Rigid Body Mechanics

Mechanics of Rigid Bodies

• Coefficient of friction is the ratio of the sliding force to the weight of a material and measures sliding resistance.
• In static equilibrium, the algebraic summation of forces in a system equals zero.
• A couple is two forces equal in magnitude, oppositely directed, that produce a moment.
• A force can be moved along its line of action without changing its external effect.
• Varignon's Theorem states the moment of two forces about the same axis.
• Provided the material follows Hooke's Law, supports are unyielding, and temperature is constant, the external virtual work done by a system of forces is equal.
• Snow, wind, pressure suction, & earthquake loads are environmental loads.
• The external effect of a force on a body is the same for all points of application along its line of action, independent of the point of application per the principle of transmissibility of a force.
• Adding a set of forces in equilibrium to any system may change the effect of the original system, and this statement represents an incorrect axiom of mechanics.
• The greatest tension on an elevator cable occurs when the elevator car is moving upward but coming to rest.
• The second moment of area of a rectangular section with base 50mm and height 100mm is 4166667 mm^4.
• Permanent or unmovable loads are dead loads.

Structures

• A Fink truss has vertical and diagonal members between the upper and lower chords, with diagonals sloping toward the center.
• Hooke’s Law states that stress is proportional to strain.
• The normal force exerted by a smooth horizontal surface on a 100-lb block is 100 lbs.
• Occupancy load that may be fully or partially in place is a live load.
• Modulus of elasticity is the ratio of unit stress to unit strain.

Strength of Materials

• A restrained beam experiences no rotation or vertical movement at either end.
• Toughness is the property of a material to absorb energy before rupturing, represented by the area under a stress-strain curve.
• Rigidity is a material's property to resist changes in physical shape.
• Ductility is the property of undergoing plastic deformation after being stressed beyond the elastic limit before rupturing.
• Brittleness is a property of a material fracturing at low stress without significant deformation.
• Axial load is a force acting perpendicular to a structural member’s cross-section at its centroid.
• Torsion is the twisting of a structural member about its longitudinal axis by equal, opposite torques.
• A propped beam features a fixed support at one end and a roller support the other.
• Stress beyond the proportional limit means the ratio of stress and strain for a material is no longer constant.
• Strain is the change in length caused by a force applied to a piece (expressed as a ratio).
• A spherical pressure vessel of 540 mm internal diameter and 3mm thick steel, with a yield stress of 450 MPa and a max allowable shear stress of 240 Mpa, has a maximum allowable internal pressure of 10 MPa.
• Poisson’s Ratio is the ratio of transverse strain to longitudinal strain.
• The modulus of elasticity of steel is 200 GPa.
• Modulus of resilience is the measure of a material's ability to absorb energy without permanent damage.
• Bitumen is a class of black or dark-colored cementitious substances that are high molecular weight hydrocarbons.
• Flexibility of a truss member with length L, cross sectional area A, and modulus of elasticity E = L/AE.
• Purlins are roof beams spanning between trusses.
• Girts are horizontal wall beams resisting bending due to wind.
• A metal specimen with 36mm diameter and has a length L=360 mm and a force of 300 Kn, elongates the length by 1.2mm, has an elastic modulus of 88419 Mpa.
• Chromium is added to steel at levels above 16% to make it corrosion resistant (stainless steel).
• Quenching is a heat treatment of steel involving shock cooling in a liquid or molten material.
• Ultimate strength is the largest stress a material can withstand based on its original cross-sectional area (the maximum ordinate on a stress-strain curve).
• A bar 1m long with a rectangular cross section 50mm x 50mm subjected to an axial tensile force of 100 N develops a stress of 0.04 MPa.
• The new position of a beam’s longitudinal centroid axis when loaded is called the elastic curve.
• A 2m solid shaft having a radius of 35mm in subjected to a torque of 950N-m. Using G=80000 Mpa, develops a maximum torsional shearing stress of 14.11 Mpa.
• The maximum angle of twist calculates to 0.01 radians.
• A cantilever beam 6m long carries a uniform load of 400kn/m throughout the span I=1.7 x 10^9 mm and e=200000mpa, has a deflection at the free end of 190.59 mm.
• The maximum moment in the beam calculates to 30 KN-m.
• The reaction at A calculates to 502.73 kN.
• Point of inflection is the point in a moment diagram where curvature changes from concave to convex.

