Problem $1.$ For each of the beam sections shown below find: a$)$ Centroid, b$)$ Iz $($bending

about horizontal axis$),$ c$)$ Mcr$+$ d$)$ Mcr$*.$ All beams are made with normal weight concrete

unless otherwise indicated.

Problem $2.$ For each of the beam sections shown below find: e$)M{n}^{+},M{n}^{+},ffM{n}^{-},Mn-$

ignoring any compression steel and any tension steel that is not located in the extreme

layer of the beam. Verify if steel has yielded at Mn$+.$

Problem $3.$ For each of the beam sections shown below find: g$)$ Stresses in concrete and

steel when the beam is subjected to the moment $M$ indicated in the figure.