structural analysis

Notes in Structural Analysis II – Glenn M. Pintor / De La Salle University

Loadings Clarify Owner’s requirements (construction timetable, function, occupancy type, material

finishes) in order to consultant to establish the corresponding design criteria Types of Loads Dead load – self weight and other immovable loads (constant in magnitude) that are

permanently attached to the structure o refer to tabulated material densities & design dead loads for building components

(walls, frame partitions, floor fills, ceiling) Live loads – loads that vary in position

o Movable – can be moved from one position to another o Moving loads – moves under their own power (vehicles, train) ASCE Provision for Live load reduction o allows live load reduction on members having influence area of 37.2 sq m or more o note the following conditions for provision to apply:

- reduced live load á 50% of unreduced design live load for members supporting 1 floor

- reduced live load á 40% of unreduced design live load for members supporting more than 1 floor

- no reduction is allowed for loads exceeding 4.79 kN/m2 Highway bridge/Railroad bridge loads – primary live loads on bridge spans due to traffic and

heaviest vehicle loading Wind loads – design structure to resist wind effects (due to conversion of the wind’s kinetic

energy to potential energy of pressure) which is dependent on the following factors: o Density & velocity of air (obtained from Wind Maps) o Relative importance of the structure (potential to cause damage loss to property & lives) o Exposure category

- Ground level, wind force is low - Hills & escarpments, wind force/pressure increases as wind is forced up an

incline o Terrain factors (presence of obstructions and building height)

- Class B: closely spaced obstructions, lower wind effects - Class C: open terrain, scattered obstructions - Class D: flat unobstructed, greater wind effects

o Shape and stiffness of the structure o Roughness of its surface

Earthquake loads – caused ground motion & lateral resistance of the structure,

o depends on the following factors: - amount & type of ground accelerations - mass & stiffness of structures


Structural design FACTOR OF SAFETY

o Consider uncertainties in the material arising from: - Variability in material properties - Residual stresses in materials (e.g. uneven cooling of welding joints) - Tolerances: Inability to fabricate to exact dimensions - Material corrosion or decay

o Consider uncertainties in the loads - Accidental loadings/change in occupancy

LOAD COMBINATIONS - Consider occurrence of different basic loads on a structure at the

same o Working stress design

- Dead load - 0.6 Dead load + Wind load - 0.6 Dead load + 0.7 Earthquake load

o Strength design

- 1.4 Dead load - 1.2 Deal load + 0.5 Live load + 1.5 Earthquake load

Tributary loadings Establishes how loads on surfaces is transmitted to the structural elements (used for their

supports) Depends on:

1. geometry of the structural system 2. materials from which it is made 3. method of construction

One-way slab system delivers load to supporting members by one-way action (e.g. RC slab reinforced in 1 direction) general rule:

o If L2 á L1 & span ratio L2 / L1 á 2, the slabs behave as 1-way slab


Two-way slab system If L2 / L1 < 2, assume load to be delivered to the beams/girder in 2 directions


Note: Consider dead load contribution of lightweight concrete approximately 1.52 kN / m2 (or 31.9 lb /ft2) Principle of superposition To determine total displacement / internal loadings (stresses) at a point in a structure subjected

to several loadings, add together the respective displacement and component stresses caused by each external load acting separately

Stability Consider necessary conditions to ensure equilibrium of structure

o Must satisfy equations of equilibrium o Must be properly be held / constrained by the supports

Review of Static Concepts, Equilibrium equations

Force and moment equations of equilibrium express the necessary condition for equilibrium that the combined resultant effect of system of forces shall neither be a force nor a couple Types of instability

o Partial constraints – have fewer reactions that equations of equilibrium o Improper constraints – even when R = 3N condition is satisfied, check for instability

due to improper constraining of supports Determinacy Equilibrium equations provide the necessary & sufficient conditions for equilibrium When all reactions can be determined from these equations, structure is deemed “statically

determinate” For coplanar structures with at most 3 equilibrium equation for each part, check for

determinacy using the ff:

o r = 3n , statically determinate o r > 3n, statically indeterminate


where r – number of force and moment reactions, n – number of parts

structural analysis

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