Theory of Structures

• For a prismatic member, the carryover factor is 0.5.
• An overhanging beam projects beyond one or both supports.
• Compatibility is the third requirement for a correct solution to a structural analysis problem, along with equilibrium and stress-strain relationship.
• The Principle of Contragradience states that given a linear transformation relationship between two force vectors P=HQ, the corresponding displacement vector transformation, is simply the transpose of the force transformation matrix H.
• In the conjugate beam method, actual slope equals fictitious shear.
• The max moment for a restrained beam is wL²/12.
• The equivalent spring constant K for a vibrating system with two springs having spring constant K1 and K2 respectively in parallel is. K=K1+K2
• A simple beam with a span of 6 m with two concentrated loads of 20kn each placed at the third points of the span. If the extreme fiber stress is 10Mpa, requires a section modulus of 4x10^6 mm^3.

Testing and Properties of Materials

• A universal testing machine conducts tests for compressive, bend, and shear properties.
• Fatigue test determines the stress level a metal can withstand without failure under repeated alternating stresses.
• Hardness testing determines a metal's resistance to penetration.
• Yield strength is the minimum stress required to create permanent deformation in a metal.
• A Brinell Testing Machine may be used to conduct harness tests on metals.
• Curing protects concrete against moisture evaporation & regulates temperature.
• Durability is the property of concrete that withstands deterioration from weathering.
• Workability is the ease with which fresh concrete can be moved without segregation.
• Soundness testing manifests cement’s resistance against deformation from temperature changes.
• Quality assurance comprises tests ensuring new supplies meet standards.
• Quality control involves tests done by a company to ensure their product meets standards.
• 200 mm is the required gage length (GL) in a rebar tension test specimen.
• Non-prestressed structural units are cast in factories with reinforcing members not under tension.
• Post-tensioned materials tension steel reinforcing after the concrete hardens.
• Prestressed structural units have stresses introduced during or after casting in molds.
• Dewatering lowers subsurface water to keep excavations dry and stable.
• Cranes are used for lifting, lowering, & transporting loads horizontally.
• Grading brings earthwork to the desired shape and elevation.
• Economic life refers to the lifetime of equipment over which it survives changes profitably.
• Spread foundations transmit loads to the soil throughout the footing.
• Piles are slender members transmitting foundation loads through low bearing capacity soil to deeper strata.
• Hydraulic cement hardens by reacting with water and forms a water-resistant product.
• Cement uses raw materials such as limestone.
• Fineness modulus measures the relative fineness of sand.
• Wash tests determine silt and clay composition in aggregates indicating cleanliness.
• Abrasion testing evaluates the strength of aggregates.
• Saturated surface dry (SSD) is a moisture condition in aggregates where the surface is dry, but the voids are fully saturated.
• Aggregate is the most important material in concrete and is held together by cement paste.
• Cold bending is used to test reinforcing steel bar amenability to bending for structural applications.
• Tension testing mechanically evaluates tensile properties of steel.

