Civil Loading Cases, Construction Stages and Modeling Uncertainty

A structural response depends not only on the magnitude of a load but also on when and where it is applied. A partially constructed structure may have different boundary conditions from its finished condition. Formwork, shoring and temporary bracing can redirect load paths; removing them prematurely can invalidate final-stage calculations. Students should learn to represent each stage with its own free-body diagram and to document assumptions rather than mixing permanent and temporary conditions. Actual design must follow adopted building codes and professionally determined load combinations; introductory case studies intentionally avoid declaring code compliance.

Engineering boundary: These exercises analyze idealized statics models for education. They do not certify structural strength, earthquake/wind resistance, geotechnical bearing, connection design, construction safety, or compliance with any jurisdiction’s building code. Real works require local standards, authoritative loading data and qualified professional checking.

Learning outcomes

• Formulate an explicit free-body model for civil loading cases, construction stages and modeling uncertainty.

• Use signed forces, consistent units and geometric measurements to construct equilibrium relations.

• Check results with an independently chosen equilibrium statement or limiting case.

• Distinguish what idealized statics establishes from what structural design and field verification must establish.

Lesson 8.1: Dead, imposed and lateral actions

Permanent actions include self-weight and fixed construction, while variable actions can depend on use and time. Wind, construction equipment, hydrostatic force and earthquake effects may act horizontally and can create couples with gravity actions.

Governing relationships

For an area load p acting over tributary width b, beam line load w=pb. For a simply supported span L, the vertical reaction under uniform w is wL/2 at each end.

Worked engineering example

A 5 m beam carries self-weight 1.2 kN/m and an assumed temporary load 2 kN/m. If both are present, each reaction is (1.2+2)×5/2=8 kN under the simple model.

Model audit and common error

A load designation is not a code load factor; local building-code inputs are required for design.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving dead, imposed and lateral actions. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.2: Construction stages and changing supports

Analyze before, during and after each critical construction operation. A beam may initially be propped, later become unpropped and finally participate in a composite floor system. Reactions and internal forces change even if the material weight remains constant.

Governing relationships

At each stage k, write the appropriate independent equilibrium equations with that stage’s available reactions and loads. If support layout changes, do not reuse reaction values from another stage.

Worked engineering example

A 6 m precast member that is supported at two ends while transported may experience a different moment diagram when temporarily lifted at internal pick points. Compute each support configuration separately.

Model audit and common error

Sequence assumptions must be recorded; a completed-structure calculation cannot be used automatically for the construction stage.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving construction stages and changing supports. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.3: Tributary areas and lateral-load accounting

Equivalent tributary loading is useful for initial gravity framing checks, but diaphragm behavior and lateral-load paths need separate structural modeling. A concentrated roof machine load cannot always be averaged across the whole floor.

Governing relationships

For a one-way slab with beam spacing s, a uniform area loading p gives an approximate interior-beam line load w=ps; edge beams may have different tributary width.

Worked engineering example

With p=4 kN/m² and spacing 3 m, the interior beam receives 12 kN/m in the assumed one-way load path. Over a 6 m simply supported span, total load is 72 kN, with 36 kN reactions each.

Model audit and common error

The one-way assumption may be invalid for two-way slab behavior or unequal support stiffness.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving tributary areas and lateral-load accounting. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.4: Sensitivity, documentation and the design boundary

An engineering hand calculation is auditable when geometry, loads, assumptions, units and uncertainty are visible. Sensitivity studies test how results shift when important unknowns vary. This is not the same as selecting legal design loads or conducting final safety assessment.

Governing relationships

For RB=Pa/L from a point load P at a, ∂RB/∂a=P/L. The right reaction increases linearly as the load moves right.

Worked engineering example

For P=18 kN, L=9 m, moving the load 0.2 m right increases RB by 18×0.2/9=0.4 kN. A survey error of that size matters when the result lies close to a threshold.

