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Engineering Mechanics: A Comprehensive Overview, Cheat Sheet of Theory of Structures

A comprehensive overview of engineering mechanics, covering fundamental concepts, types of forces and stresses, material properties, and structural elements. It delves into the behavior of rigid bodies under load, exploring statics and dynamics. The document also examines different types of loads, foundations, retaining walls, and columns, providing a solid foundation for understanding structural engineering principles.

Typology: Cheat Sheet

2022/2023

Uploaded on 11/07/2024

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ENGINEERING MECHANICS - a branch of science
that deals with the behavior of a rigid body when
the body is at rest or in motion
RIGID BODY - a body that does not deform under
load
- the distance between any 2 points on a rigid body
remains constant regardless of external forces
exerted on it
TYPES OF ENGINEERING MECHANICS
1. STATICS - The study of external forces on a rigid
body when it is at rest and remains at rest before
and after the application of forces
2. DYNAMICS - deals with the study of external
forces applied on a body inducing any motion
2. FORCE - THE CAUSE OF CHANGE IN THE
STATE OF MOTION OF A BODY. A VECTOR
QUANTITY F = m.a
Newton (N) unit of Force
Force (N) = mass (kg) x acceleration (m/s2)
Weight (N) = Mass (kg) x Agravity (m/s2)
SCALAR - a quantity that only has a magnitude
VECTOR - a quantity that has both magnitude and
direction
LOAD - the measurement of the external forces
applied to bodies
TYPES OF LOAD:
1. POINT LOAD - concentratedly imposed at a
point
2.UNIFORM LOAD -series of concentrated loads
with uniform magnitude
3. VARYING LINE LOAD - series of concentrated
loads with varying magnitude
FORCE SYSTEMS
1. PARALLEL FORCES - forces acting in the same
direction but do not converge at a common point
2. COPLANAR FORCES - forces acting on single
plane
concurrent
3. CONCURRENT FORCES - forces converging at
a common point
COMPONENTS OF A FORCE - represents the
combined vertical & horizontal forces that
combine to make the resultant force
RESULTANT FORCE - representative force of the
cumulative effects of forces
REACTION - reactive force developed by a body
on which a force acts
MOMENT - rotation of a force at a point or an axis
FREE-BODY DIAGRAM - isolated view of a body
where all considered forces are shown
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ENGINEERING MECHANICS - a branch of science that deals with the behavior of a rigid body when the body is at rest or in motion RIGID BODY - a body that does not deform under load

  • the distance between any 2 points on a rigid body remains constant regardless of external forces exerted on it **TYPES OF ENGINEERING MECHANICS
  1. STATICS -** The study of external forces on a rigid body when it is at rest and remains at rest before and after the application of forces 2. DYNAMICS - deals with the study of external forces applied on a body **inducing any motion
  2. FORCE** - THE CAUSE OF CHANGE IN THE STATE OF MOTION OF A BODY. A VECTOR QUANTITY F = m.a Newton (N) – unit of Force Force (N) = mass (kg) x acceleration (m/s2) Weight (N) = Mass (kg) x Agravity (m/s2) SCALAR - a quantity that only has a magnitude VECTOR - a quantity that has both magnitude and direction LOAD - the measurement of the **external forces applied to bodies TYPES OF LOAD:
  3. POINT LOAD -** concentratedly imposed at a point 2.UNIFORM LOAD - series of concentrated loads with uniform magnitude 3. VARYING LINE LOAD - series of concentrated loads with varying magnitude FORCE SYSTEMS 1. PARALLEL FORCES - forces acting in the same direction but do not converge at a common point 2. COPLANAR FORCES - forces acting on single plane concurrent 3. CONCURRENT FORCES - forces converging at a common point COMPONENTS OF A FORCE - represents the combined vertical & horizontal forces that combine to make the resultant force RESULTANT FORCE - representative force of the cumulative effects of forces REACTION - reactive force developed by a body on which a force acts MOMENT - rotation of a force at a point or an axis FREE-BODY DIAGRAM - isolated view of a body where all considered forces are shown

EQUILIBRIUM - state in which the resultant of the force system that acts on a body is zero CENTROID - the geometric center of all the points on an object CENTER OF GRAVITY - the point where the total weight of the body acts STRENGTH OF MATERIALS - study of the internal effects of external forces applied to a body STRESS - measurement of the amount of force held within an object internal response of an object to an external pressure resisting force per unit area PASCAL - unit of pressure, stress,& strength PRESSURE (PA) = force (n) / area (m2) PRESSURE (KPA) = force (kn) / area (m2) PRESSURE (MPA) = force (n) / area (mm2) TYPES OF FORCES & STRESS

