Tension Members, Net Area and Block Shear

Intended learning outcomes

After this unit, a student should be able to construct a relevant free-body diagram, state the controlling simplifying assumptions, calculate an appropriate order-of-magnitude response, identify a competing limit state, and explain why a real building requires detailed verification under the governing jurisdiction's adopted rules.

Design context

Analyze a tension plate with two alternative hole patterns. Calculate gross and two straight net areas and compare with an idealized force limit. Draw a block-shear path without inventing a code resistance. Discuss how a thicker plate, additional bolts and longer connection length would alter competing mechanisms; record why no one change improves every failure mode.

A productive way to study this unit is to connect its smallest material or member model to the whole building. Every force has an entry point and an exit point; every brace must connect to a supporting system; and every design resistance belongs to a particular structural limit state. The educational calculations in this book aim to train reliable modeling judgment, not to automate sign-off. When the calculation appears simple, spend additional time determining whether the assumed support, material response and loading state can actually occur.

Lesson 2.1: Gross yielding and tensile deformation

Physical principle

The gross section describes the material area that carries average axial force away from discontinuities. Initial axial strain is P/(AE) for a prismatic elastic member, and total elongation is PL/(AE). This average deformation model cannot capture stress concentration near holes, abrupt section changes, or restraint-induced secondary bending.

Engineering method and interpretation

When examining a tension member, trace the force from the applied connection into the usable steel section. Separate gross yielding from net-section rupture: one may develop distributed plastic deformation while another concentrates fracture along the least resistant connected path. Neither check implies that the connection itself is adequate.

Worked engineering illustration

A plate 180 mm wide and 12 mm thick has Ag=2160 mm². With fy=355 MPa its gross section nominal yield force is 766.8 kN. This is a mechanical comparison force, not the code design resistance after factors and all other limit states.

Model boundary and field check

A member may be long enough that service elongation is unacceptable well before gross yielding. Check deflection and connection movement alongside ultimate strength.

Technical reasoning workbook: gross yielding and tensile deformation

Prediction before computation. Identify the assumed primary action and the geometry or material parameter that governs the response. Write a one-line dimensionally consistent prediction about what happens when that parameter increases while all other inputs stay fixed. Where the response might change sign or mode, identify the physical condition that would trigger the change. Do not label an expected trend as a verified result until the force path and boundary conditions are explicit.

Independent calculation. Starting from the illustrated data, reproduce the numerical statement using SI units converted consistently to N and mm. Draw the free-body diagram or a section-force diagram. State an independent check: a reaction sum, a compatibility condition, an equilibrium closure, a limiting case, or a comparison against a fundamental textbook formula. Document numerical precision and avoid reporting more significant figures than the inputs justify.

Alternative system. Now consider the same component embedded in a real building, where the adjacent members and connections are not perfectly idealized. List the changes needed in boundary conditions, force transfer, section behavior, construction stage or local detailing. Explain which changes require a revised analysis, which create additional limit states, and which cannot be resolved without the governing design specification. The alternative should remain physically plausible and must not be treated as a certified design.

Peer-review challenge. A colleague argues that increasing nominal material strength alone will solve the structural issue addressed by “gross yielding and tensile deformation.” Examine this assertion by distinguishing stiffness, strength, global instability, local failure and connectivity. Identify at least one regime where the assertion is incomplete. Support the conclusion using the mechanisms developed above, then state what additional evidence would reverse it.

Communicating results. Prepare a brief calculation note with assumptions, dimensions, unit conversions, governing action and known exclusions. Every graph should name its x- and y-axis units. If the calculation is used to compare alternatives, state which variables were held constant; otherwise the comparison cannot attribute an observed improvement to one design choice.

Lesson 2.2: Net-section fracture and staggered holes

Physical principle

At a bolted connection the net fracture path can be shorter than the gross width because holes remove metal. Where holes are staggered, the critical rupture path may turn between adjacent rows; the geometry correction and multiple candidate paths must be evaluated instead of simply subtracting the number of all holes from one transverse line.

Engineering method and interpretation

Map the bolt arrangement and candidate fracture paths with their actual hole dimensions, edge distances and pitches. A hole nominally specified by bolt diameter is often larger because clearance is required. Net-area approaches can also be reduced by shear lag if only part of a member is connected.

Worked engineering illustration

For a straight path crossing two 22 mm holes in a 240 mm wide, 14 mm plate, the net area is (240−44)×14=2744 mm². With an illustrative ultimate stress of 510 MPa, an ideal net-section force would be 1399.44 kN before applicable effective-area rules and design factors.

