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PE Civil: Structural practice questions

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Question 1Project Planning, Means and Methods

In the critical path method, the critical path of a project network is best described as:

  1. The path containing the greatest number of activities
  2. The longest path through the network, which sets the project duration Correct answer.
  3. The path with the highest total cost
  4. The sequence of activities with the most labor hours

Explanation

The critical path is the continuous chain of activities with the longest total duration from project start to finish; it therefore governs the completion date and has zero total float. Any delay on a critical activity delays the project by the same amount.

Question 2Project Planning, Means and Methods

OSHA requires that excavated material and equipment be kept at a minimum distance of how far from the edge of an excavation?

  1. 2 ft Correct answer.
  2. 10 ft
  3. 5 ft
  4. 1 ft

Explanation

OSHA 1926.651(j)(2) requires that spoil piles, equipment, and materials be kept at least 2 ft from the edge of an excavation. The setback prevents surcharging and raveling of the excavation face.

Question 3Project Planning, Means and Methods

What is the principal purpose of reshores placed beneath a newly cast elevated slab after the formwork is stripped?

  1. To camber the slab upward during curing
  2. To carry construction loads from the new slab down to the slab below Correct answer.
  3. To allow formwork to be stripped before the concrete has set
  4. To provide lateral bracing to the building frame during erection

Explanation

Forms may be removed once the slab can support itself and the construction loads imposed on it, but the new slab is not yet at design strength. Reshores distribute the weight of subsequent floors and construction activity to the supporting slabs below.

Question 4Project Planning, Means and Methods

Curing of concrete is primarily intended to:

  1. Accelerate the rate of setting
  2. Reduce the heat of hydration
  3. Maintain moisture and favorable temperature for hydration Correct answer.
  4. Increase the cement content of the mix

Explanation

Curing keeps water available and the temperature favorable so that cement hydration can continue, which develops strength, reduces permeability, and improves durability. Curing does not change the mix proportions.

Question 5Project Planning, Means and Methods

A crane's rated lifting capacity decreases as the load radius increases primarily because:

  1. The engine power available to the hoist decreases with boom extension
  2. The outriggers carry less load at longer radii
  3. The load moment about the tipping axis increases with radius Correct answer.
  4. The strength of the wire rope is reduced at longer boom lengths

Explanation

Capacity is limited by stability and structural strength, both of which are governed by the overturning moment equal to load times radius. As radius grows, a smaller load produces the same moment, so the allowable load drops.

Question 6Project Planning, Means and Methods

A 35-ft-deep excavation on a congested urban site has almost no right-of-way beyond the excavation line, and cross-lot struts would block the excavation. Which support system is most appropriate?

  1. Open caisson sinking
  2. Sloped and benched excavation
  3. Cantilevered sheet piles
  4. Tieback ground anchors Correct answer.

Explanation

Tieback anchors transfer lateral earth pressure to grouted anchors located behind the active soil wedge, leaving the excavation clear of internal bracing. They are well suited to deep cuts where the right-of-way prevents sloping and struts would obstruct work.

Question 7Project Planning, Means and Methods

A 40-ft groundwater drawdown is required for a deep excavation in silty sand. Which dewatering approach is most suitable?

  1. Single-stage wellpoint system
  2. Deep wells with submersible pumps Correct answer.
  3. Horizontal drains drilled from the excavation face
  4. Sump pumping from the excavation bottom

Explanation

Deep wells each contain a submersible pump that can lower the water table well beyond the practical limit of a single-stage wellpoint system, which is generally about 15 to 20 ft of drawdown. Deep wells also handle the larger flows typical of silty sand.

Question 8Project Planning, Means and Methods

Compared with the Standard Proctor test, the Modified Proctor test typically produces:

  1. A higher maximum dry unit weight and a lower optimum moisture content Correct answer.
  2. The same maximum dry unit weight but a lower optimum moisture content
  3. A higher maximum dry unit weight and a higher optimum moisture content
  4. A lower maximum dry unit weight and a higher optimum moisture content

Explanation

The Modified Proctor test uses greater compactive energy (heavier hammer, larger drop, more layers). Greater energy densifies the soil more and drives the optimum moisture content down because less water is needed to lubricate particles into a dense arrangement.