1. AXIAL FORCE - forces along the longitudinal axis (or length) of the material - COMPRESSION - shortening or pushing together - TENSION - stretching or pushing apart 2. AXIAL STRESS - stress developed to resist axial force 3. TRANSVERSE FORCE - forces perpendicular to the longitudinal axis of a member 4. NORMALSTRESS - stress acting perpendicular to the area ofcontact 5. SHEAR STRESS - stress acting parallel to the area 6. SHEAR FORCE - forces perpendicular to an area, in opposition to a force acting in the opposite direction 7. BENDING STRESS (FLEXURAL STRESS) - forces producing both tension and compression on the cross-section of the body

TEMPERATURE EFFECT - effect of temperature on the material:

  • at low temperatures , ductile materials behave like brittle materials
  • at high temperatures , brittle materials behave more like ductile materials ELASTIC DEFORMATION - temporary change in the shape of a body , produced by a stress less than the elastic limit of the material PERMANENT SET - inelastic strain in a material FATIGUE FAILURE - caused by fluctuating or repeated stress leads to fracture (progressive minute cracks that grow under repeated stress) CREEP - time-dependent, gradual permanent deformation produced by continuous application of loads considered together with temperature STRESS RELAXATION - time-dependent decrease in stress under a constant strain FOUNDATION - transfers structural loads reliably from a **building into the ground TYPES OF LOADS:
  1. DEAD LOAD -** permanent load e.g. self-weight of the structure, permanently attached elements, fixtures and equipment 2. LIVE LOAD - nonpermanent load e.g. occupants, collected snow/water, movable equipment & fixtures 3. IMPACT LOAD - suddenly applied load of short duration due to moving vehicles, equipment & machinery 4. SEISMIC LOAD - highly dynamic horizontal & vertical force due to the motion of the ground during an earthquake 4. WIND LOAD - load exerted on a structure by wind may act laterally, downward and/or upward 5. LATERAL SOIL PRESSURE LOAD - caused by earth 6. HYDROSTATIC PRESSURE - load caused by earth and groundwater SOIL BEARING CAPACITY - capacity of the soil to bear the loads from the foundation SETTLEMENT - downward movement of the ground cause by a load TYPES OF SETTLEMENT: 1. UNIFORM SETTLEMENT - settling occurs at roughly the same rate throughout all parts of a building 2. TIPPING SETTLEMENT - settling occurs at one end/side only but the foundation stays intact 3. DIFFERENTIAL SETTLEMENT - settling occurs at one end/side only and the other end/side drops down or shifts TYPES OF FOUNDATION:

1. SHALLOW FOUNDATION - close to the base of the substructure - SPREAD FOOTING - takes concentrated load from above and spreads it across an areas large enough that can withstand it - MAT/RAFT FOOTING - used where the bearing capacity of the soil is low in relation to the building loads 2. DEEP FOUNDATION - extends downward to reach more stable soil or rock deeper within the earth CAISSON (DRILLED PIER) - 2’ to 12’ in diameter drilling through strata then filling it with concrete END-BEARING PILE - driven until its tip encounters firm resistance from a suitable bearing stratum FRICTION PILE - does not reach any firm bearing layer PILE CAP - rc slab joining the heads of the piles and distributes the load among the piles UNDERPINNING - strengthening and/or stabilizing an existing foundation

  1. foundation may be enlarged
    1. new foundation may be inserted under existing ones 3. soil is strengthened RETAINING WALLS - a wall that resists horizontal soil pressures at an abrupt change in ground elevation - SMALL RETAINING WALLS (<0.90M HIGH) - relies on the mass of the wall and/or interlocking units - TALL RETAINING WALLS (≥0.90M HIGH) - requires reinforcement TYPES OF RETAINING WALLS 1. CANTILEVER - relatively thin stem and hasabase slab which has a heel and toe for up to 25’ high 2. COUNTERFORT - has vertical concrete webs at regular intervals along the backside for more than 25’ high 3. GRAVITY - depends on its weight in resisting lateral forces up to10’ high very massive - CRIB - made from interlocking components forming a grid

BEAM - a rigid horizontal structural member designed to carry and transfer transverse loads across space to supporting elements BEAM SUPPORT TYPES