Model boundary and field check

Do not apply a stagger correction to an arbitrary candidate path without examining its geometry. A different path can still govern through a shorter net width or a block-shear route.

Technical reasoning workbook: net-section fracture and staggered holes

Prediction before computation. Identify the assumed primary action and the geometry or material parameter that governs the response. Write a one-line dimensionally consistent prediction about what happens when that parameter increases while all other inputs stay fixed. Where the response might change sign or mode, identify the physical condition that would trigger the change. Do not label an expected trend as a verified result until the force path and boundary conditions are explicit.

Independent calculation. Starting from the illustrated data, reproduce the numerical statement using SI units converted consistently to N and mm. Draw the free-body diagram or a section-force diagram. State an independent check: a reaction sum, a compatibility condition, an equilibrium closure, a limiting case, or a comparison against a fundamental textbook formula. Document numerical precision and avoid reporting more significant figures than the inputs justify.

Alternative system. Now consider the same component embedded in a real building, where the adjacent members and connections are not perfectly idealized. List the changes needed in boundary conditions, force transfer, section behavior, construction stage or local detailing. Explain which changes require a revised analysis, which create additional limit states, and which cannot be resolved without the governing design specification. The alternative should remain physically plausible and must not be treated as a certified design.

Peer-review challenge. A colleague argues that increasing nominal material strength alone will solve the structural issue addressed by “net-section fracture and staggered holes.” Examine this assertion by distinguishing stiffness, strength, global instability, local failure and connectivity. Identify at least one regime where the assertion is incomplete. Support the conclusion using the mechanisms developed above, then state what additional evidence would reverse it.

Communicating results. Prepare a brief calculation note with assumptions, dimensions, unit conversions, governing action and known exclusions. Every graph should name its x- and y-axis units. If the calculation is used to compare alternatives, state which variables were held constant; otherwise the comparison cannot attribute an observed improvement to one design choice.

Lesson 2.3: Block shear and connection-region failures

Physical principle

A connection region may fail along a three-sided path involving longitudinal shear surfaces and a transverse tension surface. That mechanism is different from uniform net-section fracture. The available path depends on bolt layout, edge distance, plate thickness and the actual load direction; a narrow end connection may create an unfavorable free edge.

Engineering method and interpretation

Sketch a proposed rupture block. Label gross and net shear areas separately from the net tension area, and check any holes intersecting each plane. Effective force transfer can depend on eccentricity, connection stiffness, bolt bearing and the sequence of load sharing. The teaching laboratory intentionally stops short of providing a complete block-shear strength formula.

Worked engineering illustration

Consider a plate with two rows of bolts and short end distances. Increasing bolt diameter can improve fastener strength while reducing the connected plate’s remaining net metal. Increasing plate width may improve one tensile path while doing little for a short longitudinal shear path.

Model boundary and field check

A high-grade plate connected with too few bolts can fail at the connection before the gross member is fully mobilized. The force path must remain continuous through every detail.

Technical reasoning workbook: block shear and connection-region failures

Prediction before computation. Identify the assumed primary action and the geometry or material parameter that governs the response. Write a one-line dimensionally consistent prediction about what happens when that parameter increases while all other inputs stay fixed. Where the response might change sign or mode, identify the physical condition that would trigger the change. Do not label an expected trend as a verified result until the force path and boundary conditions are explicit.

Independent calculation. Starting from the illustrated data, reproduce the numerical statement using SI units converted consistently to N and mm. Draw the free-body diagram or a section-force diagram. State an independent check: a reaction sum, a compatibility condition, an equilibrium closure, a limiting case, or a comparison against a fundamental textbook formula. Document numerical precision and avoid reporting more significant figures than the inputs justify.

Alternative system. Now consider the same component embedded in a real building, where the adjacent members and connections are not perfectly idealized. List the changes needed in boundary conditions, force transfer, section behavior, construction stage or local detailing. Explain which changes require a revised analysis, which create additional limit states, and which cannot be resolved without the governing design specification. The alternative should remain physically plausible and must not be treated as a certified design.

Peer-review challenge. A colleague argues that increasing nominal material strength alone will solve the structural issue addressed by “block shear and connection-region failures.” Examine this assertion by distinguishing stiffness, strength, global instability, local failure and connectivity. Identify at least one regime where the assertion is incomplete. Support the conclusion using the mechanisms developed above, then state what additional evidence would reverse it.

Communicating results. Prepare a brief calculation note with assumptions, dimensions, unit conversions, governing action and known exclusions. Every graph should name its x- and y-axis units. If the calculation is used to compare alternatives, state which variables were held constant; otherwise the comparison cannot attribute an observed improvement to one design choice.