Question 9Project Planning, Means and Methods

During pile driving, a pile advances only 0.1 in. over the last 10 blows. This condition is best described as:

  1. Heave, indicating the pile is being pushed upward by adjacent driving
  2. Set-up, indicating a gain in soil resistance after driving stopped
  3. Refusal, meaning the pile has reached practical penetration resistance Correct answer.
  4. Hard driving, which calls for a larger hammer before any evaluation

Explanation

Refusal occurs when the pile can no longer be advanced appreciably under the hammer energy, indicating the required penetration resistance has effectively been reached. Driving normally stops and the blow count is compared with the acceptance criterion.

Question 10Project Planning, Means and Methods

What is the standard sequence for a bolted structural steel connection during erection?

  1. Field weld the connections, then install the bolts
  2. Fully tighten all bolts as installed, then plumb the frame
  3. Plumb the frame first, then install and tighten all bolts
  4. Install and snug bolts, plumb the frame, then fully tension Correct answer.

Explanation

Connections are assembled with snug-tight bolts so the members are held in place; the frame is then plumbed and aligned, and only afterward are the bolts brought to their required tension. Tensioning before alignment would lock in distortions and induce secondary stresses.

Question 11Project Planning, Means and Methods

During erection of tilt-up wall panels, temporary bracing must be:

  1. Provided on only one panel in three, if panels are interconnected
  2. Removed as soon as the panel is plumb and the crane is released
  3. Omitted, because panels become self-supporting once set on their footings
  4. Kept in place for erection and wind loads until the roof diaphragm is complete Correct answer.

Explanation

A tilt-up panel standing on its footing is essentially an unreinforced vertical plate until it is tied into the roof system. Each panel therefore requires engineered temporary braces that resist erection and wind loads and remain until permanent connections and the diaphragm are complete.

Question 12Project Planning, Means and Methods

A project reports earned value (BCWP) of $400,000 and actual cost (ACWP) of $500,000. The cost performance index and its interpretation are:

  1. 1.25, indicating a cost overrun
  2. 0.80, indicating a cost overrun Correct answer.
  3. 0.80, indicating a cost underrun
  4. 1.25, indicating a cost underrun

Explanation

The cost performance index is CPI = BCWP/ACWP = 400,000/500,000 = 0.80. A CPI below 1.0 means each dollar spent has produced less than a dollar of earned value, so the work is overrunning its budget.

Question 13Project Planning, Means and Methods

An activity has an early start of day 12, early finish of day 20, late start of day 15, and late finish of day 23. Its total float is:

  1. 3 days Correct answer.
  2. 11 days
  3. 23 days
  4. 8 days

Explanation

Total float equals late finish minus early finish (or late start minus early start): 23 - 20 = 3 days, and 15 - 12 = 3 days. It is the amount the activity can slip without delaying the project completion date.

Question 14Project Planning, Means and Methods

Fast-tracking a construction schedule means:

  1. Adding resources and overtime to shorten activity durations
  2. Reducing the project scope to meet the completion date
  3. Overlapping activities that are normally performed in sequence Correct answer.
  4. Removing noncritical activities from the schedule

Explanation

Fast-tracking compresses the schedule by performing phases concurrently, for example starting construction before design is fully complete. It differs from crashing, which adds resources to shorten durations, and it increases coordination risk.

Question 15Project Planning, Means and Methods

The principal advantage of design-build over design-bid-build for an owner is that design-build:

  1. Provides single-point responsibility for design and construction Correct answer.
  2. Eliminates the need for a surety bond
  3. Removes the owner from any quality control involvement
  4. Guarantees the lowest cost through competitive bidding

Explanation

In design-build one entity holds both the design and construction contracts, so the owner has a single party accountable for cost, schedule, and performance. This reduces coordination disputes between a separate designer and builder.

Question 16Project Planning, Means and Methods

During excavation, the contractor encounters a rock layer that was not indicated in the geotechnical baseline report. Under a fixed-price contract containing a differing site conditions clause, this is best characterized as:

  1. A cardinal change requiring a new contract
  2. A Type I differing site condition Correct answer.
  3. A constructive acceleration claim
  4. A suspension of work directed by the owner

Explanation

A Type I differing site condition is a subsurface or latent physical condition that differs materially from what the contract documents indicated. It entitles the contractor to notice and an equitable adjustment in price and time.

