A reinforced concrete beam has a width of 300mm and an effective depth of
450mm. The beam is reinforced with 6-32mmØ bars at the bottom and 2-28mmØ
bars at the top located 65mm from the maximum compression fiber. fc’ = 34.5
MPa, Fy = 345MPa. Assume that the contribution of the compression steel may
not be neglected and that compression steel yields.
1) Which of the following gives the balanced steel ratio.
2) Which of the following gives the depth of the compression block.
3) Which of the following gives the nominal moment capacity of the beam.
Solution:
A composite beam is made up of a wide flange with two cover plates of 320mm x
12mm placed at the top and at the bottom. The beam has a simple span of 6m.
and carries a total load of 360 kN/m.
Allowable bending stress Fb = 150 MPa
Allowable shear stress Fv = 100 MPa
Allowable deflection δ = L/360
Prop. of the wide flange section.
A = 0.02 m2 tw = 0.018 m.
d = 0.56 m.
I =0.001568 m4.
E = 200,000 MPa.
1) Which of the following gives the section modulus of the section.
2) Which of the following gives the deflection of the beam.
3) Is the beam
a. Adequate
b. In adequate for flexure and shear
c. In adequate for flexure and deflection
d. In adequate for flexure, shear and deflection.
Solution:
A 590mm x 590mm reinforced concrete column with section shown is subjected
to a service axial dead load of 450kN. Live load of 500kN, dead load moment of
135 kN/m and live load moment of 150 kN/m. fc’ = 21Mpa and fy = 415Mpa
1) Which of the following gives the equivalent eccentricity of the load on the
column.
2) Which of the following gives the minimum area of steel reinforcement.
3) Which of the following gives the minimum size of steel bars.
Solution:
A rectangular reinforce concrete beam has a width of 250mm, a total depth of
600mm, and an effective depth of 500mm. It is reinforced with 3-25mmØ. Fc’ =
28MPa and fy = 415MPa. The beam is carrying a slab 150mm thick, 5m. wide. The
beam has a span of 6m. If the unit weight of concrete is 24kN/m 3.
1) Which of the following gives the unfactored dead load acting on the beam?
2) Which of the following gives the ultimate moment capacity of the beam?
3) Which of the following gives the unfactored live load that the beam could
support?
Solution:
The base of the footing is 1.8m. below the ground surface. It has a surcharge of
4.8kPa on the ground surface. The thickness of the footing is 1.2m. Allowable
bearing pressure of the soil is 280kPa. Weight of concrete is 24kN/m3 and soil is
18kN/m3.
1) Which of the following gives the effective bearing pressure of soil.
2) Which of the following gives the distance of the resultant force from the
extreme face of the column in order to have a uniform distribution of pressure.
3) Which of the following gives the dimension of the footing.
Solution:
A simply supported steel beam carries a uniform concrete slab 200mm thick. It
carries a ceiling load of 500 Pa and live load pressure equal to 2000Pa. The
length of the beam is 6meters and is spaced at 2m. on centers. Unit weight of
concrete is 24kN/m2. Allowable bending stress for steel beam is 0.66Fy. Modulus
of elasticity is 200GPa. Fy = 248MPa.
1) Which of the following gives the uniform load pressure carried by the beam?
2) Which of the following gives the load carried by the beam in kN/m?
3) Which of the following gives the most economical section?
Section
Moment of
Inertia
Depth
W 12 x
26
0.0000849 m4
0.310 m.
W 12 x
19
0.0000541 m4
0.309 m.
W 12 x
14
0.0000369 m4
0.302 m.
Solution:
Problem
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The
strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find
the width of the strip.
A. 7.1 m
B. 8.1 m
C. 8.7 m
D. 7.7 m
Solution
From ΔABC (By cosine law:)
802=722+962–2(72)(96)cos
=54 64
722=802+962–2(80)(96)cos
=47 22
tan =ch
c=htan54 64
c=0 7096h
tan =ch
c=htan47 22
c=0 9254h
a=b–c–d
a=96–0 7096h–0 9254h
a=96–1 635h
AABED=21(a+b)h
640=21[(96–1 635h)+96]h
1280=192h–1 635h2
1 635h2–192h+1280=0
h=110 34 and 7 09
A closed traverse ABCD has the following data:
