From the given continuous beam with the corresponding loads shown, determine the following.
1) Fixed-end moment @ span AB
2) Distribution factor @ BA in percent
3) Moment @ B.
Solution:
The 5kg. block is at rest at a time t = 0 and is acted upon by a horizontal force P that varies with time t as shown.
1) Which of the following gives the initial acceleration of the block.
2) Which of the following gives the velocity after 5 sec.
3) Which of the following gives the distance traveled after 5 sec.
Solution:
A simply reinforced concrete beam has a width of 250mm and an effective depth of 500mm. Concrete strength is 28MPa and steel yield strength Fy = 280MPa.
1) Which of the following gives us the balance reinforcement ration in percent.
2) Which of the following gives the max. allowable steel area As in accordance with the 1992 NSCP strength design specifications.
3) Which of the following gives the number of 25mmØ bars to be used based on NSCP specs.
Solution:
A beam AB is hinged at B and fixed at A. The beam is 6m. long and with a flexural rigidity of EI = 1200 kN.m2.
1) Which of the following gives the moment that must be applied at B to produce a unit rotation at B.
2) Which of the following gives the reaction at B.
3) Which of the following gives the moment at A.
Solution:
A steel beam having a simple span of 8m. which is laterally unsupported throughout its span carrie a uniform load of 10kN/m and an axial tensile load of 600 kN acting at its centroid. Section 4.5.1.4.5 of the NSCP specs. Which is as follows:
On extreme fibers of flexural members the allowable stresses are as follows:
1. Tension….. Fb = 0.60Fv
2. Compression:
For members meeting the requirements of section 4.9.1.2 having an axis of symmetry 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 0.60Fv.
Or when the compression flange is solid and approximately rectangular in cross section and its area is not less than of the tension flange:
In the foregoing:
L = distance between cross sections braced against twist or lateral displacement of the compression flange in mm. For cantilevers braced against twist only at the support, L may conservatively be taken as the actual length.
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 in mm.
Af = area of compression flange in mm2.
Cb = 1.75 + 1.05(M1/M2) + 0.30(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. Use the interaction formula:
The steel section has the following properties:
A = 0.012m2 Sx = 0.00208m3
rt = 0.053m. d = 0.210m.
tf = 0.016m. Fy = 248MPa
1) Which of the following gives the axial tensile stress if axial load only existed.
2) Which of the following gives the bending stress if bending stress if bending alone existed.
3) Using the interaction formula which of the following gives the value of both axial and bending moment interaction value.
Solution:
A reinforced concrete beam having a simple span of 4.3m. carries uniform dead load of 60kN/m and live load of 90kN/m. The beam has a width of 380mm and an effective depth of 570mm. Specified compressive strength of concrete is 21MPa and capacity reduction factor Ø for shear is 0.85. Section 5.11.3.1 of NSCP specifies that shear strength provided by concrete 
for members subject to shear and flexure only.
1) Which of the following gives the ultimate uniform load.
2) Which of the following gives the ultimate factored shear force.
3) Which of the following gives the nominal shear strength provided by shear reinforcement.
Solution:
A timber beam has a circular cross section having a diameter of 250mm. It has a simple span of 4m. NSCP specs. States that in a circular beam the strength is equal to the strength of square section having the same area.
Allowable stresses of wood are as follows:
Shearing stress parallel to the grain
Fv = 1.73MPa
Bending stress fb = 16.5MPa
Allowable deflection 1/240 of span
Modulus of elasticity of wood = 7.31 GPa
1) Which of the following gives the maximum uniform load so that the allowable shear stress parallel to the grain is not exceeded.
2) Which of the following gives the max. uniform load so that the allowable bending stress is not exceeded.
3) Which of the following gives the max. uniform load so that the allowable deflection is not exceeded.
Solution:
From the given frame shown compute the following:
1) Which of the following gives the reaction F if the reaction at B is 100kN.
2) Which of the following gives the reaction at A
3) Which of the following gives the angle which the resultant reaction at A makes with the horizontal axis measured counterclockwise.
Solution:
The approved agency estimate (AAE) of a Gov’t project is 500M. The bids are:
Bidder A = P354,000,000
Bidder B = P639,000,000
Bidder C = P483,000,000
Bidder D = P583,000,000
Bidder E = P295,000,000
Bidder F = P385,000,000
The implementing rules and regulation of P.D. Decree No. 1594 states that no award of contract shall be made of a bidder whose bid price is higher than the (AGE) Allowable Government Estimate or the (AAE) Approved Agency Estimate whichever is higher, or lower than 70% of the AGE. The Allowable Gov’t. Estimate (AGE) is defined as one half the sum of the (AAE) and the average of all responsive bids. For the purposes of determining the average of responsive bids, bids higher than 120% of the AAE or lower than 60% of AAE shell not be considered.
1) Which of the following are the responsive bidders.
2) Which of the following gives the value of the Allowable Gov’t. Estimate (AGE).
3) Which of the following bidders should the project be awarded.
Solution:
The approved agency estimate (AAE) of a Gov’t. project is 500M. The bids are;
Bidder A = P354,000,000
Bidder B = P639,000,000
Bidder C = P483,000,000
Bidder D = P583,000,000
Bidder E = P295,000,000
Bidder F = P385,000,000
The implementing rules and regulation of P.D. Decree No. 1594 states that no award of contract shall be made ot a bidder whose bid price is higher than the (AGE) Allowable Government Estimate or the (AAE) Approved Agency Estimate whichever is higher, or lower than 70% of the AGE. The Allowable Gov’t. Estimate (AGE) is defined as one half the sum of the (AAE) and the average of all responsive bids. For the purposes of determining the average of reponsive bids, bids higher than 120% of the AAE or lower than 60% of AAE shell not be considered.