Civil Engineering Terminology

• Concrete is a mix of water, cement, sand, gravel or other aggregates.
• Nominal maximum sizes of coarse aggregate should be greater than 1/5.
• Dimension between sides of forms is the depth of slabs.
• Minimum clear spacing between individual reinforcing bars is 3/4.
• The shortest length in meters of a commercial available rebar is 6 meters.
• Aggregates that pass through a no. 4 sieve are fine aggregates.
• #8 rebar has a nominal diameter of 25 mm.
• The 28th-day compressive strength of concrete is Fc’.
• The maximum number of rebars in a bundled bar is 4.
• The longest length of a commercially available rebar is 12 meters.
• The load factor for dead load as per NSCP 2001 is 1.4 DL (2010–1.2).
• For a live load is 1.7 LL (2010 – 1.6).
• For a wind load is 1.7 WL (2010 – 0.8).
• A composite member of concrete and reinforcing bars is reinforced concrete.
• The strength reduction factor for flexure is 0.9.
• #3 rebar has a nominal diameter of 10 mm.
• Fy relates to the yield strength of steel rebar.
• The maximum usable strain for concrete is 0.003.
• Aggregates that are retained through a No.4 Sieve are coarse aggregates.
• Workability measures the workability of fresh concrete.
• Curing protects concrete from moisture loss and maintains reasonable temperatures.
• Code limits tensile steel percentage to ensure ductile failure.
• The Modulus of Elasticity in MPa of concrete with fc' = 21 MPa calculates to 4700 * sqrt(fc’) = 21538.
• Over-reinforced design of concrete experiences brittle failure.
• A standard bag of Portland cement weighs 40 kilograms.
• In cases where fc prime is less than 30 MPa, the value of b is 0.85.
• Structures are referred to as pre-stressed.
• The maximum reinforcement ratio provided by the code is taken as 75%.
• The minimum reinforcement ratio provided by the code is taken as 1.4.
• A type of beam with fixed support and a roller support at the other end is propped beam.
• A plasticizer reduces the inter-particle forces thereby increasing the paste fluidity.
• As per NSCP 2001, the uniform liveload for residential occupancy is 2-1.9 kpa.

True/False statements

• Water coming from clear canals can be mixed in concrete FALSE.
• Reinforcing steel is strong in tension TRUE.
• The higher the water-cement ratio, the lower the strength of the concrete TRUE.
• Deformed rebar is better than plain rebar TRUE.
• Tables and chairs inside a classroom considered Dead Load FALSE.
• Live loads for classrooms are larger than the libraries FALSE.
• Elongated gravel is much better than rounded gravel FALSE.
• Structures are referred to as reinforced, but designed as unreinforced.
• Under-reinforced design is more preferred.
• A slump of zero means high workability FALSE.
• Concrete is strong in compression TRUE.
• If the water-to-cement ratio decreases, concrete strength increases TRUE.
• If the water-to-cement ratio decreases, porosity decreases TRUE.
• If the water-to-cement ratio decreases, solid-to-space ratio increases TRUE.
• Wind pressure for structures built in Manila is lesser than those in Palawan FALSE.
• A 3000 psi concrete has a 28th compressive strength equal to 27 Mpa. FALSE.

Concrete Behavior and Design

• Balanced condition: Short columns mode of failure where concrete reaches its limit strain just as tensile steel reaches yield strain.
• Given Es= 29,000 Ksi, and Econcrete = 6,000 ksi, the modular ratio is 4.83.
• The maximum shear a material can withstand due to the presence of stirrups is calculated by ⅔ sqrt f’c.
• The distance from the extreme fiber in compression to the centroid of the tension steel area is the effective depth.
• The maximum useable strain at the extreme concrete compression fiber shall be assumed to be equal to 0.003.
• Deadman: A buried plate, wall, or block attached at a distance, forming an anchorage for a retaining wall.
• Lintel beam: The beam over an opening that carries force for the wall over the opening for a door, window, etc.
• Concrete strength increases, porosity decreases, and the solid-to-space ratio increases if the water-to-cement-ratio decreases.
• Shrinkage: Describes the property of concrete by which it continues to deform with time under stresses, but within the acceptable elastic range.

