DESIGN AND CONSTRUCTION STEEL DESIGN CE LICENSURE EXAMINATION PROBLEMS STEEL DESIGN
BENDING IN BEAMS 5.
A 10 m steel wide flange beam is laterally supported. The depth of the beam is 700 mm and the web thickness is 10 mm. If Fy is equal to 250 MPa, the allowable bending stress is: (N94 D 22) a. 180 MPa c. 165 MPa b. 150 MPa d. 200 MPa
6.
The structural I-beam supporting a floor carries a floor load of 4.6 kN/m2. The beams span 6.0 m and are simply supported at their ends. Determine the centerline spacing if the allowable stress in the beam is 120 MPa and the section modulus is 534 x 103 mm3. (M95 D 9) a. 3.75 m c. 4.0 m b. 3.45 m d. 3.0 m
7.
A simple beam has a span of 5.0 m. The maximum moment in the beam is 69.0 kN-m. The allowable bending stress is 138 MPa. The required section modulus is: (M96 D 3) a. 2.0 x 103 mm3 c. 250 x 103 mm3 6 3 b. 9.522 x 10 mm d. 500 x 103 mm3
8.
A simply supported steel beam has a span of 6 m and is subjected to a vertical concentrated load of 150 kN acting at midspan. An allowance of 100% for impact is made for the concentrated load only. The beam is laterally supported only at the supports. The 1992 National Structural Code of the Philippines states that the allowable tensile stress for laterally unsupported members subject to bending is 0.60Fy while the allowable compressive stress for laterally unsupported members subject to bending is given by the equation: Fb = [ 2/3 – Fy (L/rt)2 / 10,550,000 Cb ] Fy where Cb may be taken as 1.0 since the maximum moments does not occur at the supports. rt is the radius of gyration comprising the compression flange and 1/3 of the compression web area, taken about the axis in the plane of the web.
STEEL PROPERTIES 1.
2.
The coefficient of expansion of structural steel per degree centigrade is: (N95 D 32) a. 0.25 c. 11.25 x 10-6 b. 0.0000473 d. 0.3 The coefficient of expansion of steel per degree Centigrade is: (N96 D 25) a. 0.000005 c. 11.25 x 10-6 b. 0.0025 d. 0.00125
STEEL SECTION PROPERTIES 3.
4.
The section modulus Sx of a channel with a web depth of h and thickness tw, and flange width b and thickness tf is: (N94 D 24) a. h2 (6 b tf + h tw) / 12 c. 2 b tf + h tw b. h (6 b tf + h tw) / 6d. (2 b tf + h tw3) / 3 A BW 775 x 287 steel I beam has the following dimensions: Total beam depth, H = 775 mm Web thickness, tw = 19 mm Flange width, B = 360 mm Flange thickness, tf = 32 mm The moment of inertia Ix about the principal axis is: (N95 D 21) a. 375,086 cm4 c. 375,086 mm4 6 b. 375,086 mm d. none in the list
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DESIGN AND CONSTRUCTION STEEL DESIGN Steel is A36 with yield strength Fy = 248 MPa. Which of the following most nearly gives the most economical (lightest) section that will limit the flexural stress to the allowable value? (N97 D 24) a. W18x76; beam weight = 1108 N/m, rt = 75 mm, Sx = 0.00239 m3 b. W21x62; beam weight = 911 N/m, rt = 53 mm, Sx = 0.0023 m3 c. W24x68; beam weight = 1000 N/m, rt = 57 mm, Sx = 0.00253 m3 d. W27x84; beam weight = 1234 N/m, rt = 63 mm, Sx = 0.0035 m3 Situation:
9.
