The-figure-given-below-is-the-section-of-the-reinforced-concrete-short-column-Calculate-the-stress-in-the-concrete-and-the-stress-in-the-steel-if-the-axial-load-of-780KN-is-applied-to-the-column-Yo

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Question Number 157139 by chuxx last updated on 20/Oct/21

$$Thefiguregivenbelowisthesection$$$$ofthereinforcedconcreteshortcolumn.$$$$Calculatethestressintheconcrete$$$$andthestressinthesteel,ifthe$$$$axialloadof780KNisappliedto$$$$thecolumn.$$$$$$$${Young}^{\prime }smodulusofsteel=210KN/{mm}^2$$$${Young}^{\prime }smodulusofconcrete=14KN/{mm}^2$$$$diameterofthesteelbars=20mm$$

Commented by chuxx last updated on 20/Oct/21

Answered by mr W last updated on 20/Oct/21

$$F=780KN$$$$\alpha =\frac{Y_{steel}}{Y_{concrete}}=\frac{210}{14}=15$$$$cross-sectiona\times b$$$$nsteelbarswithdiameterd$$$$A_{total}=ab+(\alpha -1)\frac{n\pi d^2}{4}$$$$stressinconcrete{\sigma }_{concrete}=\frac{F}{A_{total}}=\frac{F}{ab+(\alpha -1)\frac{n\pi d^2}{4}}$$$$stressinsteel{\sigma }_{steel}=\alpha {\sigma }_{concrete}=\frac{\alpha F}{ab+(\alpha -1)\frac{n\pi d^2}{4}}$$

Commented by chuxx last updated on 20/Oct/21

$$pleaserecommendanytextbookfor$$$$me.Theones{I}^{\prime }veseenarent$$$$comprehensive=$$

Commented by mr W last updated on 20/Oct/21

$$A_{total}isthe“cross-{section}^{″}asif$$$$allmaterialswereconcrete.since$$$$infactthesteelis\alpha timesstrong$$$$astheconcrete,in{A}_{total}wereplace$$$$thesteelareawithaconcretearea$$$$whichisequalto\alpha timesthesteel$$$$area.$$

Commented by chuxx last updated on 20/Oct/21

$$Thankyousomuch.{It}^{\prime }sbeenalong$$$$time.$$

Commented by chuxx last updated on 20/Oct/21

$$Sir,whileIwaspersonallytrying$$$$tosolveitbeforeIgotconfused$$$$andsentithereIgotthe$$$$A_{concrete}=A_{rectangle}-6A_{circle}$$$$where{A}_{circle}=regionboundedbythe$$$$steelrods$$$$$$$$howthendidyoucomeabout$$$$$$$$A_{total}=ab+(\alpha -1)\frac{n\pi d^2}{4}?$$$$Thanksinadvance.$$

Commented by mr W last updated on 20/Oct/21

$$A_{concrete}=A_{rectangle}-6A_{circle}$$$$thisisthesectionareaofconcrete.$$$$butthesteelbarsalsocarrytheload.$$$$andthesteelis\alpha timesasgoodasthe$$$$concretewith\alpha ={Young}^{\prime }sofsteel/$$$${Young}^{\prime }sofconcrete.sothetotal$$$$sectionareais$$$$A_{total}=A_{concrete}+\alpha A_{steel}$$$$A_{total}=A_{concrete}+\alpha {nA}_{circle}$$$$A_{total}=A_{rectangle}-{nA}_{circle}+\alpha {nA}_{circle}$$$$A_{total}=A_{rectangle}+(\alpha -1){nA}_{circle}$$$$A_{total}=ab+(\alpha -1)\frac{n\pi d^2}{4}$$$$thisisverybasicknowledge,better$$$$trytoreadatextbook.$$

Commented by chuxx last updated on 20/Oct/21

$$I^{\prime }llalsoliketoasksir,whatisthe$$$$differencebetweenthecross-section$$$$and{A}_{total};Ithoughttheywere$$$$supposedtobethesame.$$

Commented by mr W last updated on 20/Oct/21

$$i{can}^{\prime }trecommentyouatextbook,$$$$sinceinfacti{don}^{\prime }treadbookeither.$$$$whatitoldyouaboveisdirectlyfrom$$$$myownunderstandingofthephysics.$$

Commented by chuxx last updated on 20/Oct/21

$$Iammostgrateful.Thankyoufor$$$$alwayshelping.$$

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