Question 17Project Planning, Means and Methods

A contractor needs written clarification of an apparent conflict between two drawing sheets. The proper instrument for this request is:

  1. A request for information (RFI) Correct answer.
  2. A change order
  3. A punch list item
  4. A shop drawing submittal

Explanation

An RFI formally asks the designer to interpret or clarify the contract documents. The response may be issued as a supplemental instruction, and if it alters scope, cost, or time it is later formalized through a change order.

Question 18Project Planning, Means and Methods

A supported scaffold has a minimum base dimension of 5 ft. Without additional restraint such as guying or tying, its height should not exceed:

  1. 30 ft
  2. 15 ft
  3. 25 ft
  4. 20 ft Correct answer.

Explanation

Supported scaffolds are limited to a height-to-base ratio of 4:1 unless they are restrained by guying, tying, or bracing designed for the condition. With a 5-ft base, the limit is 4 x 5 = 20 ft.

Question 19Project Planning, Means and Methods

Under OSHA construction standards, conventional fall protection is required when employees are exposed to an unprotected edge with a fall distance greater than:

  1. 6 ft Correct answer.
  2. 4 ft
  3. 10 ft
  4. 15 ft

Explanation

OSHA 1926.501(b)(1) requires fall protection for employees on walking-working surfaces with an unprotected side or edge 6 ft or more above a lower level. The 4-ft trigger applies in general industry, not construction.

Question 20Project Planning, Means and Methods

When concrete is placed in cold weather, the most important protective measure is:

  1. Wetting the surface continuously during the first day
  2. Keeping the concrete above a specified minimum temperature Correct answer.
  3. Adding water to the mix to keep it workable
  4. Stripping forms early so the surface can be inspected

Explanation

Fresh concrete must be protected from freezing and maintained above a minimum temperature until it has gained sufficient strength to resist damage. Cold slows hydration, and early freezing can permanently destroy the paste structure.

Question 21Project Planning, Means and Methods

The slump test performed in accordance with ASTM C143 measures:

  1. The setting time of the cement paste
  2. The compressive strength of hardened concrete
  3. The air content of the plastic mix
  4. The consistency (workability) of fresh concrete Correct answer.

Explanation

Slump is an index of the consistency of fresh concrete and is used as a field check on workability and batch uniformity. It is not a strength test and does not measure air content or setting time.

Question 22Project Planning, Means and Methods

An excavation is cut in Type B soil. Absent site-specific tabulated data or an engineering analysis, the maximum allowable slope is:

  1. 2 horizontal to 1 vertical
  2. 3/4 horizontal to 1 vertical
  3. 1 horizontal to 1 vertical Correct answer.
  4. 1-1/2 horizontal to 1 vertical

Explanation

OSHA Appendix B to Subpart P assigns maximum slopes of 3/4:1 for Type A, 1:1 for Type B, and 1-1/2:1 for Type C soil. A flatter slope may be used but is not the maximum permitted.

Question 23Project Planning, Means and Methods

A crane's load chart shows a rated capacity of 24,000 lb at the required radius. The hook block weighs 800 lb and the slings and shackles weigh 400 lb. The maximum allowable payload is:

  1. 24,000 lb
  2. 23,200 lb
  3. 22,800 lb Correct answer.
  4. 21,600 lb

Explanation

All lifting gear suspended below the boom tip counts against the rated capacity, so the payload is 24,000 - 800 - 400 = 22,800 lb. The gross load, not just the payload, must remain within the chart value.

Question 24Project Planning, Means and Methods

A performance bond obtained by the contractor protects the owner against:

  1. The contractor's failure to perform the contract as agreed Correct answer.
  2. Price escalation of materials during construction
  3. Defective work discovered during the warranty period
  4. The contractor's failure to pay subcontractors and suppliers

Explanation

A performance bond guarantees that the surety will see the contract completed, either by the contractor or by a replacement, if the contractor defaults. Nonpayment of subcontractors and suppliers is covered by a separate payment bond.

Question 25Project Planning, Means and Methods

In the Last Planner System of lean construction, pull planning is characterized by:

  1. Pushing work forward from the start date using the master schedule
  2. Buffering each activity with a large individual float
  3. Awarding work to the lowest bidder at each phase
  4. Working backward from a milestone to secure trade commitments Correct answer.

Explanation

Pull planning starts at a target milestone and works backward, asking each crew what it needs from predecessors and what it can commit to deliver. The result is a plan built from reliable commitments rather than a schedule pushed down from above.