Line
Length
Bearing
AB
122.00
N 30° E
BC
149.00
N 60° E
CD
241.00
S 10° E
DA
159.00
N 70° W
1. Determine the corrected bearing of side BC using compass rule.
A. N 59° 11’E
B. N 59° 11’E
C. N 60° 12’E
D. N 60° 49’E
2. Determine the corrected bearing of side CD using the compass rule.
A. 149.632 m
B. 148.368 m
C. 149.547 m
D. 148.453 m
3. Determine the corrected length of side BC using the compass rule.
A. 242.067 m
B. 241.852 m
C. 240.148 m
D. 239.933 m
Solution:
Line
Length
Bearing
Lat
Dep
AB
122.00
N 30° E
105.655
61.000
BC
149.00
N 60° E
74.500
129.038
CD
241.00
S 10° E
-237.339
-41.849
DA
159.00
N 70° W
54.381
-149.411
Perimeter
671
Error
-2.802
-1.223
Compass rule:
The correction to be applied to the latitude (or departure) of any course is to the
total absolute correction in latitude (or departure) as the length of the course is
to the perimeter of the traverse.
Side CL
Corrected
CD
Corrected
Corrected
Corrected Bearing
Latitude
Departure
Length
AB
0.510
106.165
0.222
61.222
122.552
N 29°58’15° E
BC
0.622
75.122
0.271
129.309
149.547
N 59°50’43° E
CD
1.007
-236.332
0.439
-41.410
239.933
S 9°56’18° W
DA
0.664
55.045
0.290
-149.121
158.957
N 59°44’21° E
Concrete beam 8meters long and spaced 4m center-to-center are used to support
a concrete slab 115 mm thick. The beams have effective depth of 650 mm
measured from the slab surface, b w=300mm, and are reinforced for tension only
with six 28-mm-diameter bars. The beams are to be analyzed as T-beams. Steel
yield strength fy=350MPa and concrete strength fc=21MPa.
1. Which of the following most nearly give the width of slab effective as T-beam,
in millimeters?
A. 2000
B. 2140
C. 4000
D. 3250
2. Which of the following most nearly give the depth of compression block in
millimeters?
A. 36.2
B. 45.2
C. 56.3
D. 62.4
3. Which of the following most nearly give the nominal moment capacity of the
beam in KiloNewton-Meter.
A. 563
B. 784
C. 952
D. 817
Solution:
Steel column 3.6m long and hinged at both ends is used to carry an axial load of
800kN. The column is subject to end moments about its strong axis (single
curvature) with M1 = 90%M2. The frame is braced against joint translation and is
not subjected to any transverse loading. F y =248MPa, E=200GPa.
The properties of the section are as follows:
A=0.013 m2 rb=94 mm
Sx=0.00099 m2 K=1.0
1. Which of the following most nearly gives the computed (actual) axial stress of
the column in MegaPascals.
A. 57
B. 75
C. 62
D. 68
2. Which of the following most nearly gives the allowable axial compressive
stress of the column in MegaPascals.
A. 114
B. 120
C. 133
D. 148
3. From a separate calculation with Fb = 149MPa, which of the following most
nearly gives the maximum moment that the column can carry, in KiloNewtonMeter.
A. 85.6
B. 75.4
C. 71.4
D. 78.8
Solution:
A 4-m single span beam having a cross-section of 300mm x 500 mm carries a
uniformly distributed load throughout its span. The beam is 80% stress grade
Apitong with allowable bending stress of 16.5 MegaPascals, allowable shearing
stress of 1.73 MPa and modulus of elasticity of 7.31 GigaPascals. Allowable
deflection is 1/240 of the span.
1. Which of the following most nearly gives the value of the uniform load without
exceeding the allowable bending stress of the beam, in KiloNewton per Meter.
A. 118
B. 103
C. 132
D. 124
2. Which of the following most nearly gives the value of the uniform load without
exceeding the allowable shearing stress of the beam, in KiloNewton per Meter.
A. 63
B. 54
C. 87
D. 75
3. Which of the following most nearly gives the value of the uniform load without
exceeding the allowable deflection, in KiloNewton per Meter.
A. 102
B. 98
C. 124
D. 114
Solution:
A rectangular reinforced concrete beam has a width of 300mm and an effective
depth of 450mm to tension bars. The beam is reinforced with six 32-mmdiameter tension bars and two 28-mm-diameter compression bars with centroid
65mm from extreme concrete fiber. Concrete strength f c=34.5MPa and steel
strength fy=345MPa. Assume that the contribution of the compression steel
cannot be neglected and that compression steel yields.
1. Which of the following most nearly gives the balanced steel ratio if the beam
were
singly
reinforced:
A0.044
B.0.033
C.0.055
D.0.022
2. Which of the following most nearly gives the balanced steel ratio for doubly
reinforced
considering
the
effect
of
the
compression
steel:
A.0.048
B.0.059
C.0.062
D.0.053
3. Which of the following most nearly gives the ultimate moment capacity of the
beam
A.632
B.724
C.517
D. 571
Solution:
in
KiloNewton-Meter.
