Concept
Terminology
Application
Materials
CHAPT ER
3
Materials
Properties of Materials Equipment Production
Actual vs. Ultimate Strength Breaking Strength
Wire Rope Elastic Stretch Design Factors Lifting Load
Standard Productivity Operating Costs Job Size Productivity NCEES – FE Civil Engineering Topics
Materials 8% = 5/60 A. Concrete mix design
B. Asphalt mix design
C. Test methods (e.g., steel, concrete, aggregates, and asphalt)
D. Properties of aggregates
E. Engineering properties of metals
MECHANICAL PROPERTIES OF MATERIALS
61. - Question The breaking strength of a material is also known as its:
a. Ultimate Strength b. Yield Point
c. Proportional Limit d. Elastic Limit
Solution: This question aids to further Review Stress Strain Curves of Mechanical Properties of Materials as shown in Figures 1, 2 and 3 below:
fast facts
Knowledge of the mechanical properties is obtained by testing materials.
Results from the tests depend on the size and shape of material to be tested (specimen), how it is held, and the way of performing the test. The most
common procedures, or standards, that are used in Construction are published by the ASTM.
Strength, hardness, toughness, elasticity, plasticity, brittleness, and ductility and malleability are mechanical properties used as measurements of how metals behave under a load. These properties are described in terms of the types of force or stress that the metal must withstand and how these are resisted.
Common types of stress are compression, tension, shear, torsion, impact, or a combination of these stresses, such as fatigue. Compression stresses develop within a material when forces compress or crush the material.
A column that supports an overhead beam is in compression, and the internal stresses that develop within the column are compression.
Tension (or tensile) stresses develop when a material is subject to a pulling load; for example, when using a wire rope to lift a load or when using it as a guy to anchor an antenna. "Tensile strength" is defined as resistance to longitudinal stress or pull and can be measured in pounds per square inch of cross section. Shearing stresses occur within a material when external forces are applied along parallel lines in opposite directions. Shearing forces can separate material by sliding part of it in one direction and the rest in the opposite direction.
Stress is force per unit area and is usually expressed in pounds per square inch. If the stress tends to stretch or lengthen the material, it is called tensile stress; if to compress or shorten the material, a compressive stress; and if to shear the material, a shearing stress.
Tensile and compressive stresses always act at right-angles to (normal to) the area being considered; shearing stresses are always in the plane of the area (at right-angles to compressive or tensile stresses).
Unit strain is the amount by which a dimension of a body changes when the body is subjected to a load, divided by the original value of the dimension. The simpler term strain is often used instead of unit strain.
Proportional limit is the point on a stress-strain curve at which it begins to deviate from the straight-line relationship between stress and strain.
Elastic limit is the maximum stress to which a test specimen may be subjected and still return to its original length upon release of the load. A material is said to be stressed within the elastic region when the working stress does not exceed the elastic limit, and to be stressed in the plastic region when the working stress does exceed the elastic limit. The elastic limit for steel is for all practical purposes the same as its proportional limit.
Yield point is a point on the stress-strain curve at which there is a sudden increase in strain without a corresponding increase in stress. Not all materials have a yield point.
Yield strength, Sy, is the maximum stress that can be applied without permanent deformation of the test specimen.
Ultimate strength, Su, (also called tensile strength) is the maximum stress value obtained on a stress-strain curve. (answer is a)
Modulus of elasticity, E, (also called Young's modulus) is the ratio of unit stress to unit strain within the proportional limit of a material in tension or compression.
Modulus of elasticity in shear, G, is the ratio of unit stress to unit strain within the proportional limit of a material in shear.
Poisson's ratio, is the ratio of lateral strain to longitudinal strain for a given material subjected to uniform longitudinal stresses within the proportional limit. The term is found in certain
equations associated with strength of materials.
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62. - Question Which of the following stress-strain curves represents a soft and weak material:
Solution: As depicted, stress is on the y-axis while the x-axis represents strain. When a is compared to b, the stress is less. Comparatively, both c and d are characteristically brittle and fail relatively quickly when stress is applied (for example, concrete). (answer is a --- “soft and weak”)
ε σ
ε σ
ε σ
ε σ
c
.
d
.
b
.
a
.
