Two concrete spans that form a bridge of length L are placed...

Two concrete spans that form a bridge of length $L$ are placed end to end so that no room is allowed for expansion (Fig. $\mathrm{P} 19.55 \mathrm{a} ) .$ If a temperature increase of $\Delta$ Toccurs, what is the height $y$ to which the spans rise when they buckle (Fig. Pl9.55b)?

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Key Concepts

Constrained Expansion and Induced Stress

When thermal expansion is restricted by physical constraints, like fixed supports, the inability of a structure to elongate freely results in the buildup of compressive stresses. Once these stresses reach a critical level, they may cause the structure to buckle, producing out-of-plane deformations such as an upward arch. This interplay between thermal expansion and structural stability is key in design considerations for bridges and similar constructions.

Thermal Expansion

Thermal expansion is the tendency of a material to change its dimensions in response to a change in temperature. Typically, the amount of expansion is proportional to the coefficient of thermal expansion, the original length, and the temperature change. This concept is fundamental in understanding how structures respond to temperature variations.

Structural Buckling

Structural buckling is the phenomenon where a structural element subjected to compressive stress suddenly deforms laterally. When materials or structures are compressed beyond a critical limit, they become unstable and can deflect out of their original alignment. This process is essential in analysis for preventing failure in slender or long-span components.

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