Lesson 2.4: Tension-member systems and serviceability

Physical principle

Tie rods, hangers, cables, truss members and bracing diagonals all carry tensile forces but differ in geometry, end conditions and the role of pretension. A tension-only element can become slack when load reverses. Adjacent braces may then become necessary to close the lateral force path.

Engineering method and interpretation

Use a whole-system model to determine which members are active in each loading direction. Confirm geometric compatibility: slackness, connection slip and thermal movement can alter the effective stiffness of a nominally axial system. For connection details, check the ability to inspect, replace and protect exposed tension members.

Worked engineering illustration

For a 3 m tie with area 1200 mm², E=200 GPa, and 150 kN tension, elongation is 150,000×3000/(1200×200,000)=1.875 mm. If the same tie must restrain a rotating mechanism, this displacement could be important even when stress remains modest.

Model boundary and field check

The truss model assumes pinned joints and axial bars. Real eccentricities, weld details or asymmetric connections may introduce bending and fatigue demands.

Technical reasoning workbook: tension-member systems and serviceability

Prediction before computation. Identify the assumed primary action and the geometry or material parameter that governs the response. Write a one-line dimensionally consistent prediction about what happens when that parameter increases while all other inputs stay fixed. Where the response might change sign or mode, identify the physical condition that would trigger the change. Do not label an expected trend as a verified result until the force path and boundary conditions are explicit.

Independent calculation. Starting from the illustrated data, reproduce the numerical statement using SI units converted consistently to N and mm. Draw the free-body diagram or a section-force diagram. State an independent check: a reaction sum, a compatibility condition, an equilibrium closure, a limiting case, or a comparison against a fundamental textbook formula. Document numerical precision and avoid reporting more significant figures than the inputs justify.

Alternative system. Now consider the same component embedded in a real building, where the adjacent members and connections are not perfectly idealized. List the changes needed in boundary conditions, force transfer, section behavior, construction stage or local detailing. Explain which changes require a revised analysis, which create additional limit states, and which cannot be resolved without the governing design specification. The alternative should remain physically plausible and must not be treated as a certified design.

Peer-review challenge. A colleague argues that increasing nominal material strength alone will solve the structural issue addressed by “tension-member systems and serviceability.” Examine this assertion by distinguishing stiffness, strength, global instability, local failure and connectivity. Identify at least one regime where the assertion is incomplete. Support the conclusion using the mechanisms developed above, then state what additional evidence would reverse it.

Communicating results. Prepare a brief calculation note with assumptions, dimensions, unit conversions, governing action and known exclusions. Every graph should name its x- and y-axis units. If the calculation is used to compare alternatives, state which variables were held constant; otherwise the comparison cannot attribute an observed improvement to one design choice.

Numerical case studies

Case 2.1: A straight net section through holes

Given: b=260 mm, t=12 mm, two holes d=22 mm, Fu=510 MPa.

Computation: An=(260−44)×12=2592 mm²; ideal force=1321.92 kN.

Interpretation: This ideal force is not design resistance and ignores stagger, shear lag, block shear and connection strength.

Independent audit: Before accepting the numerical answer, identify the dimension of the resulting quantity and confirm it matches the left-hand side of the formula. Replace the nominal input with an independently selected second input and repeat the calculation by hand. A single correct number can conceal an incorrect sign convention, wrong load level, or missing connection effect. State the physical phenomenon left outside the formula.

Case 2.2: Service extension of a long tension rod

Given: P=115 kN, L=7500 mm, A=980 mm², E=200000 MPa.

Computation: δ=PL/(AE)=4.40 mm.

Interpretation: Whether this movement is tolerable is a functional question; the yield-force check alone does not answer it.

Independent audit: Before accepting the numerical answer, identify the dimension of the resulting quantity and confirm it matches the left-hand side of the formula. Replace the nominal input with an independently selected second input and repeat the calculation by hand. A single correct number can conceal an incorrect sign convention, wrong load level, or missing connection effect. State the physical phenomenon left outside the formula.

Unit engineering studio

Analyze a tension plate with two alternative hole patterns. Calculate gross and two straight net areas and compare with an idealized force limit. Draw a block-shear path without inventing a code resistance. Discuss how a thicker plate, additional bolts and longer connection length would alter competing mechanisms; record why no one change improves every failure mode.

Deliverables: A one-page model statement; free-body diagrams with force directions; a tabulated input sheet with units and named sources; independent hand checks; one critical alternative model; a note on code and construction-stage exclusions; and a short professional-style design review. No project outcome should be labeled an approved structural capacity.

