# Beam Forces - Architectural Structures - Lecture Slides, Slides for Structural Design and Architecture. Alagappa University

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Beam Forces, Span Horizontally, Loaded Transversely, Internal Forces, Beam Loading, Uniformly Distributed, Beam Supports, Statically Determinate, Statically Indeterminate, Modeled Type. Its lecture of Architectural Struc...
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Internal Beam Forces 1 Lecture 13

A

ARCHITECTURAL STRUCTURES I: STATICS AND STRENGTH OF MATERIALS 8

thirteen

beam forces – internal

lecture

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Internal Beam Forces 2 Lecture 13

n

Beams span horizontally

floors bridges roofs

loaded transversely by gravity loads may have internal axial force will have internal shear force will have internal moment (bending)

R

V

M

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Internal Beam Forces 3 Lecture 13

Internal Forces trusses

axial only, (compression & tension)

in general axial force shear force, V bending moment, M

A

A

B

B

F

F′ F

F

F F′

V

T

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Internal Beam Forces 4 Lecture 13

A

spandrel beams

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Internal Beam Forces 5 Lecture 13

A

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Internal Beam Forces 6 Lecture 13

Beam Supports statically determinate

statically indeterminate

L L L

simply supported (most common)

overhang cantilever

L

continuous (most common case when L1=L2)

L L L

Propped Restrained

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Internal Beam Forces 7 Lecture 13

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Beam Supports in the real world, modeled type

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Internal Beam Forces 8 Lecture 13

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Internal Forces in Beams like method of sections / joints

no axial forces section must be in equilibrium want to know where biggest internal

forces and moments are for designing

R

V

M

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Internal Beam Forces 9 Lecture 13

V & M Diagrams tool to locate Vmax and Mmax necessary for designing have a different sign convention than

external forces, moments, and reactions

R

(+)V (+)M

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Internal Beam Forces 10 Lecture 13

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Sign Convention shear force, V:

cut section to LEFT if Fy is positive by statics, V acts down

and is POSITIVE beam has to resist shearing apart by V

R

(+)V (+)M

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Internal Beam Forces 11 Lecture 13

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Shear Sign Convention

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Internal Beam Forces 12 Lecture 13

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Sign Convention bending moment, M:

cut section to LEFT if Mcut is clockwise, M acts ccw and is

POSITIVE – flexes into a “smiley” beam has to resist bending apart by M

R

(+)V (+)M

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Internal Beam Forces 13 Lecture 13

Bending Moment Sign Convention

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Internal Beam Forces 14 Lecture 13

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Deflected Shape

positive bending moment tension in bottom, compression in top

negative bending moment tension in top, compression in bottom

zero bending moment inflection point

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Internal Beam Forces 15 Lecture 13

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Constructing V & M Diagrams along the beam length, plot V, plot M

V

L

+

M +

-

L

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Internal Beam Forces 16 Lecture 13

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Mathematical Method cut sections with x as width write functions of V(x) and M(x)

V

L

+

M +

-

x

L

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Internal Beam Forces 17 Lecture 13

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Method 1: Equilibrium cut sections at important places plot V & M

V

L

+

M +

-

L/2

L

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Internal Beam Forces 18 Lecture 13

A abn

important places supports concentrated loads start and end of distributed loads concentrated moments

free ends zero forces

Method 1: Equilibrium

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Internal Beam Forces 19 Lecture 13

Method 2: Semigraphical by knowing

area under loading curve = change in V area under shear curve = change in M concentrated forces cause “jump” in V concentrated moments cause “jump” in M

∫−=− D

C

CD

x

x wdxVV ∫=−

D

C

CD

x

x VdxMM

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Internal Beam Forces 20 Lecture 13

Architectural Structures I ENDS 231

S2008abn

Method 2 relationships

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Internal Beam Forces 21 Lecture 13

Method 2: Semigraphical Mmax occurs where V = 0 (calculus)

V

L

+

M +

-

L no area

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Internal Beam Forces 22 Lecture 13

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integration of functions line with 0 slope, integrates to sloped

ex: load to shear, shear to moment

Curve Relationships

x

y

x

y

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Internal Beam Forces 23 Lecture 13

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line with slope, integrates to parabola

ex: load to shear, shear to moment

Curve Relationships

x

y

x

y

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Internal Beam Forces 24 Lecture 13

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parabola, integrates to 3rd order curve

ex: load to shear, shear to moment

Curve Relationships

x

y

x

y

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Internal Beam Forces 25 Lecture 13

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Basic Procedure 1. Find reaction forces & moments

Plot axes, underneath beam load diagram

V: 2. Starting at left 3. Shear is 0 at free ends 4. Shear jumps with concentrated load 5. Shear changes with area under load

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