slab thickness = 150 mm Beams: Beams: W350 x 142 Girders: Girders: W460 x 143 Dead load = 4.8 kPa (superimposed) Live load = 3.0 kPa Longitudinal beams and girders shown are simply supported at their continuous and discontinuous ends. The plan is that of an office building, if only panel BCFG and CGDH are occupied. Dimensions are: S1 = 6.0 m S2 = 6.0 m S3 = 6.0 m S4 = 2.5 m S5 = 2.5 m S6 = 2.5 m What is the maximum reaction at C (kN)? a. 71.74 b. 89.79 c. 91.84 d. 73.23 What is the maximum reaction at G (kN)? a. 197.29 b. 201.79 c. 172.54 d. 177.04 What is the maximum negative moment (kN.m) for beam GK? a. -100.61 b. -114.11 c. -98.62 d. -112.12 Determine the axial compressive strength (kN) of an HSS 200 x 100 x 3 with an effective length of 5.0 m with respect to each principal axis. Use F Use F y = 317 MPa. Properties of HSS 200 x 100 x 3: 2 Ag = 1742 mm W = 14.67 kg/m d = 100 mm b = 200 mm t = 3 mm Ix = 9.53 x 106 mm4 Iy = 3.29 x 106 mm4 a. 135.53 b. 138.66 c. 155.34 d. 158.59
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The shape factor of a compact wide flange section is 1.12, which of the following gives the load factor. a. 1.5 b. 0.9 c. 1.7 d. 1.4 Steel trusses of 25 m or greater in span should generally cambered for approximately the dead load deflection. Crane girders of 20 m or greater in span should generally be cambered for approximately____. a. dead load deflection plus one half live load deflection b. dead load deflection plus plus live load deflection c. live load deflection only d. live load deflection plus one half dead load deflection A curvature built into a beam, truss or other structural element to offset anticipated deflection so that the element will not bow under dead load. a. deflection b. chamfer c. buckling d. camber It is the point through which the resultant of the resistance to the applied lateral force acts. a. shear wall b. center of mass c. eccentricity d. center of rigidity The maximum size of standard holes diameter for rivets less than 22 mm diameter. a. d + 1.5 mm b. d + 3 mm c. d + 4.5 mm d. d + 8 mm The slenderness ratio of compression members shall not exceed: a. 200 b. 240 c. 300 d. 120 A stiffening plate in a bridge between the main girders in a bridge or a stiffening web across a hollow building block. block. a. beam b. slab c. base plate d. diaphragm A gap or space in the steel or the concrete to accommodate both thermal expansion and contraction. a. expansion joint b. seismic gap c. construction joint d. none of these The lowering of the breaking-load of a member by repeated reversals of stress so that the member fails at a much lower stress than it can withstand under static loading. a. fatigue b. stiffness c. creep d. hydration In pin connected plates other than eye bars, the bearing stress on the projected area of the pin shall not exceed: a. 0.90Fy b. 0.75Fy c. 0.70Fy d. 0.80Fy Composite beams with formed steel deck, the slab thickness above the steel deck shall be less than______. a. 50 mm b. 100 mm c. 150 mm d. 38 mm The difference between gross diameter and nominal diameter f or the rivets up to 25 mm diameter is a. 1.0 mm b. 1.6 mm c. 2.0 mm d. 2.5 mm Is a structural element that transmits lateral loads to the vertical resisting elements of a structure. a. shear wall b. slab c. base plate d. diaphragm An upright compression member whose height does not exceed three times its average least lateral dimension. a. pedestal b. slab c. column d. strut An upright compression member whose height exceeds three times its average lea st lateral dimension. a. pedestal b. slab c. column d. beam The rights and duties of the parties following a contractor’s determination