A simply supported beam with span of 8 meters is subjected to a uniform vertical downward load equal to 50 kN/m acting on the plane of the minor axis of the beam section, which includes the beam weight. The beam is restrained against lateral buckling on the top and bottom flanges for the entire span. The material is A36 steel with Fy = 248 MPa and modulus of elasticity = 200 GPa. The allowable flexural stress for laterally braced compact sections is 0.66Fy. The allowable deflection is 1/360 of the span. Three compact sections are being considered, as follows, with their respective properties relevant of this problem (length units are in meters): Section Moment of Inertia (Ix) Beam depth (d) W24x55 0.000558 0.598 W21x62 0.000554 0.533 W21x68 0.000616 0.537
Which of the following most nearly gives the minimum section modulus (Sx), in m3, such that the maximum flexural stress will not be exceeded? (M98 D 13) a. 0.0018 c. 0.0024 b. 0.0015 d. 0.0021
10.
11.
Which of the following most nearly gives the minimum moment of inertia (Ix), in m4, such that maximum deflection will not be exceeded? (M98 D 14) a. 0.00065 c. 0.00060 b. 0.00050 d. 0.00055 Assuming that shear stress is not critical, which of the sections being considered is the most economic section that is adequate for the given load? (M98 D 15) a. W21x62 b. W24x55 c. W21x68 d. none of the sections are adequate
Situation:
A floor is made up of a 150 mm thick concrete slab and a 50 mm thick floor finish both of which has a unit weight of 24 kN/m3. The floor also carries a ceiling whose weight is 720 Pa and a live load of 2400 Pa. The floor is supported by simply supported steel beams with a span of 6 m spaced at 3 m on centers. The beam is W14x30, with weight of 440 N/m, depth of 352 mm, and moment of inertia I = 0.000121 m4.
12.
Which of the following most nearly gives the uniform pressure carried by the floor in Pa? (N99 D 7) a. 8200 c. 7840 b. 7200 d. 7920
13.
Which of the following most nearly gives the uniform weight carried by the beam in kN/m? (N99 D 8) a. 32 c. 18 b. 24 d. 28
14.
Which of the following most nearly gives the maximum flexural stress in the beam in MPa? (N99 D 9) a. 160 c. 210 b. 140 d. 120
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DESIGN AND CONSTRUCTION STEEL DESIGN Situation:
16.
17.
Situation:
The properties of W21x147 are as follows: d = 560 mm tw = 18 mm Ix = 1,511 x 106 mm4
Which of the following most nearly gives the minimum section modulus Sx, in m3, such that the maximum flexural stress will not be exceeded? (M00 D 25) a. 0.00382 c. 0.00523 b. 0.00376 d. 0.00315 Which of the following most nearly gives the minimum moment of inertia Ix, in m4, such that the maximum deflection will not be exceeded? (M00 D 26) a. 0.00128 c. 0.00104 b. 0.00098 d. 0.00117 Assuming that shear stress is not critical, which of the sections being considered is the most economic section that is adequate for the given load? (M00 D 27) a. W30x74 b. W24x62 c. W26x66 b. none of the sections are adequate
A simply supported beam has the cross-section shown in the figure. The section is W21x147 A36 steel, compact section with Fy = 248 MPa and reinforced with 12 mm x 360 mm A36 steel plate at the top and bottom. The beam is laterally supported over the entire span of 6 m and carries a uniformly distributed load of 360 kN/m including its own weight. The allowable bending stress for laterally supported compact section is 0.66Fy and allowable shearing stress is 0.4Fy. Allowable deflection is 1/360 of the span.
560 mm
15.
A simply supported beam with span of 10 m is subjected to a uniform vertical downward load equal to 50 kN/m acting on the plane of the minor axis of the beam section, which includes the beam weight. The beam is restrained against lateral buckling on the top and bottom flanges for the entire span. The material is A36 steel with Fy = 248 MPa and modulus of elasticity = 200 GPa. The allowable flexural stress for laterally braced compact sections is 0.66Fy. The allowable deflection is 1/360 of the span. Three compact sections are being considered, as follows, with their respective properties relevant of this problem (length units are in meters): Section Moment of Inertia (Ix) Beam depth (d) W26x66 0.00124 0.654 W30x74 0.00146 0.772 W24x62 0.00119 0.618
12 mm x 360 mm Y
X
18.