1. ROLLER - one reaction allows lateral movement (expansion and contraction) 2. PINNED - two reactions restrains translation allows (moment) 3. FIXED (RIGID) - three reactions restrains translation and rotation (moment) DETERMINATE - if the equations of equilibrium are sufficient to analyze a structure r = 3 INDETERMINATE - if the equations of equilibrium are not sufficient to analyze a structure r > 3 DEGREE = r- 3 TYPES OF BEAMS 1. SIMPLE - rests on simple supports at both ends 2. CANTILEVER - projecting beam supported only at one fixed end 3. OVERHANGING - beam extending beyond one of its supports 4. PROPPED - a beam fixed at one end and the other end placed on a roller support 5. FIXED/RESTRAINED - fixed at both ends 6. CONTINUOUS BEAM - extending over more than two supports ELASTIC CURVE - deformation of a beam expressed in terms of its deflection from its original unloaded position

SHEAR DIAGRAM - graphic representation of the variation in magnitude of the external shears present in a structure MOMENT DIAGRAM - graphic representation of the variation in magnitude of the bending moment present in a structure INFLECTION POINT - a point of zero moment the point at which a structure changes curvature as it deflects CAMBER - slight convex curvature intentionally built to compensate for an anticipated deflection ANALYSIS: BALANCED SECTION - stresses in concrete & steel reach permissible value at same time concrete and steel theoretically fail at the same time OVER REINFORCED SECTION - concrete is crushed before steel yields sudden failure without warning UNDER REINFORCED SECTION - steel yields first causing the beam to deflect prior to failure REINFORCEMENT: SLAB - a rigid, flat structural element constructed to create flat and useful surfaces such as floors, roofs and ceilings TYPES OF SLAB

1. ONE-WAY - supported by beams on 2 opposite sides to carry the load along one direction longer span (l) / shorter span (b) ≥ 2 - BANDED SLAB - reduces the span between the bands = reduced thickness for the slab bands have smaller depth than beams = more clear height / reduced storey height - RIBBED SLAB - reinforcements are concentrated in spaced ribs or joists to make the slab thinner and lighter - WIDE-MODULE / SKIP JOIST - thicker slabs that can span greater spans **4’ to 6’ apart

  1. TWO-WAY -** supported by beams on all 4 sides to carry the load along both directions longer span (l) / shorter span (b) < 2

CONTROL JOINTS - purposely created lines along of weakness which cracking will occur as a surface of brittle material shrinks (contraction)

  1. at regular intervals in long or large surfaces (2- times the slab thickness)
  2. geometric disontinuities (corners, changes in height/width, openings) BUILDING SEPARATION JOINTS - divides a large or complex building mass into smaller structures that can move independently VOLUME CHANGE JOINT - relieves large-scale effects of expansion and contraction VOLUME CHANGE JOINT - relieves large-scale effects of expansion and contraction SETTLEMENT JOINT - designed to avoid distress caused by different rates of anticipated settlement CONSTRUCTION JOINT - joint between 2 successive placements of concrete, often keyed or doweled to provide lateral stability across the joint COLD JOINT - weakened planes between hardened and fresh concrete due to delay or interruption in concreting works SLUMP TEST - for determining the consistency and workability of the concrete mixture shall be made at the time of placement, as often as necessary for control checks (astm c94) TRUE SLUMP: only slump that can be measured ZERO SLUMP: very low w-c ratio COLLAPSED SLUMP: very high w-c ratio SHEAR SLUMP: incomplete; for retesting RECOMMENDED SLUMP BY ACI COMPRESSION TEST - for determining the strength of a concrete batch during the delivery of concrete, cylinder samples (4” x 8” or 6” x 12”) are taken to a testing laboratory to determine if the cured concrete meets the desired strength - STANDARD-CURED CYLINDERS - for acceptance testing for specified strength for verifying mixture proportions for strength quality control - FIELD-CURED CYLINDERS - for determining when structure can be put into service comparing results with standard cured specimens scheduling removal of forms and/or shoring at least two 150 by 300 mm or at least three 100 by 200 mm field-cured cylinders shall be molded samples for preparing strength test shall be taken
    1. at least once a day
    2. at least once for each 110 cubic meter of concrete
    3. at least once for each 460 sq.m of structure area for slabs or walls a strength test shall be the average of strengths of at least two 150 x 300 mm cylinders or at least three 100 x 200 mm cylinders made from the same sample of concrete and tested at 28 days or at test ge designated for f’c; CORE TEST - concrete sample is cut from a hardened concrete structure