Question 26Project Planning, Means and Methods

A project requires 20,000 compacted cubic yards of embankment fill. The borrow soil has a shrinkage of 12 percent from the bank state to the compacted state. The bank volume of soil that must be excavated is most nearly:

  1. 24,000 cy
  2. 20,000 cy
  3. 22,700 cy Correct answer.
  4. 17,600 cy

Explanation

Shrinkage is the volume reduction between the in-place bank condition and the compacted fill, so compacted volume equals bank volume multiplied by (1 minus the shrinkage fraction). Rearranging, bank volume = 20,000 / 0.88 = 22,727 cy, which rounds to 22,700 cy.

Question 27Project Planning, Means and Methods

For ordinary portland cement concrete placed under normal conditions, ACI 347 guidance permits removal of elevated slab soffit forms, with the supporting shores left in place, after a minimum curing period of:

  1. 24 hours
  2. 14 days
  3. 21 days
  4. 7 days Correct answer.

Explanation

ACI 347 sets minimum form-removal times by member type: walls, columns, and beam sides may be stripped within about a day, slab soffits at 7 days, and beam and joist soffits at 14 days. The governing criterion is that the concrete must have gained enough strength to carry its own weight plus construction loads.

Question 28Project Planning, Means and Methods

The maximum temperature of ordinary concrete as placed is generally limited to:

  1. 100 deg F
  2. 90 deg F
  3. 95 deg F Correct answer.
  4. 85 deg F

Explanation

ACI 301 and ACI 305 limit the temperature of concrete as placed to 95 deg F for normal conditions. Higher placement temperatures accelerate slump loss, increase water demand, and reduce later-age strength and durability.

Question 29Project Planning, Means and Methods

In the turn-of-nut method for installing high-strength structural bolts, the specified rotation is applied to the nut after the bolt has been:

  1. tensioned with a calibrated wrench to 50 percent of the required pretension
  2. aligned with drift pins and had all drift pins removed
  3. fitted with a direct tension indicator that has closed to the required gap
  4. brought to a snug-tight condition Correct answer.

Explanation

Turn-of-nut relies on controlled thread deformation, and the required rotation is measured from the snug-tight condition, in which the plies are drawn into firm contact. Snugging is done with an impact wrench or a few turns of a spud wrench before the rotation is marked and applied.

Question 30Project Planning, Means and Methods

For concrete specified as f'c = 4,000 psi, ACI 318 acceptance criteria for standard-cured strength tests require that the average of any three consecutive tests equal or exceed f'c and that no individual strength test fall below f'c by more than:

  1. 300 psi
  2. 500 psi Correct answer.
  3. 1,000 psi
  4. 700 psi

Explanation

ACI 318 requires every pair of consecutive tests to average at least f'c and no single test to fall more than 500 psi below f'c. A test result below that threshold triggers investigation of the concrete and possible core testing.

Question 31Project Planning, Means and Methods

Under OSHA construction standards, spoil piles and equipment must be kept back from the edge of an excavation a minimum distance of:

  1. 2 ft Correct answer.
  2. 4 ft
  3. 1 ft
  4. 5 ft

Explanation

OSHA 1926.651(j)(2) requires that excavated material and equipment be placed at least 2 ft from the edge of the excavation. The setback reduces surcharge loading and the risk of spoil falling back into the cut.

Question 32Project Planning, Means and Methods

A crane must operate near an energized overhead power line rated at 46 kV. Absent a permitted option such as a dedicated spotter with a documented encroachment plan, the minimum required clearance between any part of the crane or load and the line is:

  1. 10 ft Correct answer.
  2. 8 ft
  3. 6 ft
  4. 15 ft

Explanation

OSHA 1926.1408 Table A establishes 10 ft as the minimum clearance for power lines rated up to 50 kV. Greater clearances apply as line voltage increases, reaching 20 ft for lines over 350 kV.

Question 33Project Planning, Means and Methods

A crew conflict is resolved by delaying the start of an activity that has 5 days of total float by 4 days. The effect on the schedule is that:

  1. the successor activity must be delayed by the same amount.
  2. completion is unchanged, but only 1 day of total float remains. Correct answer.
  3. the delay is not permitted because float belongs to the owner.
  4. the project completion date is delayed by 4 days.

Explanation

Total float is the amount an activity can slip without moving the project completion date. Delaying by 4 days consumes 4 of the 5 available days, leaving 1 day of float and no change to the project finish.

