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Bending​ ​Stresses​ ​in​ ​Beams Q.1.​ ​Explain​ ​the​ ​concept​ ​of​ ​Simple​ ​bending? 

Q:1:​ ​State​ ​the Q.1.

Q.2.State​ ​the​ ​assumptions​ ​in​ ​Pure(simple)​ ​bending.(VVimp) 

Q​ ​3:​ ​State​ ​the​ ​Flexural​ ​formula​ ​(Bending​ ​Eqn),​ ​State​ ​meaning​ ​of​ ​each​ ​term​ ​in​ ​it?  The​ ​bending​ ​equation​ ​is​ ​given​ ​as,

M I

=

f y

=

E R

Where​ ​M=​ ​Bending​ ​moment​ ​in​ ​N-mm ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​I=​ ​Moment​ ​of​ ​Inertia​ ​in​ ​mm​4 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​f=​ ​bending​ ​stress​ ​in​ ​N/mm​2 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​y=​ ​Distance​ ​of​ ​extreme​ ​fibre​ ​from​ ​neutral​ ​axis​ ​in​ ​mm ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​E=​ ​Youngs​ ​modulus​ ​in​ ​ ​N/mm​2 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​R=​ ​Radius​ ​of​ ​curvature​ ​in​ ​mm Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:8856996116 

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Q.4.What​ ​is​ ​Neutral​ ​axis​ ​ ​in​ ​case​ ​of​ ​Bending? 

In​ ​a​ ​beam​ ​subjected​ ​to​ ​bending,​ ​at​ ​a​ ​level​ ​between​ ​the​ ​top​ ​and​ ​bottom​ ​of​ ​beam,​ ​there​ ​is​ ​a​ ​layer​ ​which​ ​is neither​ ​shortened​ ​nor​ ​elongated.​ ​This​ ​layer​ ​has​ ​neither​ ​tension​ ​nor​ ​compression,​ ​this​ ​layer​ ​is​ ​called neutral​ ​axis. for​ ​a​ ​circular​ ​cross-section​ ​neutral​ ​axis​ ​is​ ​at​ ​centre,​ ​for​ ​rectangular​ ​section​ ​the​ ​neutral​ ​axis​ ​is​ ​at​ ​a distance​ ​of​ ​half​ ​the​ ​thickness​ ​from​ ​upper​ ​or​ ​lower​ ​end.

Q:5.What​ ​do​ ​you​ ​mean​ ​by​ ​Section​ ​modulus​ ​?​ ​State​ ​the​ ​formula​ ​for​ ​section​ ​modulus  of​ ​rectangular​ ​and​ ​circular​ ​section.  The​ ​ratio​ ​of​ ​moment​ ​of​ ​inertia​ ​at​ ​neutral​ ​axis​ ​to​ ​the​ ​maximum​ ​distance​ ​from​ ​neutral​ ​axis​ ​is​ ​called​ ​section Modulus.​ ​It​ ​is​ ​denoted​ ​by​ ​“Z”​ ​and​ ​its​ ​unit​ ​is​ ​mm​3​​ ​. In​ ​bending​ ​equation,

M I

=

f y

f

,

M = yI ,

simplif ying M =

I y

f ​ ​ , M = Z .f

Here​ ​z=I/y​ ​is​ ​called​ ​section​ ​modulus. Section​ ​modulus​ ​for​ ​rectangular

z=

I Y

=

bd3 12 d 2

=

bd2 6

Section​ ​Modulus​ ​for​ ​circular​ ​section

z=

I Y

=

πd4 64 d 2

=

πd3 32

Q:6.​ ​Define​ ​the​ ​term​ ​Moment​ ​of​ ​resistance​ ​. ​ ​ ​ ​ ​In​ ​a​ ​beam​ ​subjected​ ​to​ ​bending​ ​,at​ ​any​ ​ ​section,​ ​compressive​ ​stresses​ ​are​ ​above/below​ ​neutral​ ​axis and​ ​tensile​ ​stresses​ ​are​ ​below/above.​ ​ ​The​ ​resultants​ ​of​ ​these​ ​opposite​ ​stresses​ ​forms​ ​a​ ​couple.​ ​The moment​ ​of​ ​these​ ​couple​ ​is​ ​called​ ​moment​ ​of​ ​resistance. ​ ​ ​ ​ ​“The​ ​algebraic​ ​sum​ ​of​ ​the​ ​moment​ ​about​ ​neutral​ ​axis​ ​of​ ​the​ ​internal​ ​forces​ ​developed​ ​in​ ​a beam​ ​due​ ​to​ ​bending​ ​is​ ​called​ ​the​ ​moment​ ​of​ ​resistance.”

Shaikh​ ​sir’s​ ​Reliance​ ​Academy,​ ​Near​ ​Malabar​ ​Hotel,​ ​Station​ ​road,​ ​Kolhapur​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Contact​ ​:8856996116 

I M f y R E

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