of employment under the contract (remedies of either party). a. contractor’s right b. accrued rights c. parity rights d. human rights The maximum center to center spacing of stud connectors in a composite beam shall not exceed_______. a. 8 times the total slab thickness b. 6 times the slab thickness thickness c. 150 mm d. 300 mm The clear distance between oversized and slotted shall not be less than: a. 2 2/3 bolt diameter b. one bolt diameter c. 150 mm d. 300 mm When two or more rolled beams or channels are used side by side to form an open-box type beams and grillages for a flexural member, they shall be connected together at intervals of not more than_______. a. 1.5 m b. 2.0 m c. 2.5 m d. 1.0 m The rolled steel I-sections are most commonly used as beams because these provide a. large moment of inertia with less cross-sectional area b. large moment of resistance as compared compared to other section c. greater lateral stability d. all of the above
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P1
P2
P3 E
D
C
S2 B
A F
G
J
I
H 6 @ S1
Fig. SD-07Q001 SD-07Q001 x
H2 C
D
A
B
y
H1
Fig. SD-07Q002
Tie rod Sag rod purlin
Fig. SD-07Q003 B
C
D
Roof beam
Pipe Column S1
d 2 L
F
E S2
G S3
FRAMING PLAN Fig. SD-07Q004
H S4
Fig. SD-07Q006
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D
H
L
P
S4
G
C
O
K
S5
FRAMING PLAN Fig. SD-07Q007 N
J
F
B
S6
A
M
I
E S1
S2
S3
Tie rod
S
Sag rod
S
purlin
Fig. SD-07Q005
TRUSS
Sag rod
L
Tie rod
purlins
TRUSS
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1. CONTINOUS BEAM – TWO SPANS – ALL SPANS LOADED w
LOAD
A
C
B L
L R B=1.25wL =1.25wL
R A=0.375wL =0.375wL
R C=0.375wL =0.375wL
+0.625wL +0.625wL
+0.375wL +0.375wL SHEAR
0.375 L
-0.375wL -0.375wL
-0.625wL -0.625wL 2
+0.0703wL +0.0703wL2
+0.0703wL +0.0703wL
MOMENT -0.125wL -0.125wL
2
2. CONTINOUS BEAM – TWO SPANS – ONE SPAN LOADED w
LOAD
A
C
B L
L
R C=0.0625wL =0.0625wL
R B=0.625wL =0.625wL
R A=0.4375wL =0.4375wL +0.4375wL +0.4375wL
+0.0625wL +0.0625wL
SHEAR
0.4375 L
-0.5625wL -0.5625wL
+0.0957wL +0.0957wL2 MOMENT -0.0625wL -0.0625wL
2
(0.472 L from A)
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3. CONTINOUS BEAM – THREE SPANS – ALL SPANS LOADED w
LOAD
A
C
B
D
L
L
L
R B=1.10wL =1.10wL
R A=0.40wL =0.40wL
R C=1.10wL =1.10wL
+0.50wL +0.50wL
+0.40wL +0.40wL
R D=0.40wL =0.40wL
+0.60wL +0.60wL
SHEAR
0.40 L
-0.60wL -0.60wL
+0.080wL +0.080wL
0.40 L
-0.50wL -0.50wL
2
+0.025wL +0.025wL
+0.080wL +0.080wL
2
-0.40wL -0.40wL
2
MOMENT 2
-0.100wL -0.100wL
-0.100wL -0.100wL
2
(0.446 L from A or or D)
4. CONTINOUS BEAM – THREE SPANS – ONE END EN D SPAN UNLOADED w
LOAD
A
C
B
D
L
L R A=0.383w =0.383w
L R C=0.45wL =0.45wL
R B=1.20wL =1.20wL +0.583wL +0.583wL
+0.383wL +0.383wL
R D=-0.033wL =-0.033wL
+0.033wL +0.033wL
SHEAR
0.383 L
-0.617wL -0.617wL
+0.0735wL +0.0735wL2
0.417 L
-0.417wL -0.417wL +0.080wL +0.080wL
2
+0.0534wL +0.0534wL
2
MOMENT -0.1167wL -0.1167wL
2
2
-0.0333wL -0.0333wL
(0.430 L from A)
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5. CONTINOUS BEAM – THREE SPANS –END SPANS LOADED w
w
LOAD
A
C
B
D
L
L
L R C=0.55wL =0.55wL
R B=0.55wL =0.55wL
R A=0.45wL =0.45wL
R D=0.45wL =0.45wL
+0.55wL +0.55wL
+0.45wL +0.45wL SHEAR
0.45 L
-0.55wL -0.55wL
0.45 L
+0.1013wL +0.1013wL2
+0.1013wL +0.1013wL
-0.45wL -0.45wL
2
MOMENT 2
-0.050wL -0.050wL
(0.479 L from A or D)
6. CONTINOUS BEAM – THREE SPANS – ONE END EN D SPAN LOADED w
LOAD
A
C
B
D
L
L R B=0.650wL =0.650wL
R A=0.433wL =0.433wL +0.433wL +0.433wL
L R D=0.0167wL =0.0167wL
R C=0.100wL =0.100wL
+0.0833wL +0.0833wL
SHEAR
-0.167wL -0.167wL
0.433 L
-0.567wL -0.567wL
+0.0937wL +0.0937wL
2 2
+0.0167wL +0.0167wL MOMENT 2
-0.0667wL -0.0667wL
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