Question 34Project Planning, Means and Methods

In a unit-price contract, the contractor is paid on the basis of:

  1. documented cost plus a prenegotiated fee
  2. actual measured quantities at the bid unit prices Correct answer.
  3. the engineer's estimated quantities and an agreed margin
  4. the lump sum bid, adjusted only for owner-directed changes

Explanation

A unit-price contract pays for the work actually performed at the contractor's bid price per unit of measurement. Because quantities are estimated in advance, the owner carries the quantity risk while the contractor carries the price risk.

Question 35Project Planning, Means and Methods

A shallow footing excavation in coarse gravel encounters a small, steady seepage that collects in one corner of the excavation. The most suitable and economical dewatering method is:

  1. a wellpoint system connected to a vacuum header
  2. a sump pit with a centrifugal pump at the low corner Correct answer.
  3. deep wells with submersible pumps around the perimeter
  4. eductor wells operating on the venturi principle

Explanation

Sump pumping is the simplest and most economical approach where inflow is small and the soil is coarse enough that water can be collected rather than drawn down. A pit at the low point collects the seepage and a pump removes it, with the pit kept ahead of the excavation bottom.

Question 36Project Planning, Means and Methods

A formal constructability review provides the greatest benefit to the project when it is performed:

  1. at the preconstruction conference after the contract is signed
  2. after bid opening but before contract award
  3. during the contractor's mobilization period
  4. during design, as drawings and specifications are developed Correct answer.

Explanation

Constructability reviews identify conflicts, access problems, and inefficient details while drawings are still being produced, when changes cost almost nothing. Once documents are complete or the contract is awarded, incorporating the same recommendations requires change orders.

Question 37Project Planning, Means and Methods

A new basement excavation will extend 8 ft below the base of an existing spread footing that sits 3 ft from the property line, and the adjacent structure must remain in service. The most appropriate measure is:

  1. A sheeted wall with cross-lot bracing along the property line
  2. Tieback anchors drilled through the adjacent foundation wall
  3. Pit underpinning that carries the footing on new piers Correct answer.
  4. Pressure grouting of the soil beneath the existing footing

Explanation

Underpinning extends the existing foundation down to competent bearing at the new excavation level, transferring the structure's load to new piers or piers and needles. It is the standard solution when a new cut would undermine an adjacent footing that must remain in service.

Question 38Project Planning, Means and Methods

Under OSHA excavation standards, a competent person must inspect an excavation and the adjacent areas:

  1. at the start of the job and after each concrete pour
  2. once per week unless the cut exceeds 10 ft in depth
  3. daily, before each shift, and after rainstorms or other events Correct answer.
  4. only where the excavation exceeds 5 ft and workers enter

Explanation

OSHA 1926.651(k)(1) requires inspection by a competent person at least daily, before the start of each shift, and after any occurrence that could affect stability, such as a rainstorm or vibration. Workers may not enter an excavation that has not been inspected.

Question 39Project Planning, Means and Methods

Two activities on the critical path can be crashed: Activity A can be shortened up to 3 days at an added cost of $2,000 per day, and Activity B up to 4 days at $3,500 per day. The lowest added cost to reduce the project duration by 5 days is:

  1. $14,500
  2. $6,000
  3. $16,000
  4. $13,000 Correct answer.

Explanation

Crashing is applied to critical activities in order of increasing cost per day saved. Crashing A for its full 3 days costs $6,000 and leaves 2 days to recover, which come from B at $3,500 per day ($7,000), for a total of $13,000.

Question 40Project Planning, Means and Methods

For a trench 6 ft deep, OSHA requires a means of exit such as a ladder, stairway, or ramp so that workers need travel no more than what maximum lateral distance to reach it?

  1. 25 ft Correct answer.
  2. 15 ft
  3. 10 ft
  4. 50 ft

Explanation

OSHA 1926.651(c)(2) requires that trench excavations 4 ft or deeper have a means of egress within 25 ft of lateral travel for employees. The limit ensures workers can exit quickly in an emergency.

Question 41Structural Mechanics and Analysis

A single-span beam is fixed at both ends and carries only transverse loading. Its degree of static indeterminacy is:

  1. 1
  2. 3 Correct answer.
  3. 2
  4. 0

Explanation

Each fixed support supplies three reaction components, so six unknowns must be found from only three equations of equilibrium. The excess, 6 minus 3, is the degree of static indeterminacy, which equals 3.