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fast facts
ACTUAL VERSUS ULTIMATE STRENGTH
The major distinction between ASD and LRFD is that the Allowable Stress Design (ASD) compares actual and allowable stresses. Load and
Resistance Factor Design (LRFD) compares required strength to actual strengths. The difference between designing for strengths vs. stresses does not present much of a problem since the difference is normally just multiplying or dividing both sides of the limit state inequalities by a section property.
Figure-1 illustrates the member strength levels computed by the two methods on a typical mild steel load vs. deformation diagram. The combined force levels, Load, Moment, and Shear (Pa, Ma, Va)
for ASD are typically kept below the yield load for the member by computing member load capacity as the nominal strength, Rn, divided by a factor of safety,
that reduces the capacity to a point below yielding. For LRFD, the combined force levels
(ultimate) Load (Pu), Moment (Mu), and Shear (Vu) are kept below a computed member load capacity that is the product of the nominal strength, Rn, times a resistance factor, .
When considering member strengths, the governance is to always keep the final design's actual loads below yielding so as to prevent permanent
deformations in the structure.
Consequently, if the LRFD approach is used, then load factors greater than 1.0 must be applied to the applied loads to express them in terms that are safely comparable to the ultimate strength levels. This is accomplished in the load combination equations that consider the probabilities associated with simultaneous occurrence of different types of loads. For structures subjected to highly unpredictable loads (live, wind, and seismic loads for example) the LRFD eff is higher than the ASD which results in stronger structures.
Figure -1: ASD vs. LRFD Strength Comparison
Rn/ = ASD Capacity
Rn = LRFD Capacity Rn = Nominal Capacity
ELASTIC STRETCH
63. - Question A 70-ft long, ¾” diameter, 6 x 7 FC wire rope is resisting a tension force of 12-kips. The elastic stretch of the steel wire rope given the following properties is most nearly: E = 10,000-ksi; A = 0.288-in2
a. 0.75-in b. 3.5-lb c. 6.3-in d. 9.8-in
Solution: The elongation or “stretch” of wire ropes must be considered in designing temporary bracing and lifting configurations. Elongation comes from two sources: (1) constructional stretch is dependent on the
classification and results primarily from a reduction in diameter as load is applied and the strands compact against each other. Constructional stretch is provided by the manufacturer and is always given. (2) Elastic stretch is caused by deformation of the metal itself when load is applied. Use the following equation to establish a value for elastic stretch:
Where: P= change in load; L=length; A=area of wire rope; E=modulus of elasticity.
Elastic Stretch = 12-kips x 70-ft x 12-in/ft = 3.5-in 0.288-in2 x 10,000-ksi
= 3.5-in (answer is b)
Two popular types of wire rope are: (1) FC or Fiber Core where there are 7 bundles of 7-strands of steel with a fiber rope core (see illustration nearby); and, (2) IWRC or Independent Wire Rope Core where there is an
independent wire rope core inside a wire rope outer wrap.
Elastic Stretch = PL AE
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THERMAL EXPANSION
64. - Question A continuous mullion within an aluminum curtain wall is supported on the edge of a spandrel beam at 40-ft vertical intervals on a 20-story building façade. The linear expansion (in) of the aluminum mullion due to the 100°F thermal extremes and using a factor of safety of two is most nearly:
Apply the following thermal expansion equation (page 33 – Thermal deformations) using the coefficient of linear expansion (α) from the Materials Table on page 38 for aluminum alloy:
Curtain wall is a term used to describe a building façade which does not carry any dead load from the building other than its own dead load, and to transfer horizontal loads (wind loads) applied on the curtain wall. These loads are transferred to the main building structure through connections at floors or columns of the building. A curtain wall is designed to resist air and water infiltration, wind forces acting on the building, seismic forces (usually only those imposed by the inertia of the curtain wall), and its own dead load forces.
