Suspension bridge cable behavior with temperature rise Identify the incorrect statement about a suspension bridge cable when temperature increases (all else equal).

Introduction / Context:
Suspension bridge main cables behave like flexible strings supported at towers and anchored at ends. Temperature changes alter cable length and geometry. Understanding the qualitative effects of thermal expansion is important for expansion joint design, hanger lengths, and serviceability checks.

Given Data / Assumptions:

• Uniform temperature rise; no traffic or wind changes.
• Anchorage and tower supports permit geometric accommodation.
• Cable modeled as a flexible catenary/parabola under uniform load.

Concept / Approach:

Thermal expansion increases the unstressed length. For fixed support spacing, an increase in length necessarily increases sag (dip) to accommodate the extra length. The corresponding horizontal component of cable tension typically drops as sag increases, for the same uniform load and span, because H ≈ wL²/(8f) for a parabolic approximation; larger f (sag) gives smaller H.

Step-by-Step Solution:

Verification / Alternative check:

Simple parametric checks with parabolic cable theory confirm that for constant span and load, increased length correlates with increased dip and reduced horizontal tension.

Why Other Options Are Wrong:

(a) and (b) are true effects; (e) is also generally true. Therefore (c) stating “dip decreases” is incorrect.

Common Pitfalls:

Confusing the influence of live load (which also increases sag) with temperature; assuming fixed tension regardless of geometry.

Final Answer:

The dip of the cable decreases.