Which of the following gives the section modulus of the section in m3? (M01 D 28) a. 0.0076 c. 0.0054 b. 0.0095 d. 0.0058
19.
Which of the following gives the maximum deflection of the beam in mm? (M01 D 29) a. 12.1 c. 15.9 b. 13.7 d. 14.8
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DESIGN AND CONSTRUCTION STEEL DESIGN 20.
Which of the following statements is true for the given section? (M01 D 30) a. The section is adequate for flexure only. b. The section is adequate for shear and deflection only. c. The section is adequate for deflection only. d. The section is not adequate for flexure, shear, and deflection.
Situation: 1. 2.
Section 4.5.1.4 of NSCP states the following for bending of laterally unsupported beam:
Or, when the compression flange is solid and approximately rectangular in cross section and its area is not less than that of the tension flange: Fb =
83000 Cb Af Ld
(4.5-7)
In the foregoing: l distance between cross-section braced against twist or lateral displacement of the compression flange, mm. For cantilevers braced against twist only at the support, l may conservatively be taken as the actual length.
Tension: Fb = 0.60Fy Compression: a. For members meeting the requirements of Sect. 4.9.1.2, having axis of symmetry in, and loaded in, the plane of their web, and compression on extreme fibers of channels bent about their major axis: The larger value computed by formula (4.5-6a) or (4.5-6b) and (4.5.7), as applicable (unless a higher value can be justified on the basis of a more precise analysis), but not more than 0.60Fy.
When
√
703000 Cb L ≤ ≤ Fy rT Fb =
[
2 3
–
When L > rT
√
√
3520000 Cb Fy
Fy ( L / rT )2 10.55 x 106 Cb
]
Fy
(4.5-6a)
3520000 Cb Fy
Fb =
1170 x 103 Cb ( L / rT )2
rT
radius of gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web, mm.
Af
area of the compression flange, mm2.
Cb
= 1.75 + 1.05(M 1/M2) + 0.3(M1/M2)2 but not more than 2.3, where M1 is the smaller and M2 the larger bending moment at the ends of the unbraced length, taken about the strong axis of the member, and where M1/M2 the ratio of end moments, is positive when M1 and M2 have the same sign (reverse curvature bending) and negative when they are of opposite signs (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, the value of Cb shall be taken as unity. When computing Fbx and Fby to be used in formula (4.6-1a), Cb may be computed by the formula given above for frames subject to joint translation, and it shall be taken as unity for frames braced against joint translation. Cb may conservatively be taken as unity for cantilever beams.
W21x62 steel is used as a beam simply supported over a span of 8 m. The beam is laterally unsupported over the entire span. Fy = 250 MPa.
(4.5-6b)
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DESIGN AND CONSTRUCTION STEEL DESIGN The properties of the section are as follows: Depth, d = 533 mm Flange width, bf = 210 mm Flange thickness, tf = 15.6 mm Web thickness, tw = 10.2 mm Radius of gyration, rT = 53.34 mm Section modulus, Sx = 2,077 x 103 mm3 21.
22.
23.
Section 4.5.1.4.5 of the 1992 NSCP gives the allowable stresses, in MPa, for beams not restrained against lateral buckling as follows: 1.
Fb = 0.60Fy 2.
Which of the following gives the value of the ratio L/rT? (N01 D 28) a. 130 c. 170 b. 150 d. 160 Which of the following gives the allowable bending stress in MPa in accordance with the provisions of the National Structural Code of the Philippines? (N01 D 29) a. 150 c. 52.01 b. 78.21 d. 63.77 Which of the following gives the safe uniformly distributed load that the beam can carry in kN/m? (N01 D 30) a. 19.98 c. 16.56 b. 15.21 d. 18.32
Situation:
Tension:
A simply supported beam with span of 8 m is subjected to a counterclockwise moment at the left support and a clockwise moment at the right equal to 25% of the moment at the left support, both acting in the plane of the minor axis of the beam. The beam is not restrained against lateral buckling. The beam is A36 steel with yield strength Fy = 248 MPa. The provisions of the 1992 National Structural Code of the Philippines relevant to this problem are given below. The beam is a W21x62 steel shape, whose relevant properties for this problem are: rT = 0.053 m d = 0.533 m bf = 0.210 m tf = 0.016 m S = 0.002077 m3 ------- 5 -------
Compression: The larger value computed by formula (4.5-6a) or (4.56b) and (4.5-7), as applicable, but not more than 0.60Fy.