The beam is 150mm wide and 300mm deep, The allowable bending stress on
extreme fiber is 12MPa. If x=2.5m:
1. Which of the following gives the maximum moment that the beam can resist,
in KiloNewton-meter.
A. 24
B. 16
C. 18
D. 27
2. Which of the following gives maximum value of P, in KiloNewton?
A. 12.5
B. 8.6
C. 9.5
D. 16.4
3. Which of the following gives maximum value of P, in KiloNewton?
A. 27
B. 24
C. 16
D. 18
Solution:
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:
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 Tbeams. 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:
A bar metal 25mm in diameter is tested on a length of 250mm. in tension the
following results were recorded:
Load (kN)
Extension (mm)
10.4
31.2
0.036
0.089
The Young Modulus E is nearly:
Solution:
A strip of steel 1mm thick is bent into an arc of a circle of radius 1.0m E is equal
to 200GPa. The maximum bending stress is:
Solution:
Two pieces of 75mm x 400mm Yacal members under tension are connected
together by means of a lap splice with 9pcs of 25mm dia. Bolts as shown. The
working stresses for 80% visually stress-graded unseasoned Yacal are as
follows:
From table TM-6
Bending and tension parallel to grain
Compression parallel to grain
Compression perpendicular to grain
Shear parallel to grian
-24.5 MPa
-15.8 MPa
-6.27 MPa
-2.49 MPa
1) Which of the following gives the net area of a timber member? Consider hole
diameter to be 2mm larger than the bolt diameter
2) Which of the following gives the safe value of P considering the net area of the
timber member?
3) Which of the following gives the safe value of P considering the bearing of the
bolts on the timber.
Solution:
The T-section shown is formed by joining two rectangular pieces of wood
together. The beam is subjected to a maximum shearing force of 60kN.
1) Which of the following gives the moment of inertia at the neutral axis.
2) Which of the following gives the shearing stress at the neutral axis.
3) Which of the following gives the shearing stress at the junction between the
two pieces of wood.
Solution:
Concrete beam 8meters long and spaced 4m center-to-center are used to support
a concrete slab 115 mm thick. The beams have effective depth of 650 mm
measured from the slab surface, b w=300mm, and are reinforced for tension only
with six 28-mm-diameter bars. The beams are to be analyzed as T-beams. Steel
yield strength fy=350MPa and concrete strength fc=21MPa.
1. Which of the following most nearly give the width of slab effective as T-beam,
in millimeters?
A. 2000
B. 2140
C. 4000
D. 3250
2. Which of the following most nearly give the depth of compression block in
millimeters?
A. 36.2
B. 45.2
C. 56.3
D. 62.4
3. Which of the following most nearly give the nominal moment capacity of the
beam in KiloNewton-Meter.
A. 563
B. 784
C. 952
D. 817
Solution:
A wall footing is shown. The unit weight of soil above footing is 18 kN/m 3 and
unit weight of concrete is 23.5 kN/m 3. Concrete strength fc = 21 MPa and steel
yield strength is fy = 414 MPa. The allowable soil bearing capacity is 210 kPa.
1. Which of the following most nearly gives the effective soil bearing capacity at
the bottom of the footing in KiloPascals.
A. 172
B. 195
C. 186
D. 164
2. Which of the following most nearly gives the dimension (width) of the footing
in meter?
A. 2.5
B. 2.1
C. 3.2
D. 2.8
3. Which of the following most nearly gives the spacing of the 28-mm diameter
main bars, in millimeters?
A. 300
B. 250
C. 400
D. 350
Solution:
A built up section is made up of 3 rectangular plates welded to form an H-beam.
The overall depth is 400mm and is 13 meters long. The slenderness ratio L/r =
200. The max. load in tension is 1600 kN and a min. load in compression is
260kN. The member is to carry a load P = max load + ½ min. load.
1) Compute the required area of the section if allowable stress is 185MPa.
2) Compute the width of the flange if r = ¼ width of flange.
3) Compute the thickness of the plate.
Solution:
A rectangular beam has a width of 250mm and an effective depth of 400mm. The
beam is reinforced at the top and bottom section with a steel covering of 75mm
for the compression bars and has a simple span of 6m.. If carries a uniform live
load of 36kN/m and a dead load of 15kN/m. If fc’=21MPa, fy = 276MPa.
1) Which of the following gives the ultimate uniform load?
2) Which of the following gives the nominal moment capacity of the beam at
balanced condition?
3) Which of the following gives the total steel area in tension.
Solution: