Understanding Beam Bending Stress in Architectural Structures: Pure Bending & Stress Deriv, Slides of Structural Design and Architecture

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ARCHITECTURAL Beam Bending Stress 1Lecture 18

S^ TRUCTURES

I:

STATICS AND

S

TRENGTH OF

M

ATERIALS

eighteen beams:bending and shear

lecture

Beam Bending Stress 2Lecture 18

A

Beam Bending •^

Galileo^ –

relationship betweenstress and depth

2

-^

can see^ –

top squishing – bottom stretching

-^

what are the stress across the section?

Beam Bending Stress 4Lecture 18

A

Bending Moments •^

sign convention:

-^

size of maximum internal moment willgovern our design of the section

V

M

+^

-

Beam Bending Stress 5Lecture 18

A

Normal Stresses •^

geometric fit^ –

plane sectionsremain plane – stress varies linearly

Beam Bending Stress 7Lecture 18

A

Derivation of Stress from Strain •^

pure bending =arc shape

θR

L^

R

θ

L^

y

c

½δ

½δ

(^

y R

Loutside

(^

)

y R

R

R

y R

L

L

L

L

outside

Beam Bending Stress 8Lecture 18

A

Derivation of Stress

Ey^ R

E f^

-^

zero stress at n.a.

f^ max y c f^

Ec^ R

f^

max

R

θ

L^

y

c

½δ

½δ

Beam Bending Stress 10Lecture 18

A

Bending Stress Relations

I c

S^

=

section modulus

My^ I

f^ b

=

general bending stress

M EI

R

= 1^ curvature

M^ S

f^ b

=

maximum bending stress

b

required

M F

S^

≥

required sectionmodulus for design