Curtain walls are typically designed with extruded aluminum members, although the first curtain walls were made of steel. The aluminum frame is typically in filled with glass, which provides an architecturally pleasing building, as well as benefits such as day lighting. However, parameters related to solar gain control such as thermal comfort and visual comfort are more difficult to control when using highly-glazed curtain walls. Other common infill include: stone veneer, metal panels, louvers, and operable windows or vents.
Curtain walls differ from storefront systems in that they are designed to span multiple floors, and take into consideration design requirements such as: thermal expansion and contraction;
building sway and movement; water diversion; and thermal efficiency for cost-effective heating, cooling, and lighting in the building.
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LIFTING LOAD – OFFSET
65. - Question The rigging configuration shown below will be used to lift a bridge girder using a 200-ton capacity luffing jib crane onto the foundation abutment. The tension force (lb.) in Sling A is most nearly:
a. 12,000 b. 20,000 c. 28,000 d. 40,000
Solution:
By inspection, the center of gravity of the load is offset causing an eccentric load condition. The reaction load is heavier on the left side (RL). The
distribution of the 40,000-lbs load at RL is: (40-ft ÷ 60-ft) ( 40,000-lbs) = 26,667-lbs. The reaction force RL must be adjusted for the slope of the slings. The vector force length of Sling A is √ 602 + 202 = 63.25-ft. The force in Sling A is (63.25-ft ÷ 60-ft) (26,667-lbs) = 28,111-lbs (answer=c)
60-ft
Section View Not to Scale
G
Spreader Beam = 60-ft Sling A
Sling B To Crane Hook
C
40,000-lbs
20-ft 20-ft 40-ft 40-ft
EQUIPMENT PRODUCTION
fast facts
In order to affect job-site productivity, it is necessary to select equipment with proper operating characteristics and a size based on site conditions. The following is a listing of factors which can affect the selection and operation of equipment.
a. Size of the job: Determines size of equipment and quantity.
b. Activity time constraints: Dependent on the project schedule.
c. Availability of equipment: Affected by specialty equipment.
d. Cost of transportation of equipment: Mobilize and demobilize
e. Type of job needed to be performed. Based on equipment capacities f. Workflow: Coordinated to the project sequence
g. Work crowding: Effect of too much activity in one location
h. Space constraints: The performance of equipment is influenced by the spatial limitations for the movement of excavators.
i. Location of dumping areas: Effect on cycle time
j. Weather and temperature: Rain, snow and severe temperature conditions affect the job-site productivity of labor and equipment.
Dump trucks are usually used as haulers for excavated materials as they can move freely with relatively high speeds on city streets as well as on
highways.
The cycle capacity C of a piece of equipment is defined as the number of output units per cycle of operation under standard work conditions. The capacity is a function of the output units used in the measurement as well as the size of the equipment and the material to be processed. The cycle time T refers to units of time per cycle of operation. The standard production rate R of a piece of construction equipment is defined as the number of output units per unit time. Rate = Cycle Capacity Time = Cycle Capacity
Time Rate
DAILY STANDARD PRODUCTION RATE OF EQUIPMENT
66. - Question An excavator with a bucket capacity of 3-yd3 has a standard operating cycle time of 40 seconds. The daily standard production rate of the excavator is most nearly:
a. 2,140-yd3 b. 2,150-yd3 c. 2,160-yd3 d. 2,180-yd3
Solution: The daily standard production rate is as follows:
P = ( )( )( , ) = 2,160 − yd
(answer is c)
Excavator works in tandem with a dump truck to remove spoils off-site.