1) Which of the following gives the max. value of bid to be considered?
2) Which of the following gives the min. value of bid to be considered.
3) Which of the following are considered responsive bidders?
Solution:
A spiral column having a diameter of 500mm is reinforced with 8-22mmØ vertical bars. The diameter of spiral is 12mmØ and clear steel covering is 40mm. Using fc’ = 28MPa, fy = 415MPa.
1) Which of the following gives the ratio in percent.
2) Which of the following gives the ratio of the center to center reinforcement diameter to the diameter of the column.
3) Which of the following gives the value of the eccentric load P having an eccentricity of 200mm using the interaction diagram.
Solution:
A simply supported steel beam is to be supported over an8m. span. It is to carry a total uniformly distributed load of 40 kN/m on the beam. Assume the compression flange is laterally supported throughout the whole span and the section is a compact section. Fy = 248MPa, fb = 0.66Fy. Allowable delfection is 1/360 of span.
| Section | Ix(m4) | d(m) |
| W 24 x55 | 0.0005619 m4 | 0.599m. |
| W 21 x 57 | 0.0004810m4 | 0.535m. |
| W 21 x 62 | 0.0005536 m4 | 0.533m. |
| W 18 x 71 | 0.0004870 m4 | 0.469m. |
1) Which of the following gives the required section modulus?
2) Which of the following gives the required moment of inertia?
3) Which of the following gives the most economical section?
Solution:
The table shown lists the activities for making up a network diameter for a project together with the duration and the costs of carrying out the work.
| Activity | Duration(days) | Cost/Activity |
| A(0-1) | 4 | P6000 |
| B(1-3) | 10 | P5000 |
| C(1-2) | 12 | P10000 |
| D(3-2) | 3 | P2500 |
| E(2-6) | 12 | P6200 |
| F(2-5) | 6 | P4000 |
| G(2-4) | 10 | P15000 |
| H(5-4) | 3 | P1200 |
| I(4-7) | 4 | P3600 |
| J(7-8) | 8 | P4800 |
| K(6-8) | 11 | P8000 |
| L(8-9) | 2 | P2100 |
1) Which of the following gives the critical path?
2) Which of the following gives the number of days to complete the work?
3) Which of the following gives the total cost of the project?
Solution:
For purposes of implementing the rules and regulations of P.D. 1594 an unbalanced bid shall be defined as a bid containing one or more pay items that are thirty percent (30%) higher than the unit AGE (Approved Government Estimate) in respect to major items whereas other pay items are priced lower than the unit AGE, major items being defined as pay items representing at least twenty percent(20%) of the AAE or the first two items having the highest percentage of the AAE (Approved Agency Estimate) or those indicated/specified in the instructions to Bidders. The quantities, AAE and contract prices for a project are as follows:
| Items | Quantity | AAE
(unit price) |
Contract
(unit price) |
| 1 | 80 | P6000 | P5500 |
| 2 | 400 | P500 | P600 |
| 3 | 50 | P4000 | P4000 |
| 4 | 150 | P2400 | P2700 |
| 5 | 120 | P3500 | P3000 |
1) Which of the following gives the total cost of contract?
2) Which of the following gives the value of the AAE?
3) Which of the following items are considered as major items?
Solution:
A cantilever beam 6m. long is supported by a roller at the right end. It carries a uniform load of 400 kN/m throughout the span.
1) Which of the following gives the nearest deflection at the right end if the roller support is removed.
2) Using super position method, which of the following gives the deflection at the right end if a unit upward force is applied at the right end if the roller is removed.
3) Which of the following gives the reaction at the roller support.
Solution:
From the figure shown, the spring is subjected to an initial tension of 200 N and has a spring constant of 10.2kN/m. A force P is applied at B and D as shown.
1) Which of the following is the force acting on the spring.
2) Which of the following gives the force acting on AB.
3) Which of the following gives the value of P.
Solution:
From the given bracket shown, which consists of two plates riveted to the column by 4-22 mmØ rivets which is subjected to an eccentric load of 150kN.
1) Which of the following gives the shearing stress due to axial load only?
2) Which of the following gives the shearing stress due to moment alone?
3) Which of the following gives the max. shearing stress?
Solution:
Section 5.11.6.1 of the NSCP states that torsion effects shall be included with shear and flexure when the factored torsional moment
Where x = is the shorter overall dimension of a rectangular cross section and y – is the longer overall dimension of a rectangular cross section and θ = 0.85. For members with rectangular or flanged section the sum ∑ x2y shall be taken for the component rectangles of the section but the overhanging flange width used in design shall not exceed 3 times the flange thickness.
A concrete beam having a web thickness of 300mm has a total depth of 700mm with slab thickness of 100mm. If the beam has a spacing of 2m. center to center and fc’ = 20.7
1) Which of the following gives the length of the overhang of the flange.
2) Which of the following gives the values of the torsional property ∑x2y.
3) Which of the following gives the value of the limiting torque (Tu) that the beam could resist.
Solution:
A force of 60kN is acting horizontally, then another force of 50kN is acting upward to the right. If the resultant of these two forces is 95.4kN.
1) At what angle does the resultant makes with the horizontal?
2) At what angle does the 50kN force makes with the horizontal?
3) Compute the horizontal component of the resultant?
Solution:
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