BIZOMAT MAKEOS · Strength
C-Frame Throat Check (Curved-Beam Stress, Straight-Beam Comparison, Depth Needed)
Is the throat of this C-frame press or clamp strong enough, how much does the inside corner curvature raise the stress, and what throat depth would meet my allowable?
Check of the throat section of an open-gap C-frame (press frame, punch frame, clamp or hook-shaped bracket) under the working force: direct tension plus bending from the force acting at the gap depth, with the curved-beam stresses at the inner and outer fibres from the neutral-axis shift (as the curved beam tool), the straight-beam combined stress for comparison (as the combined axial and bending stress tool), the curvature factor, and the throat depth needed to bring the inner fibre to your allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Working force across the gap | kN | Force the frame resists across its gap (press tonnage, clamp force). |
| Gap depth (load line to inner face of throat) | mm | Horizontal distance from the line of the force to the inner face of the throat. |
| Throat depth (inner to outer face) | mm | Depth of the rectangular throat section from inner to outer face. |
| Throat width (total plate thickness) | mm | Width of the throat section (total thickness of the side plates for a plate frame). |
| Inner radius of the throat corner | mm | Radius of the inside corner of the throat, measured to the inner face. |
| Allowable stress | MPa | Allowable tensile stress for the frame material and duty. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Working force across the gap
- What it is
- The force acting across the open gap of the C-frame, trying to open the jaws: the press or punch force, or the clamp force the frame reacts.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All stresses rise in proportion to the force.
- Get it right
- Use the largest working force, including any overload the press can deliver, not the average force.
What this means: Gap depth (load line to inner face of throat)
- What it is
- The horizontal distance from the line of action of the force to the inner face of the throat, the reach of the frame’s open side.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bending moment is P × (a + h ÷ 2), so a deeper gap raises the stresses almost in proportion.
- Get it right
- Measure to the inner face of the throat, not to its centre; the tool adds half the throat depth itself.
What this means: Throat depth (inner to outer face)
- What it is
- The depth of the rectangular throat section, measured from the inner face (on the gap side) to the outer face at the back of the frame.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A deeper throat lowers the stresses; the tool also reports the depth that brings the inner fibre stress to the allowable.
- Get it right
- This is the depth in the plane of bending, not the plate thickness.
What this means: Throat width (total plate thickness)
- What it is
- The width of the throat section across the frame, square to the plane of bending; for a frame made of side plates, the total thickness of all plates.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stresses are inversely proportional to the width.
- Get it right
- Add the thickness of every side plate; do not use the width of one plate only.
What this means: Inner radius of the throat corner
- What it is
- The radius of the inside corner of the throat, from the centre of curvature to the inner face, where the curved-beam stress is highest.
- Units and format
- Enter a number in mm: millimetres. The form accepts 1 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger radius reduces the curvature effect and the inner fibre stress.
- Get it right
- A sharp corner (small radius) raises the inner fibre stress well above the straight-beam value.
What this means: Allowable stress
- What it is
- The largest stress you accept in the frame, from the material supplier’s data, your design code or your rules for the duty (static or cyclic press loading).
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For cyclic press loads, use an allowable based on fatigue strength, not static yield.
Method and formulas
- Moment = P × (a + h ÷ 2) about the section centroid.
- Curved beam: r_n = h ÷ ln(r_o ÷ r_i), e = r_c − r_n; σ_i = P ÷ A + M (r_n − r_i) ÷ (A e r_i); σ_o = P ÷ A − M (r_o − r_n) ÷ (A e r_o) (as the curved beam tool).
- Straight beam σ = P ÷ A + 6M ÷ b h² (as the combined axial and bending stress tool); depth needed found by solving σ_i = allowable.
- Example: the inner corner carries 99.063 MPa against 60 MPa by straight-beam theory (×1.651); a 258.48 mm throat meets 120 MPa.
Limitations
- Rectangular throat; I or T sections need their own neutral-axis shift.
- Static stress; press frames also need a fatigue and gap-deflection check.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a C-frame press or punch frame
- Size the throat of a clamp or bracket
- Show why the inside corner of a frame cracks first
Who it is for
- Machine designers
- Press tool designers
- Design engineers
What you get
- Curved-beam inner and outer fibre stresses
- Straight-beam stress and curvature factor
- Throat depth needed
Interpreting the result
- The tighter the corner radius, the more the inner fibre stress exceeds the straight-beam value.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218, 257–260. Topic reference; no source tables or recommended settings are reproduced.
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