Which one of the following statements is NOT a property of the curves ?
- ABoth the systems of the curves cross each other at 45°.Correct
- BEach system crosses the N.A at 45°.
- CAt any point of a curve the tangent and normal give the directions of the two principal stresses.
- DThe intensity of stress along each curve is the greatest when it is parallel to the length of the beam and diminishes along the curve to zero, where it cuts a face of beam at right angles.
Solution
Concept
Principal stress trajectories (isostatics) in a beam
Step-by-step solution
1. The two systems of trajectories (tensile and compressive) intersect at right angles, since they follow the principal stress directions (statement a says 45°, so it is not a property). 2. Each system crosses the neutral axis at 45° (b true). 3. The tangent and normal give the principal directions (c true). 4. The stress along a trajectory is maximum where it is parallel to the axis and zero where it meets a free face at right angles (d true).
Explanation
Principal stresses act on mutually perpendicular planes, so the trajectories of the two systems cross at 90°.
Why the other options are wrong
(b), (c) and (d) are accepted properties of stress trajectories.
Shortcut
Trajectories: 90° to each other, 45° at the neutral axis.
Common mistake
Confusing 45° at the NA with the angle between the systems.
Correct answer: A) Both the systems of the curves cross each other at 45°.