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STRUCTURES - SUSPENSION ROOF
Assume:1 Cable roof structure 2 Parabolic cable by graphic method Process: Draw AB and AC (tangents of cable at supports) Divide tangents AB and AC into equal segments Lines connecting AB to...
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STRUCTURES - FORCE TYPES
Forces on structures include tension, compression, shear, bending, and torsion. Their effects and notations are tabulated below and all but bending and related shear are described on the following...
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STRUCTURES: FORCE VS. STRESS
Force and stress refer to the same phenomena, but with different meanings. Force is an external action, measured in absolute units: # (pound), k (kip); or SI units: N (Newton), kN (kilo Newton)....
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STRUCTURES: AXIAL STRESS
Axial stress acts in the axis of members, such as columns. Axial tension is common in rods and cables; wile axial compression is common in walls and columns. The following examples illustrates axial...
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STRUCTURES: SHEAR STRESS
Shear stress occurs in many situations, including the following examples, but also in conjunction with bending, described in the next chapter on bending. Shear stress develops as a resistance to...
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STRUCTURES: TORSION
Torsion is very common in machines but less common in building structures. The examples here include a small detail and an entire garage. 1 Door handle 2 Tuck-under parking Note: The torsion moment is...
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STRUCTURES - PRINCIPLE STRESS
Shear stress in one direction, at 45 degrees acts as tensile and compressive stress, defined as principle stress. Shear stress is zero in the direction of principle stress, where the normal stress is...
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STRUCTURES - STRAIN EXAMPLES
1 Elevator cables Assume Elongation under load 2 Suspended building 3 Differential strainAssume4 Shorten hangers under DL to reduce differential strain, or prestress strands to reduce ∆L by half Note:...
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Buildings: Thermal examples
1 Curtain wallAssume: Aluminum curtain wall, find required expansion joint Thermal strain2 High-rise building, differential expansionAssume: Steel columns exposed to outside temperature Differential...
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STABILITY OF STRUCTURES
Stability is more complex and in some manifestations more difficult to measure than strength and stiffness but can be broadly defined as capacity to resist: • Displacement • Overturning • Collapse...
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Structures: Bending Elements
Bending elements are very common in structures, most notably as beams. Therefore, the theory of bending is also referred to as beam theory, not only because beams are the most common bending elements...
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Structures: Bending and Shear Stress
ending and shear stresses in beams relate to bending moment and shear force similar to the way axial stress relates to axial force (f = P/A). Bending and shear stresses are derived here for a...
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STRUCTURES EQUILIBRIUM METHOD
Cantilever beam with point load Assume a beam of length L = 10 ft, supporting a load P = 2 k. The beam bending moment and shear force may be computed, like the external reactions, by equations of...
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STRUCTURES SIMPLE BEAM WITH UNIFORM LOAD
1 Beam of L= 20 ft span, with uniformly distributed load w = 100 plf 2 Free-body diagram of partial beam x units long 3 Shear diagram 4 Bending moment diagram To find the distribution of shear and...
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STRUCTURES - AREA METHOD FOR BEAM DESIGN
The area method for beam design simplifies computation of shear forces and bending moments and is derived, referring to the following diagrams: 1 Load diagram on beam 2 Beam diagram 3 Shear diagram 4...
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STRUCTURES EXAMPLE BEAM DESIGN
V Shear diagram. M Bending diagram. ∆ Deflection diagram. I Inflection point (change from + to - bending). Reactions R= 400plf (24)/2 R = 4800 lbs Shear Moment Try 4x10 beam Bending...
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STRUCTURES EXAMPLE BEAM ANALYSIS
ReactionsShear Find x, where shear = 0 and bending = maximum: Vbr-w2 x = 0; x = Vbr/w2 = 2000/200 x = 10 ft Moment Section modulus Bending stressShear stress Note: stress is figured, using...
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STRUCTURES INDETERMINATE BEAMS
Indeterminate beams include beams with fixed-end (moment resistant) supports and beams of more than two supports, referred to as continuous beams. The design of statically indeterminate beams cannot...
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BEAMS FLEXURE FORMULA
The flexure formula gives the internal bending stress caused by an external moment on a beam or other bending member of homogeneous material. It is derived here for a rectangular beam but is valid for...
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BEAMS SECTION MODULUS
Rectangular beams of homogeneous material, such as wood, are common in practice. The section modulus for such beams is derived here. 1 Stress block in rectangular beam under positive bending. 2...
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