Model audit and common error

Never describe an educational equilibrium calculation as structural design approval.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving sensitivity, documentation and the design boundary. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Integrated civil case study

Construction-stage analysis: track support reactions of a precast slab beam as a temporary point load moves across a span, then demonstrate how removing temporary support assumptions changes the model. Include a list of what must be checked by a qualified structural engineer.

Worked problem studio

Each problem below is a separate numerical case. Work it first without looking at the answer, then compare the force and moment checks. Changing dimensions can reveal near-singular geometry or support reactions that switch direction.

Worked problem 8.1

Given: Construction sequence on a 4.00 m simply supported beam: permanent load 1.00 kN/m always acts; during a later stage add uniform 2.00 kN/m and point 3.00 kN at x=1.00 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.000 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=6.750 kN and RA=(dead+temp)L/2+P(L−a)/L=8.250 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.2

Given: Construction sequence on a 4.35 m simply supported beam: permanent load 1.12 kN/m always acts; during a later stage add uniform 2.25 kN/m and point 3.75 kN at x=1.30 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.436 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=8.455 kN and RA=(dead+temp)L/2+P(L−a)/L=9.955 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.3

Given: Construction sequence on a 4.70 m simply supported beam: permanent load 1.24 kN/m always acts; during a later stage add uniform 2.50 kN/m and point 4.50 kN at x=1.65 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.914 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=10.364 kN and RA=(dead+temp)L/2+P(L−a)/L=11.714 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.4

Given: Construction sequence on a 5.05 m simply supported beam: permanent load 1.36 kN/m always acts; during a later stage add uniform 2.75 kN/m and point 5.25 kN at x=2.02 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=3.434 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=12.478 kN and RA=(dead+temp)L/2+P(L−a)/L=13.528 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.5

Given: Construction sequence on a 5.40 m simply supported beam: permanent load 1.48 kN/m always acts; during a later stage add uniform 3.00 kN/m and point 6.00 kN at x=2.43 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=3.996 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=14.796 kN and RA=(dead+temp)L/2+P(L−a)/L=15.396 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.6

Given: Construction sequence on a 5.75 m simply supported beam: permanent load 1.60 kN/m always acts; during a later stage add uniform 3.25 kN/m and point 6.75 kN at x=2.88 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=4.600 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=17.319 kN and RA=(dead+temp)L/2+P(L−a)/L=17.319 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.7

Given: Construction sequence on a 6.10 m simply supported beam: permanent load 1.72 kN/m always acts; during a later stage add uniform 3.50 kN/m and point 7.50 kN at x=3.35 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=5.246 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=20.046 kN and RA=(dead+temp)L/2+P(L−a)/L=19.296 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.8

Given: Construction sequence on a 6.45 m simply supported beam: permanent load 1.84 kN/m always acts; during a later stage add uniform 3.75 kN/m and point 8.25 kN at x=3.87 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=5.934 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=22.978 kN and RA=(dead+temp)L/2+P(L−a)/L=21.328 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.9

Given: Construction sequence on a 6.80 m simply supported beam: permanent load 1.96 kN/m always acts; during a later stage add uniform 4.00 kN/m and point 9.00 kN at x=1.70 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=6.664 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=22.514 kN and RA=(dead+temp)L/2+P(L−a)/L=27.014 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.10

Given: Construction sequence on a 7.15 m simply supported beam: permanent load 2.08 kN/m always acts; during a later stage add uniform 4.25 kN/m and point 9.75 kN at x=2.15 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=7.436 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=25.555 kN and RA=(dead+temp)L/2+P(L−a)/L=29.455 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.11

Given: Construction sequence on a 7.50 m simply supported beam: permanent load 2.20 kN/m always acts; during a later stage add uniform 4.50 kN/m and point 10.50 kN at x=2.62 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=8.250 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=28.800 kN and RA=(dead+temp)L/2+P(L−a)/L=31.950 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.12