When
√
703000 Cb L ≤ ≤ Fy rT Fb =
[
2 3
–
When L > rT
√
√
3520000 Cb Fy
Fy ( L / rT )2 10.55 x 106 Cb
]
Fy
(4.5-6a)
3520000 Cb Fy
Fb =
1170 x 103 Cb ( L / rT )2
(4.5-6b)
Or, when the compression flange is solid and approximately rectangular in cross-section and its area is not less than that of the tension flange: Fb =
83000 Cb Af Ld
(4.5-7)
Where Cb = 1.75 + 1.05(M 1/M2) + 0.3(M1/M2)2 but not more than 2.3, where M1 is the smaller and M2 the larger bending moment at the ends of the unbraced length, taken about the strong axis of the member, and where M1/M2 the ratio of end moments, is positive when M1 and M2 have the same sign (reverse curvature bending) and negative when they are of opposite signs (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this
DESIGN AND CONSTRUCTION STEEL DESIGN
rT
24.
25.
26.
length, the value of Cb shall be taken as unity. When computing Fbx and Fby to be used in formula (4.6-1a), Cb may be computed by the formula given above for frames subject to joint translation, and it shall be taken as unity for frames braced against joint translation. Cb may conservatively be taken as unity for cantilever beams. radius of gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web, mm.
d
depth of beam
bf
width of flange
tf
thickness of flange
Situation:
A simply supported beam with span of 8 m is subjected to a counterclockwise moment at the left support and a counterclockwise moment at the right support equal to 25% of the moment at the left support, both acting in the plane of the minor axis of the beam. The beam is not restrained against lateral buckling. The beam is A36 steel with Fy = 248 MPa. The provisions of the 1992 NSCP is given below. The beam is a W21x62 whose relevant properties are: rT = 0.053 m d = 0.533 m bf = 0.210 m tf = 0.016 m S = 0.002077 m3
Which of the following most nearly gives the slenderness ratio, above which the beam is long with respect to lateral buckling? (M03 D 22) a. 146 c. 86 b. 221 d. 373 Which of the following most nearly gives the allowable flexural stress in the compression flange, in MPa? (M03 D 23) a. 71.5 c. 98.5 b. 64.9 d. 83.1
Section 4.5.1.4.5 of the 1992 NSCP gives the allowable stresses, in MPa, for beams not restrained against lateral buckling as follows: 1. 2.
Tension: Fb = 0.60Fy Compression: The larger value computed by formula (4.5-6a) or (4.56b) and (4.5-7), as applicable, but not more than 0.60Fy.
When
√
Which of the following most nearly gives the maximum value of the moment at the left support, in kN-m? (M03 D 24) a. 82 c. 205 b. 193 d. 378
703000 Cb L ≤ ≤ Fy rT Fb =
[
2 3
–
When L > rT
√
Fy ( L / rT )2 10.55 x 106 Cb
]
Fy
3520000 Cb Fy
Fb =
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√
3520000 Cb Fy
1170 x 103 Cb ( L / rT )2
(4.5-6b)
(4.5-6a)
DESIGN AND CONSTRUCTION STEEL DESIGN Or, when the compression flange is solid and approximately rectangular in cross-section and its area is not less than that of the tension flange: Fb =
83000 Cb Af Ld
Which of the following most nearly gives the allowable flexural stress in the compression flange according to equation 4.5-6a or equation 4.5-6b, as applicable? (N03 D 17) a. 99.9 MPa c. 68.7 MPa b. 86.3 MPa d. 75.4 MPa
29.