Question 42Structural Mechanics and Analysis

At a truss joint with no external load or support, two non-collinear members meet. The forces in those members are:

  1. Both carry equal tension
  2. Both carry equal compression
  3. The forces are indeterminate
  4. Both are zero-force members Correct answer.

Explanation

Summing forces perpendicular to one member eliminates its unknown and shows the other member force must be zero; repeating perpendicular to the second member shows the first is also zero. Two equilibrium equations at the joint therefore force both member forces to vanish.

Question 43Structural Mechanics and Analysis

A simply supported beam carries a downward uniform load over its full span. Its bending moment diagram is:

  1. A parabolic curve with maximum at midspan Correct answer.
  2. A cubic curve with maximum at quarter span
  3. Constant over the full span
  4. A straight line peaking at midspan

Explanation

For a uniform load w, the moment is w x (L minus x) divided by 2, which is a second-degree curve peaking at wL squared over 8 at midspan. The shear diagram, not the moment diagram, is the straight line in this case.

Question 44Structural Mechanics and Analysis

In a solid circular shaft of diameter d subjected to torque T, the maximum shear stress occurs at:

  1. One-third of the radius from the center
  2. The outer surface Correct answer.
  3. The neutral axis
  4. The centroid of the section

Explanation

Torsional shear stress is tau equal to T r over J and grows linearly with radial distance from the centroid. The largest value therefore occurs at the maximum radius, which is the outer surface.

Question 45Structural Mechanics and Analysis

The Euler buckling load of a pin-ended column of length L and constant flexural rigidity EI is:

  1. π²EI/(4L²)
  2. π²EI/(2L²)
  3. 4π²EI/L²
  4. π²EI/L² Correct answer.

Explanation

The general Euler expression is pi squared EI divided by the square of the effective length. For a pin-ended column the effective length factor is 1.0, so the buckling load is pi squared EI over L squared.

Question 46Structural Mechanics and Analysis

The shear center of a cross section is the point through which a transverse load must pass so that the member experiences:

  1. Maximum torsional moment
  2. Uniform shear distribution
  3. No twisting of the section Correct answer.
  4. Zero bending stress

Explanation

When the transverse load acts through the shear center, the resultant of the shear-flow stresses is collinear with the applied load, so no torque develops. For singly symmetric or unsymmetric sections this point generally does not coincide with the centroid.

Question 47Structural Mechanics and Analysis

A displacement at a specific point of a structure is computed by applying a fictitious unit load at that point and integrating the resulting work. This procedure is the:

  1. Unit load method Correct answer.
  2. Portal method
  3. Moment distribution method
  4. Slope-deflection method

Explanation

The unit load method is the virtual work approach in which a fictitious unit load is placed at the point and in the direction of the required displacement. The internal virtual work computed from that unit load system equals the desired displacement.

Question 48Structural Mechanics and Analysis

In the portal method for approximate lateral load analysis of a multistory frame, the shear carried by an interior column of a story compared with an exterior column of the same story is:

  1. One-quarter as large
  2. Twice as large Correct answer.
  3. One-half as large
  4. Equal in both

Explanation

The portal method assumes inflection points at mid-height of columns and mid-span of girders, and distributes story shear so that an interior column carries twice the shear of an exterior column. This reflects the larger tributary width assigned to interior columns.

Question 49Structural Mechanics and Analysis

For a plane truss with m members, j joints, and r reaction components, the degree of static indeterminacy is:

  1. m + 2j − r
  2. m − r + 2j
  3. 2j − m − r
  4. m + r − 2j Correct answer.

Explanation

A plane truss provides two independent equilibrium equations at each joint, giving 2j equations for m member forces plus r reactions. Indeterminacy is the number of unknowns minus the equations, m plus r minus 2j.

Question 50Structural Mechanics and Analysis

A simply supported beam of span 8 m carries a concentrated load of 12 kN located 3 m from the left support. The vertical reaction at the right support is:

  1. 9.0 kN
  2. 6.0 kN
  3. 4.5 kN Correct answer.
  4. 7.5 kN

Explanation

Taking moments about the left support, the right reaction times 8 m equals 12 kN times 3 m. Solving gives 36 divided by 8, or 4.5 kN, and the remaining 7.5 kN goes to the left support.