Dept. of Civil and Environmental Engineering, Seoul National University Junho Song 457.201 Mechanics of Materials and Lab. [email protected]Chapter 10 Statically Indeterminate Beams 10.1 Introduction Statically Indeterminate Beams 1. Statically Indeterminate: the number of r_______ forces ( ) the number of independent equations of e__________ 2. For statically indeterminate structures, the e_________ equations are not enough to obtain all reactions, shear forces and bending moments from free-body diagrams 3. Additional information such as equations of c____________ should be provided to augment equations of equilibrium (f_______-d_______ relationship is needed to relate the beam deflections and applied loads) 4. Section 10.3: Differential equations (practical for only the simplest types) 5. Section 10.4: Superposition method (applicable to a wide variety of structures) ~ See Section 2.4 (axially loaded members) and Section 3.8 (circular shafts under torsion) 6. Assumption (throughout this chapter): l________ e________ materials 10.2 Types (or Examples) of Statically Indeterminate Beams Propped Cantilever Beam 1. Propped cantilever beam with both horizontal and vertical loads 1) Degree of static indeterminacy: number of reactions ( ) – number of equilibrium equations ( ) = _________ degree 2) Static redundants: boundary conditions to be released to apply c_________ conditions (Q: How many?) 3) Example choices on static redundants: the reaction force (Cantilever) the moment reaction (Simple beam)
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Dept. of Civil and Environmental Engineering, Seoul National University Junho Song 457.201 Mechanics of Materials and Lab. [email protected]
Chapter 10 Statically Indeterminate Beams
10.1 Introduction
Statically Indeterminate Beams
1. Statically Indeterminate:
the number of r_______ forces ( ) the number of independent equations of
e__________
2. For statically indeterminate structures, the e_________ equations are not enough to
obtain all reactions, shear forces and bending moments from free-body diagrams
3. Additional information such as equations of c____________ should be provided to
augment equations of equilibrium ( f_______-d_______ relationship is needed to
relate the beam deflections and applied loads)
4. Section 10.3: Differential equations (practical for only the simplest types)
5. Section 10.4: Superposition method (applicable to a wide variety of structures) ~
See Section 2.4 (axially loaded members) and Section 3.8 (circular shafts under
torsion)
6. Assumption (throughout this chapter): l________ e________ materials
10.2 Types (or Examples) of Statically Indeterminate Beams
Propped Cantilever Beam
1. Propped cantilever beam with both horizontal and
vertical loads
1) Degree of static indeterminacy: number of
reactions ( ) – number of equilibrium
equations ( ) = _________ degree
2) Static redundants: boundary conditions to be released to apply c_________