Given: Construction sequence on a 7.85 m simply supported beam: permanent load 2.32 kN/m always acts; during a later stage add uniform 4.75 kN/m and point 11.25 kN at x=3.14 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=9.106 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=32.250 kN and RA=(dead+temp)L/2+P(L−a)/L=34.500 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Unit assessment (with guidance)

Q1. Separate permanent actions, variable imposed actions and construction-stage actions in a simple floor system.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q2. A 6 m beam bears permanent 1.5 kN/m and temporary 3 kN/m. Find reactions for each stage if simply supported.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q3. Explain why temporary shoring cannot be deleted from a construction-stage model before checking the actual sequence.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q4. List the minimum geometry, load, support and uncertainty data to include in an auditable statics calculation.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Interactive experiment

Open [simulation 8](../simulations/simulation-08.html) and vary at least three parameters. Create an observation table from the CSV. Describe one change for which the response is nonlinear, ill-conditioned or physically infeasible.

End-of-unit checklist

• External forces and reactions identified on isolated body.

• Dimensions, datums, load units and sign convention documented.

• Vertical/horizontal resultant and moment balance checked separately.

• Real-world limits and uncertainty recorded before any design interpretation.

Unit 8: Civil loading cases, construction stages and modeling uncertainty

A structural response depends not only on the magnitude of a load but also on when and where it is applied. A partially constructed structure may have different boundary conditions from its finished condition. Formwork, shoring and temporary bracing can redirect load paths; removing them prematurely can invalidate final-stage calculations. Students should learn to represent each stage with its own free-body diagram and to document assumptions rather than mixing permanent and temporary conditions. Actual design must follow adopted building codes and professionally determined load combinations; introductory case studies intentionally avoid declaring code compliance.

Engineering boundary: These exercises analyze idealized statics models for education. They do not certify structural strength, earthquake/wind resistance, geotechnical bearing, connection design, construction safety, or compliance with any jurisdiction’s building code. Real works require local standards, authoritative loading data and qualified professional checking.

Learning outcomes

• Formulate an explicit free-body model for civil loading cases, construction stages and modeling uncertainty.

• Use signed forces, consistent units and geometric measurements to construct equilibrium relations.

• Check results with an independently chosen equilibrium statement or limiting case.

• Distinguish what idealized statics establishes from what structural design and field verification must establish.

Lesson 8.1: Dead, imposed and lateral actions

Permanent actions include self-weight and fixed construction, while variable actions can depend on use and time. Wind, construction equipment, hydrostatic force and earthquake effects may act horizontally and can create couples with gravity actions.

Governing relationships

For an area load p acting over tributary width b, beam line load w=pb. For a simply supported span L, the vertical reaction under uniform w is wL/2 at each end.

Worked engineering example

A 5 m beam carries self-weight 1.2 kN/m and an assumed temporary load 2 kN/m. If both are present, each reaction is (1.2+2)×5/2=8 kN under the simple model.

Model audit and common error

A load designation is not a code load factor; local building-code inputs are required for design.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving dead, imposed and lateral actions. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.2: Construction stages and changing supports

Analyze before, during and after each critical construction operation. A beam may initially be propped, later become unpropped and finally participate in a composite floor system. Reactions and internal forces change even if the material weight remains constant.

Governing relationships

At each stage k, write the appropriate independent equilibrium equations with that stage’s available reactions and loads. If support layout changes, do not reuse reaction values from another stage.

Worked engineering example

A 6 m precast member that is supported at two ends while transported may experience a different moment diagram when temporarily lifted at internal pick points. Compute each support configuration separately.

Model audit and common error

Sequence assumptions must be recorded; a completed-structure calculation cannot be used automatically for the construction stage.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving construction stages and changing supports. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.3: Tributary areas and lateral-load accounting

Equivalent tributary loading is useful for initial gravity framing checks, but diaphragm behavior and lateral-load paths need separate structural modeling. A concentrated roof machine load cannot always be averaged across the whole floor.