Self-assessment

1. Using Gross yielding and tensile deformation, prepare a short calculation or diagram that exposes the role of force-path evidence. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: A plate 180 mm wide and 12 mm thick has Ag=2160 mm². With fy=355 MPa its gross section nominal yield force is 766.8 kN. This is a mechanical comparison force, not the code design resistance after factors and all other limit states.

1. Using Net-section fracture and staggered holes, prepare a short calculation or diagram that exposes the role of unit conversion. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a straight path crossing two 22 mm holes in a 240 mm wide, 14 mm plate, the net area is (240−44)×14=2744 mm². With an illustrative ultimate stress of 510 MPa, an ideal net-section force would be 1399.44 kN before applicable effective-area rules and design factors.

1. Using Block shear and connection-region failures, prepare a short calculation or diagram that exposes the role of alternative restraint. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: Consider a plate with two rows of bolts and short end distances. Increasing bolt diameter can improve fastener strength while reducing the connected plate’s remaining net metal. Increasing plate width may improve one tensile path while doing little for a short longitudinal shear path.

1. Using Tension-member systems and serviceability, prepare a short calculation or diagram that exposes the role of material assumption. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a 3 m tie with area 1200 mm², E=200 GPa, and 150 kN tension, elongation is 150,000×3000/(1200×200,000)=1.875 mm. If the same tie must restrain a rotating mechanism, this displacement could be important even when stress remains modest.

1. Using Gross yielding and tensile deformation, prepare a short calculation or diagram that exposes the role of connection transfer. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: A plate 180 mm wide and 12 mm thick has Ag=2160 mm². With fy=355 MPa its gross section nominal yield force is 766.8 kN. This is a mechanical comparison force, not the code design resistance after factors and all other limit states.

1. Using Net-section fracture and staggered holes, prepare a short calculation or diagram that exposes the role of serviceability. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a straight path crossing two 22 mm holes in a 240 mm wide, 14 mm plate, the net area is (240−44)×14=2744 mm². With an illustrative ultimate stress of 510 MPa, an ideal net-section force would be 1399.44 kN before applicable effective-area rules and design factors.

1. Using Block shear and connection-region failures, prepare a short calculation or diagram that exposes the role of local stability. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: Consider a plate with two rows of bolts and short end distances. Increasing bolt diameter can improve fastener strength while reducing the connected plate’s remaining net metal. Increasing plate width may improve one tensile path while doing little for a short longitudinal shear path.

1. Using Tension-member systems and serviceability, prepare a short calculation or diagram that exposes the role of global stability. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a 3 m tie with area 1200 mm², E=200 GPa, and 150 kN tension, elongation is 150,000×3000/(1200×200,000)=1.875 mm. If the same tie must restrain a rotating mechanism, this displacement could be important even when stress remains modest.

1. Using Gross yielding and tensile deformation, prepare a short calculation or diagram that exposes the role of design-code dependence. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: A plate 180 mm wide and 12 mm thick has Ag=2160 mm². With fy=355 MPa its gross section nominal yield force is 766.8 kN. This is a mechanical comparison force, not the code design resistance after factors and all other limit states.

1. Using Net-section fracture and staggered holes, prepare a short calculation or diagram that exposes the role of inspection feasibility. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a straight path crossing two 22 mm holes in a 240 mm wide, 14 mm plate, the net area is (240−44)×14=2744 mm². With an illustrative ultimate stress of 510 MPa, an ideal net-section force would be 1399.44 kN before applicable effective-area rules and design factors.

1. Using Block shear and connection-region failures, prepare a short calculation or diagram that exposes the role of limiting-case check. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: Consider a plate with two rows of bolts and short end distances. Increasing bolt diameter can improve fastener strength while reducing the connected plate’s remaining net metal. Increasing plate width may improve one tensile path while doing little for a short longitudinal shear path.

1. Using Tension-member systems and serviceability, prepare a short calculation or diagram that exposes the role of model uncertainty. Explain the chosen boundary conditions and identify one omission that could reverse a preliminary conclusion. Answer guide: Your reasoning must identify the relevant physical action, demonstrate dimensional consistency, and state why the illustrative output is not automatically code-based resistance. In particular, start from: For a 3 m tie with area 1200 mm², E=200 GPa, and 150 kN tension, elongation is 150,000×3000/(1200×200,000)=1.875 mm. If the same tie must restrain a rotating mechanism, this displacement could be important even when stress remains modest.