DAILY STANDARD PRODUCTION RATE OF A DUMP TRUCK
67. - Question A dump truck with a capacity of 26 cubic yards is used to dispose of excavated materials at a dump site 6 miles away. The load time is 40-seconds using a 3-yd3 bucket. The average speed of the dump truck is 25 mph and the dumping time is 46 seconds. A fleet of dump trucks of this capacity is used to dispose of the excavated materials in 8-hours per day. The number of trucks needed daily using a swell of 10% for the soil is most nearly:
a. 5 b. 6 c. 7 d. 8
Solution: Calculate the daily standard production rate of a dump truck:
P = ( )( )( , ) = 2,160yd x 1.1 swell = 2,376yd /day
= ( )( )( , ) = 1,728
= (40 ) = 347
= 1,728 + 347 + 46 = 2,121 The daily dump truck productivity is:
=( )( )( , )
( , ) = 353 Calculate the number of trucks required:
= ( , / ) = 6.73
Therefore, 7 trucks should be used. (answer is c)
PRODUCTIV ITY ANALYSIS AND IMP ROVEMENT
68. - Question An excavator with a bucket capacity of 3-yd3 has a standard production rate of 2,160-yd3 for an 8-hour day. The job site productivity and the actual cycle time of this excavator under the work conditions at the job site that may affect its productivity as shown in the Table, is most nearly:
a. 1,034-yd3 / day and cycle time of 57-sec b. 1,034-yd3 / day and cycle time of 68-sec c. 1,134-yd3 / day and cycle time of 72-sec d. 1,134-yd3 / day and cycle time of 76-sec
Solution: Note that all the factors are less than 1, as such; the job site productivity of the excavator per day is given by:
, (. )(. )(. )(. ) ,
The actual cycle time can be determined as follows:
(. )(. )(. )(. )
(answer is d)
Work Conditions at the Site Factor
Bulk composition 0.954
Soil properties and water content 0.983 Equipment idle time for worker breaks 0.8
Management efficiency 0.7
Soil Compaction 0.83
Cycle time (sec) 40
Dump Truck Volume (CY) 26
Fuel Consumption (gal/hr.) 6.4
Daily Excavator Maintenance (after work hr.) .50
OPERATING COSTS
69. - Question A 160-HP Diesel engine (peak fuel consumption = 0.04-gal/HP-hr) hydraulic excavator operates on a cycle time of 20 seconds during a 50-min/hr. During the filling of the bucket cycle, the excavator’s engine is at full power for 5-seconds. The remainder of the time, the
engine operates at half-power. The fuel consumed per hour is most nearly:
a. 3.33-gal/hr b. 3.63-gal/hr c. 4.00-gal/hr d. 4.33-gal/hr Solution:
Step 1: Calculate the Time Factor (TF):
Time Factor = 50 x 100 = 83.3%
60
Step 2: Calculate the Engine Factor (EF):
Filling the bucket = (5 / 20) x 1 power = 0.25 Rest of Cycle = (15 / 20) x .50 power = 0.375
TOTAL 0.625
Operating Factor = Time Factor x Engine Factor = 0.625 x 0.833 = 0.520 Step 3: Calculate the Fuel Consumed
Fuel consumed = 0.52 x 160-HP x 0.04-gal/HP-hr = 3.33-gal/hr Hr
(answer is a)
Note: Typical Fuel Consumption Standards:
1. Gas engine = 0.06 gal/HP-hr 2. Diesel engine = 0.04 gal/HP-hr
EFFECTS OF JOB SIZE ON PRODUCTIV ITY
70. - Question A general building contractor has established that under a set of "standard" work conditions for building construction, a job requiring 500,000 labor hours is considered standard in determining the base labor productivity. All other factors being the same, the labor productivity index will increase to 1.1 or 110% for a job requiring only 400,000 labor-hours. Assume that a linear relation exists for the range between jobs requiring 300,000 to 700,000 labor hours, the labor
productivity index for a new job requiring 650,000 labor hours under otherwise the same set of work conditions is most nearly:
a. .50 b. .65 c. .78 d. .85 Solution:
Illustrate the Relationship between Productivity Index and Job Size
The labor productivity index “I” for the new job can be obtained by linear interpolation of the available data as follows:
( . . ) , ,
, , .
The result implies that labor is 15% less productive on the large job than on the standard project.