Material Science

• Honeycomb structures have small arches with chain particles, and a void ratio of 0.35 for pyramidal packing; these have negative relative densities.
• Balanced strain where steel and concrete reach desired condition.
• Cementitious materials bound aggregates.
• Heat of hydration is generated when compound in cement react with water to acquire stable low energy state.
• Plasticizers reduce the interparticle forces, so that the paste fluidity increases.
• Slippage: Separation of aggregate due to faster water adsorption.
• Water-cement ratio estimates concrete strength.
• Air entertainment contains small amount of disconnected air bubbles uniformly distributed throught the mass in concrete.
• Mobility describes the ability of fresh concrete to flow under momentum transfer or under mechanical stress
• Trueness: There is progressive weakening due to increase in porosity resulting in lower performance in concrete mixes. A lower water cement ratio is preferable.
• Cofferdam structures used around excavations.
• Workability is not a property of hardened hydraulic cement concrete.
• LEAST influence to the quality of concrete: Colors, texture, and shape of aggregates.
• Provide expansion joints to minimize shrinkage of soil.

Steel And Wood Design

• In structural steel design, for supports of elevators a 100% increase accounts for induced impact from live load.
• The AISC maximum slenderness ratio kL/r for tension members is 300
• The slenderness ratio of compression members shall not exceed 200

Section Properties and Loads

• The allowable bending stress of a compact wide-flange section bent about their weaker axis equals 0.75 Fy..
• Structural Steel’s modulus of elasticity is 200,000 MPa.
• A reaction of timber to applied loads is 85%% of its cross-sectional area.
• Allowable tensile stress shall equal 0.60Fy on the gross area, with reference to NSCP 504.2.2.1
• Compaction of earth, where there is an increased void and water ratio.
• The ratio between maximum earth supported in structures needs greater resistance to fire.
• There is added durability in the structures or elements which contribute as additives, especially on the surface.
• Flexural stress is when steel and wood is under bending..
• Adherence with materials such as steel when applied.

#CE REVIEWER

• NSCP504.4.1.1 refers to for for pin-connected members, the allowable stress on the net area of the pinhole for pin-connected numbers, and the allowable tensile stress not to exceed 0.45Fy

• With the connection, a minimum net area beyond the pinpoint is applicable but does not pass the original standards for construction.. (⅔)

• The ratio L/r is 140mm

• Provided Soil pressure does not exceed 50Kpa for temporary open air portable bleachers during the construction phase.

• (a. 10 mm): The Minimum diameter of the Steel Bolts (NSCP305.60)

• To account for Seismic Forces within Construction: Use no higher than 10 percent of the largest column with vertical load bearing.

• The most important thing or percentage is to account for earth and soil slope resistance. (50%)

• Steel reinforcement is needed between 50% or 60%

• 10 days until excavation is performed

• Deep Continuous Flexural members has total depth for each span ratio to not go over deep.

• The length calculation is 300mm development which the tension has calculated.

• Braced Frame System (earth).

• The horizontal lateral forces resist vertical elements.

• (a. Moment resisting forces): A frame is which members and joints are capable of forces

• The slope cut surface needs to be no higher than 50%

• Some specifications: (CE REVIEWER A)

1. Essential Facilities when safety is in mind.
2. One of the most important elements is the water resistance, especially for natural causes.
3. 20% of Seismic Designs applies with horizontal distribution (CE. REVIEW)
4. L24/ is necessary for excavation and/or foundation of construction. 5)0.60 or what has been specified has been applied for the concrete mix with steel to the concrete and structure needs to be 0%.
5. 5 diameter with a 6% rate calculation for support and composite beams.
6. the force to not exceed for elements is only 26.70 KN within tension

Steel and the related

• In computing net. the width of applied stress is only 1.6 mm greater or not to exceed with applied force.
• To follow the ratio or resistance, at least 8Mpa is needed.
• The load capacity needs to be not less than 50%.
• The length or ratio need for lacing bars is almost only 140mm.

One and and is continuous: L20 is what only. Aviation: Special and unique as it is also only essential. The minimum needs to be 25mm for beams in structures.