Governing relationships

For a one-way slab with beam spacing s, a uniform area loading p gives an approximate interior-beam line load w=ps; edge beams may have different tributary width.

Worked engineering example

With p=4 kN/m² and spacing 3 m, the interior beam receives 12 kN/m in the assumed one-way load path. Over a 6 m simply supported span, total load is 72 kN, with 36 kN reactions each.

Model audit and common error

The one-way assumption may be invalid for two-way slab behavior or unequal support stiffness.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving tributary areas and lateral-load accounting. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Lesson 8.4: Sensitivity, documentation and the design boundary

An engineering hand calculation is auditable when geometry, loads, assumptions, units and uncertainty are visible. Sensitivity studies test how results shift when important unknowns vary. This is not the same as selecting legal design loads or conducting final safety assessment.

Governing relationships

For RB=Pa/L from a point load P at a, ∂RB/∂a=P/L. The right reaction increases linearly as the load moves right.

Worked engineering example

For P=18 kN, L=9 m, moving the load 0.2 m right increases RB by 18×0.2/9=0.4 kN. A survey error of that size matters when the result lies close to a threshold.

Model audit and common error

Never describe an educational equilibrium calculation as structural design approval.

Interpretation task

Prepare a free-body sketch of a civil infrastructure element involving sensitivity, documentation and the design boundary. Mark coordinate axes, every restraint action, all known magnitudes and signed reference distances. Explain which connections or soil assumptions would invalidate the model. Report results in both a compact table and an independent equilibrium check.

Engineering discussion

This topic should be evaluated with the full load path rather than by its equation alone. For civil loading cases, construction stages and modeling uncertainty, the quantities that matter are the action itself, where it enters the idealized body, and which physical connection or foundation provides the balancing action. A model that omits one of these produces a formally neat answer without identifying the actual mechanism. Separating gross structural equilibrium from local member strength prevents that confusion. The analyst should first decide what the isolated body is, then measure or state geometry, then apply equilibrium. If an intermediate step changes the sign convention or datum, it should be flagged in the calculation record. Numerical solutions should preserve enough precision for checks but not imply more site accuracy than the input geometry supports.

Integrated civil case study

Construction-stage analysis: track support reactions of a precast slab beam as a temporary point load moves across a span, then demonstrate how removing temporary support assumptions changes the model. Include a list of what must be checked by a qualified structural engineer.

Worked problem studio

Each problem below is a separate numerical case. Work it first without looking at the answer, then compare the force and moment checks. Changing dimensions can reveal near-singular geometry or support reactions that switch direction.

Worked problem 8.1

Given: Construction sequence on a 4.00 m simply supported beam: permanent load 1.00 kN/m always acts; during a later stage add uniform 2.00 kN/m and point 3.00 kN at x=1.00 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.000 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=6.750 kN and RA=(dead+temp)L/2+P(L−a)/L=8.250 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.2

Given: Construction sequence on a 4.35 m simply supported beam: permanent load 1.12 kN/m always acts; during a later stage add uniform 2.25 kN/m and point 3.75 kN at x=1.30 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.436 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=8.455 kN and RA=(dead+temp)L/2+P(L−a)/L=9.955 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.3

Given: Construction sequence on a 4.70 m simply supported beam: permanent load 1.24 kN/m always acts; during a later stage add uniform 2.50 kN/m and point 4.50 kN at x=1.65 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=2.914 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=10.364 kN and RA=(dead+temp)L/2+P(L−a)/L=11.714 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.4

Given: Construction sequence on a 5.05 m simply supported beam: permanent load 1.36 kN/m always acts; during a later stage add uniform 2.75 kN/m and point 5.25 kN at x=2.02 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=3.434 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=12.478 kN and RA=(dead+temp)L/2+P(L−a)/L=13.528 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.5