Productivity
5
Labor-hours (00,000)
Figure 1: Linear Interpolation of Productivity Index and Job Size
4 6
1.1 1.0 .85
3 7
MATERIAL SPECIFICATIONS
71. - Question Which of the following statements regarding construction material testing are correct:
I. Construction specifications of required quality and components represent part of the necessary documentation to describe a project.
II. General specifications of work quality are available in numerous fields and are issued in publications of organizations such as the American Society for Testing and Materials (ASTM), the American National Standards Institute (ANSI), or the Construction Specifications Institute (CSI).
III. Distinct specifications are formalized for particular types of construction activities, such as welding standards issued by the American Welding Society (AWS), or for particular facility types, such as the Standard
Specifications for Highway Bridges issued by the American Association of State Highway and Transportation Officials (AASHTO). These general specifications must be modified to reflect local conditions, policies, available materials, local regulations and other special circumstances.
IV. Construction specifications normally consist of a series of instructions or prohibitions for specific operations.
V. Performance specifications have been developed for many construction operations. They specify the required construction process. These
specifications refer to the requirements of the finished facility. The exact method by which this performance is obtained is left to the project owner.
a. I & II b. I, II, & III c. I, II, III, & IV d. I, II, III, IV, & V
Solution: Statement V should read “Rather than specifying the required construction process, these specifications refer to the required performance or quality of the finished facility. The exact method by which this performance is obtained is left to the construction contractor.” For example, traditional specifications for asphalt pavement specified the composition of the asphalt material, the asphalt temperature during paving, and compacting procedures. In contrast, a performance specification for asphalt would detail the desired performance of the pavement with respect to impermeability, strength, etc. How the desired performance level was attained would be up to the paving contractor. In some cases, the payment for asphalt paving might increase with better quality of asphalt beyond some minimum
QUALITY CONTROL PROCESS (QA/QC)
72. - Question Which of the following statements about error analysis are true:
I. The expected value (or: most likely; probable value) of a measurement is the value that has the highest value of being correct.
II. The most probable values are the observed values corrected by an equal part of the total error.
III. Measurements of a given quantity are assumed to be normally distributed.
IV. The interval between the extremes is known as the 50% confidence interval.
V. The probable error of a quantity that has a mean [ μ ] and a standard deviation [ s ] represents that the probability is 50% (or; confidence interval) that a measurement of that quantity will fall within the range of μ ± 0.6745 s or the probable ratio of
precision is μ / 0.6745 s. were measured as: 69°, 168°, 99°, 99°and 107°. The most probable interior angles are most nearly:
The correction to 540° is -2°. As such, subtract 2/5 from all angles to arrive at the most probable interior angle.
69° – (+2/5) = 68.6°
168° – (+2/5) = 167.6°
99° – (+2/5) = 98.6°
99° – (+2/5) = 98.6°
107° – (+2/5) = 106.6° (answer is c)
CONCRETE MIX DESIGN
74. - Question A concrete mix design is 1 : 1.9 : 2.8 by weight. The water cement ratio is 7 gallons of water per sack. The aggregates are SSD and have specific weight of 165 lb/ft3 for both the fine and coarse
aggregate. The concrete yield in cubic feet per sack of cement is most nearly:
a) 3.18 b) 3.53 c) 4.10 d) 4.26
Solution: Create a table and compute the ratios:
Material Ratio Weight per
Sack
Specific Weight
(lbf/ft3)
Absolute Volume (ft3/sack)
Cement 1.0 1 x 94 = 94 195 94/195 = .48
Sand 1.9 1.9 x 94 = 179 165 179/165 = 1.08
Aggregate 2.8 2.8 x 94 = 263 165 263/165 = 1.60
Water 7 / 7.48 = .94
Total = 4.10
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75. - Question A highway bridge project requires a concrete mix.
The mix design has the proportions 1 : 2.7 : 3.65, on a weight basis.
Cement content was specified at 5.6 sacks/yd3. The aggregates are SSD and have specific gravities of 2.65 for both the fine and coarse aggregate.
Cement content was specified at 5.6 sacks/yd3. The aggregates are SSD and have specific gravities of 2.65 for both the fine and coarse aggregate.