According to the steel beam theory for doubly reinforced concrete beams, which statements describe the assumed force-resisting mechanism?

Introduction / Context:“Steel beam theory” is an idealized approach for doubly reinforced beams in which concrete is assumed not to participate in resisting either compression or tension. The steel on both faces forms a couple, akin to a pure steel section embedded in concrete.

Given Data / Assumptions:

• Concrete in both tension and compression is neglected for flexural resistance.
• Tension and compression steel form the resisting couple.
• Both steels are designed up to the same permissible stress when of the same grade.

Concept / Approach:Under this theory, the internal moment is M = Tz = Cz where T and C are forces in tension and compression steel, respectively, and z is the lever arm. Since concrete is ignored in flexure, the role of concrete is primarily to hold steel in position and provide bond and cover.

Step-by-Step Solution:Assume concrete carries no flexural stress → compression taken by compression steel, tension by tension steel.For identical steel grade and working-stress design, both steels may reach the same permissible stress → equal allowable stress assumption.Hence, all four listed statements follow from the steel beam theory idealization.

Verification / Alternative check:While modern limit-state design considers concrete in compression, the steel beam idealization is used in some theoretical derivations and conservative checks for heavily reinforced sections.

Why Other Options Are Wrong:Each of (a)–(d) is consistent with the theory, so selecting any single statement would be incomplete; “all the above” best represents the model.

Common Pitfalls:Confusing steel beam theory with actual behavior where concrete compression block exists; misapplying the theory to serviceability calculations where concrete stiffness matters.

Final Answer:all the above