Which of the following most nearly gives the maximum value of the moment at the left support, in kN-m? (N03 D 18) a. 254.7 c. 302.1 b. 275.8 d. 287.4
(4.5-7)
Where Cb = 1.75 + 1.05(M 1/M2) + 0.3(M1/M2)2 but not more than 2.3, where M1 is the smaller and M2 the larger bending moment at the ends of the unbraced length, taken about the strong axis of the member, and where M1/M2 the ratio of end moments, is positive when M1 and M2 have the same sign (reverse curvature bending) and negative when they are of opposite signs (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, the value of Cb shall be taken as unity. When computing Fbx and Fby to be used in formula (4.6-1a), Cb may be computed by the formula given above for frames subject to joint translation, and it shall be taken as unity for frames braced against joint translation. Cb may conservatively be taken as unity for cantilever beams.
27.
28.
rT
radius of gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web, mm.
d
depth of beam
bf
width of flange
tf
thickness of flange
SHEAR IN BEAMS 30.
The shear capacity V of a steel wide flange section, 600 mm deep whose web is 9 mm thick, is closest to: (Assume Fy = 200 MPa) (N94 D 36) a. 486 kN c. 432 kN b. 864 kN d. 684 kN
31.
A structural steel I-beam is subjected to a shear of 90 kN. The top and bottom flanges are 12 mm by 150 mm, while the web is 9 mm by 300 mm. The average shearing stress is V/dtw or 33.33 MPa. The moment of inertia I of the section is 108 x 106 mm4 and the first moment of the area Q above the neutral axis is 382,050 mm3. However, the maximum shearing stress is: (M95 D 8) a. 35.37 MPa c. 33.33 MPa b. 14.29 MPa d. 7.77 MPa
32.
A floor is made up of a 150-mm thick concrete slab and 50-mm thick floor finish both of which has a unit weight of 24 kN/m3. The floor also carries a ceiling whose weight is 720 Pa and a live load of 2,400 Pa. The floor is supported by simply supported steel beams with a span of 10 m spaced at 4.6 m on centers, with compression flange rigidly attached to the concrete floor. The steel is A36 with yield strength Fy = 248 MPa. The allowable shear stress specified in the 1992 National Structural Code of the Philippines is 0.40Fy. Considering the weight of the beam, which of the following sections is the most economic (lightest) section for
Which of the following most nearly gives the slenderness ratio, below which the beam is short with respect to lateral buckling? (N03 D 16) a. 65.8 c. 86.3 b. 75.9 d. 95.7
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DESIGN AND CONSTRUCTION STEEL DESIGN the given load, assuming that shear stress governs the design? (N97 D 9) a. W12x19; beam weight = 278 N/m, depth = 309 mm, web thickness = 6 mm b. W10x33; beam weight = 484 N/m, depth = 247 mm, web thickness = 7 mm c. BW300x41; beam weight = 407 N/m, depth = 300 mm, web thickness = 6 mm d. BW300x47; beam weight = 460 N/m, depth = 300 mm, web thickness = 6 mm Situation:
33.
34.
35.
BOLTED AND RIVETED CONNECTIONS 36.
A steel plate is 360 mm wide and 20 mm thick with four bolt holes cut into a plate as shown in the figure. The general expression for the specification method for computing the net area is: An = T [ B – summation (H) + summation (S2/4g) ] where T = thickness of the plate, B is the width, H = diameter of the holes, S = pitch, and g = gage. Which of the following most nearly gives the critical net area (An) of the section in accordance with the 1992 National Structural Code of the Philippines? (N97 D 1)
A beam has a T-section built up by two plates as follows: a 200 mm x 40 mm plate as flange and a 100 mm x 20 mm plate as web. The maximum shear force acting on the beam is 60 kN.
