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Perkins 403D-15 workshop manual Engr.Saiful
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COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL & ARCHITECTURAL ENGINEERING
CVEN 214: STRENGTH OF MATERIALS
Chapter 6: BENDING Dr Mohammed Elshafie
Fall, 2017
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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
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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
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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.
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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.
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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
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EXAMPLE 5
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EXAMPLE 5 (CONTINUED)
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EXAMPLE 5 (CONTINUED) EXAMPLE 6.11 (CONTINUED)
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EXAMPLE 6
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EXAMPLE 6 (CONTINUED)
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EXAMPLE 7
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UNSYMMETRICAL BENDING
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UNSYMMETRICAL BENDING (cont.)
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