15

COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL & ARCHITECTURAL ENGINEERING

CVEN 214: STRENGTH OF MATERIALS

Chapter 6: BENDING Dr Mohammed Elshafie

Fall, 2017

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.







BENDING DEFORMATION OF A STRAIGHT MEMBER As A s s u m p t i o n s : 1. 2. 3. 4.

Plane se section remains plane Leng Length th of long longiitudi tudina nall ax axis rem remai ains ns unch uncha anged nged Plane lane sect sectio ion n rem remai ains ns perp perpen endi dicu cula larr to to the the longitudinal axis In-pl n-plan ane e dis disttorti ortion on of sec secti tion on is negl neglig igib ible le









FLEXURAL FORMULA As A s s u m p t i o n s : Material behaves in a linear-elastic manner so that Hooke’s Law Applies; i.e. σ=E.є σ

=−

My I

( M R ) Z = ∑ M Z ;

∫

M = ydF = M =

σ max

∫

A

∫

A

2

y (σ dA) =

y dA

∫

A

 y  σ max dA  c 

y









EXAMPLE 4 The simply supported beam in Fig. 6–26a 6–26 a has the crosssectional area shown in Fig. 6–26b 6–26b. Determine the absolute maximum bending stress in the beam and draw the stress distribution over the cross section at this location.









EXAMPLE 4 (cont.) Solutions • The maximu maximum m inter interna nall momen momentt in in the the beam, beam, 22.5 22.5 kN.m, kN.m, occurs at the center. • By reas reasons ons of symme symmetry, try, the neutra neutrall axis axis passe passes s throu through gh the the centroid C at the mid-height of the beam, Fig. 6–26b 6–26b.

(

I = ∑ I + Ad

2

)

= 2[121 (0.25)(0.02) + (0.25)(0.02)(0.16) ]+ [121 (0.02 )(0.3) 3

= 301.3(10 −6 ) m 4

2

3

]









EXAMPLE 4 (cont.) Solutions • •

A three three-di -dimen mensio sional nal view view of of the the stres stress s distri distribut bution ion is is shown shown in in Fig. Fig. 6–26 6–26d. At point B,

σ B

=−

My B I

;

σ B

=−

22.5(103 )(0.15) 301.3(10

−6

)

= −11.2 MPa











EXAMPLE 5











EXAMPLE 5 (CONTINUED)











EXAMPLE 5 (CONTINUED) EXAMPLE 6.11 (CONTINUED)











EXAMPLE 6




































EXAMPLE 7


























UNSYMMETRICAL BENDING













UNSYMMETRICAL BENDING (cont.)









































































15

Recommend Documents