A steel frame is braced against joint translation (sideway). The girders are W21 x 402 with I = 0.0051m4. The columns are W 21 x 93 with I = 0.00086 m4. It is required to determine the effective length of column KL using the alignment chart given. The subscripts A and B in the chart refer to the joints at the two ends of the column section being considered. The factor G is defined as
In which ∑ indicates a summation of all members rigidly connected to that joint. Ic is the moment of inertia and Lc the unsupported length of a column section, and Ig is the moment of inertia and Lg the unsupported length of a girder or other restraining member. In calculating G, only rigidly attached girders or columns are included.
For column ends supported by but not rigidly connected to a footing or foundation, G is theoretically infinity, but, unless actually designed as a true friction free pin, may be taken as “10” for practical designs. If the column end is rigidly attached to a properly designed footing, G may be taken as 1.0.
1. Which of the following most nearly gives the factor G for the top end of member KL.
A. 2.14
B. 1.54
C. 2.87
D. 1.77
2. Which of the following most nearly gives the factor G for the bottom end of member KL.
A. 2.57
B. 1.73
C. 1.54
D. 3.21
3. Which of the following most nearly gives the effective length of column KL in meters.
A. 2.95
B. 3.25
C. 2.64
D. 3.87
Solution:
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A spiral column 500-mm in diameter is reinforced with 8-28mm diameter bars as shown. The interaction diagram for the column is also given.
1. Which of the following most nearly gives the reinforcement ratio in percent.
A. 0.025
B. 0.032
C. 0.016
D. 0.041
2. Which of the following most nearly gives the ratio of eccentricity to column dimension in the direction of bending.
A. 0.40
B. 0.30
C. 0.25
D. 0.35
3. Which of the following most nearly gives the nominal load capacity of the column.
A. 2800
B. 2600
C. 2700
D. 2500
Solution:
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A 200mm wide and 260mm deep Apitong is used as a beam simply supported over a span of 4m and to carry a uniformly distributed load of 10KiloNewton per meter including its own weight. The beam dimension was reduced by 10mm after being planned. The properties of Philippine woods at 80% stress grade is given.
1. Which of the following most nearly gives the maximum bending stress on the beam is MegaPascals.
A. 14
B. 16
C. 12
D. 10
2. Which of the following most nearly gives the maximum shearing stress on the beam in MegaPascals.
A. 0.63
B. 0.25
C. 0.95
D. 0.87
3. Which of the following most nearly gives the maximum deflection in mm.
A. 15.2
B. 18.4
C. 21.3
D. 12.4
Solution:
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Rectangular beams 300mm wide 600mm effective deep and 5.8m long are spaced 3m on centers. These beams are used to support a 90-mm thick concrete slab poured monolithically with the beam, thus the beams may be considered as T-beams. The beams are reinforced for tension only with eight 28-mm diameter bars. Concrete strength fc = 27MPa and steel strength fy = 345 MPa. The provisions of the 1992 Structrural Code of the Philippines regarding T-Beams is given.
1. Which of the following most nearly gives the effective flange width according to the 1992 NSCP, in millimeters.
A. 1450
B. 1740
C. 3000
D. 1250
2. Which of the following most nearly gives the depth of compression block measured from the top of the beam, in millimeters.
A. 68
B. 72
C. 60
D. 51
3. Which of the following most nearly gives the nominal capacity of the beam in KiloNewton-Meter.
A. 854
B. 976
C. 753
D. 1104
Solution:
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The uniform 50-kg plank is resting on rough surfaces at A and B. The coefficients of static friction are shown in the figure. A 100-kg woman starts walking form A toward B. It is required to determine the distance x when the plank starts to slide.
1. Which of the following most nearly gives the total reaction at B in Newtons.
A. 758
B. 742
C. 817
D. 863
2. Which of the following most nearly gives the total reaction at B in Newtons.
A. 680
B. 690
C. 700
D. 670
3. Which of the following most nearly gives the value of x in meters.
A. 1.73
B. 1.85
C. 1.62
D. 1.54
Solution:
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A non-prismatic beam AB is shown. The beam is fixed at B and hinged at A. The beam is loaded with a concentrated moment at A causing a 1-radian rotation at A.
1. Which of the following gives the value of the moments at A.
A. 530EI/1101
B. 532EI/1201
C. 520EI/1301
D. 540EI/1111
2. Which of the following gives the vertical reaction at A.
A. 73EI/1301
B. 96EI/1101
C. 75EI/1111
D. 87EI/1201
3. Which of the following gives the ratio of the moment at B and moment at A.
A. 169/266
B. 185/456
C. 184/385
D. 132/541
Solution:
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For the cable shown
1. Which of the following most nearly gives the tension in segment CD, in KiloNewton:
A. 7.3
B. 6.8
C. 5.2
D. 6.9
2. Which of the following most nearly gives the tension in segment AB, in KiloNewton:
A. 6.8
B. 5.2
C. 6.9
D. 7.3
3. Which of the following most nearly gives the value of h in meters:
A. 2.74
B. 2.57
C. 2.32
D. 3.12
Solution:
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The coplanar force system shown consists of two forces and a couple. All coordinates are in meters.
1. Which of the following most nearly gives the resultant of the force system in Newtons.
A. 16.8
B.14.3
C. 12.2
D. 13.1
2. Which of the following most nearly gives the angle that the resultant forces make with the horizontal axis in degrees (positive counterclockwise)?
A. 72.4
B. 55.2
C. 68.9
D. 65.2
3. Which of the following most nearly gives the y-intercept of the resultant force in meters.
A. 3.14
B. 6.38
C. 2.46
D. 5.34
Solution:
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