45 mm 45 mm
Which of the following most nearly gives the moment of inertia of the section about the neutral axis, in mm4? (M03 D 7) a. 10,600,000 c. 8,700,000 b. 39,000,000 d. 24,500,000
25 mm hole typ. 3 @ 90 mm
Which of the following most nearly gives the shear stress at the neutral axis, in MPa? (M03 D 8) a. 4.63 c. 1.94 b. 3.28 d. 2.71 Which of the following most nearly gives the shear stress on the web at the junction of the flange and the web, in MPa? (M03 D 9) a. 19.6 c. 31.8 b. 48.2 d. 52.2
60 mm a. b. Situation:
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An = 4,125 mm2 An = 5,625 mm2
c. d.
An = 4,625 mm2 An = 5,125 mm2
A plate with width of 300 mm and thickness of 20 mm is to be connected to two plates of the same width with half the thickness by 25 mm diameter rivets, as shown. The rivet holes have a diameter 2 mm larger than the rivet diameter. The plate is A36 steel with yield strength Fy = 248 MPa, allowable tensile stress of 0.60Fy, and allowable bearing stress of 1.35Fy. The rivets are A502, Grade 2, hot-driven rivets with allowable shear stress of 150 MPa.
400 mm
300 mm
DESIGN AND CONSTRUCTION STEEL DESIGN
60 mm
b
1 2
P P
t
t
/2
P
/2
4
3
100 mm 100 mm
P
100 mm
P
37.
38.
39.
/2 Which of the following most nearly gives the maximum load, in kN, that can be applied to the connection without exceeding the allowable tensile stress in the plates? (M98 D 4) a. 750 c. 700 b. 780 d. 730 Which of the following most nearly gives the maximum load, in kN, that can be applied to the connection without exceeding the allowable shear stress in the rivets? (M98 D 5) a. 640 c. 550 b. 590 d. 700 Which of the following most nearly gives the maximum load, in kN, that can be applied to the connection without exceeding the allowable bearing stress between the plate and the rivets? (M98 D 6) a. 670 c. 620 b. 650 d. 700
Situation:
150 mm P 40.
t = 12 mm
t = 12 mm
P Which of the following most nearly gives the value of b in millimeters? (M02 D 10) a. 28.6 c. 52.1 b. 37.4 d. 19.7
41.
Which of the following most nearly gives the value of the net area for tension in plates in square millimeters? (M02 D 11) a. 3,624 c. 3,867 b. 3,214 d. 4,178
42.
Which of the following most nearly gives the value of P so that the allowable tensile stress on net area will not be exceeded? (M02 D 12) a. 575 kN c. 539 kN b. 687 kN d. 424 kN
A plate with width of 400 mm and thickness of 12 mm is to be connected to a plate of the same width and thickness by 34 mm diameter bolts, as shown in the figure. The holes are 2 mm larger than the bolt diameter. The plate is A36 steel with yield strength Fy = 248 MPa. Allowable tensile stress is 0.60Fy. It is required to determine the value of b so that the net width along bolts 1-2-3-4 is equal to the net width along bolts 1-2-4. ------- 9 -------
DESIGN AND CONSTRUCTION STEEL DESIGN BEAM-COLUMN CONNECTION Situation:
A W16x58 is connected to W18x31 as shown in the figure. The material is A36 steel with Fy = 248 MPa. The allowable bearing stress is 1.35Fy. The rivets are A502 Grade 2 hot-driven rivets with allowable shearing stress of 120 MPa. The support is to be designed using the full strength of the W16x58 beam based on gross section. The properties of the section are: W16x58 Total depth, d = 403 mm Thickness of web, tw = 10 mm W18x31 Flange thickness, tf = 11 mm W18x31 W16x58
2 angles 90 x 90 x 10 43.
Which of the following most nearly gives the minimum diameter of the rivets without exceeding the allowable shearing stress in the rivets? (N98 D 10) a. 20 mm c. 23 mm b. 25 mm d. 28 mm
44.
Which of the following most nearly gives the minimum diameter of the rivets without exceeding the allowable bearing stress in steel? (N98 D 11) a. 30 mm c. 25 mm b. 22 mm d. 36 mm
45.
Which of the following most nearly gives the required diameter of the rivets? (N98 D 12) a. 23 mm c. 30 mm b. 28 mm d. 25 mm ------- 10 -------