Given: Construction sequence on a 5.40 m simply supported beam: permanent load 1.48 kN/m always acts; during a later stage add uniform 3.00 kN/m and point 6.00 kN at x=2.43 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=3.996 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=14.796 kN and RA=(dead+temp)L/2+P(L−a)/L=15.396 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.6

Given: Construction sequence on a 5.75 m simply supported beam: permanent load 1.60 kN/m always acts; during a later stage add uniform 3.25 kN/m and point 6.75 kN at x=2.88 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=4.600 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=17.319 kN and RA=(dead+temp)L/2+P(L−a)/L=17.319 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.7

Given: Construction sequence on a 6.10 m simply supported beam: permanent load 1.72 kN/m always acts; during a later stage add uniform 3.50 kN/m and point 7.50 kN at x=3.35 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=5.246 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=20.046 kN and RA=(dead+temp)L/2+P(L−a)/L=19.296 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.8

Given: Construction sequence on a 6.45 m simply supported beam: permanent load 1.84 kN/m always acts; during a later stage add uniform 3.75 kN/m and point 8.25 kN at x=3.87 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=5.934 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=22.978 kN and RA=(dead+temp)L/2+P(L−a)/L=21.328 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.9

Given: Construction sequence on a 6.80 m simply supported beam: permanent load 1.96 kN/m always acts; during a later stage add uniform 4.00 kN/m and point 9.00 kN at x=1.70 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=6.664 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=22.514 kN and RA=(dead+temp)L/2+P(L−a)/L=27.014 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.10

Given: Construction sequence on a 7.15 m simply supported beam: permanent load 2.08 kN/m always acts; during a later stage add uniform 4.25 kN/m and point 9.75 kN at x=2.15 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=7.436 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=25.555 kN and RA=(dead+temp)L/2+P(L−a)/L=29.455 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.11

Given: Construction sequence on a 7.50 m simply supported beam: permanent load 2.20 kN/m always acts; during a later stage add uniform 4.50 kN/m and point 10.50 kN at x=2.62 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=8.250 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=28.800 kN and RA=(dead+temp)L/2+P(L−a)/L=31.950 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Worked problem 8.12

Given: Construction sequence on a 7.85 m simply supported beam: permanent load 2.32 kN/m always acts; during a later stage add uniform 4.75 kN/m and point 11.25 kN at x=3.14 m. Compare the support reactions.

Solution: Initial stage each reaction = dead×L/2=9.106 kN. During the temporary stage, RB=(dead+temp)L/2+Pa/L=32.250 kN and RA=(dead+temp)L/2+P(L−a)/L=34.500 kN. These values require the same support model at both stages; altered props demand a new free-body diagram.

Review check: State the units and verify whether the result reflects the applied load path. Identify one assumption whose failure would require a new analysis.

Unit assessment (with guidance)

Q1. Separate permanent actions, variable imposed actions and construction-stage actions in a simple floor system.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q2. A 6 m beam bears permanent 1.5 kN/m and temporary 3 kN/m. Find reactions for each stage if simply supported.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q3. Explain why temporary shoring cannot be deleted from a construction-stage model before checking the actual sequence.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Q4. List the minimum geometry, load, support and uncertainty data to include in an auditable statics calculation.

Guidance: Use the governing equation and a labeled diagram from Unit 8; report direction, magnitude, units and model assumptions. Numerical assessment answers should be obtained from the worked methods, not from inspection of figures alone.

Interactive experiment

Open [simulation 8](../simulations/simulation-08.html) and vary at least three parameters. Create an observation table from the CSV. Describe one change for which the response is nonlinear, ill-conditioned or physically infeasible.

End-of-unit checklist

• External forces and reactions identified on isolated body.

• Dimensions, datums, load units and sign convention documented.

• Vertical/horizontal resultant and moment balance checked separately.

• Real-world limits and uncertainty recorded before any design interpretation.