# LATERAL LOAD ANALYSIS OF TWO DIMENSIONAL FRAME

INTRODUCTION
In seismic analysis the earthquake forces are considered as lateral forces which represent the ground motion caused by earthquake. These lateral loads can seriously damage the structure and might even cause collapse of the structure. Comparison of portal method, D-value method and computer program has been made for analysis of two dimensional frame.

PORTAL METHOD
The portal method is based on the assumptions that the shear force in an interior column is twice the shear force in an exterior column, there is a point of inflection at the center of each column, and there is a point of inflection at the center of each beam.

Shear force (V)
Portal method assumes that internal columns will take twice as much shear than the external columns, so therefore, the ratio in which shear force is distributed here will be 1:2:2:1.
Equation for exterior column:

Equation for interior column:

Bending moment (M)
Equation for calculating bending moments:
M = Shear force x (0.5xcolumn height)

D-VALUE METHOD
This method gives a tool for solving high static indeterminacy of the structural framing of the building. The D-value of a resisting elements at any one story is defined by the amount of shear reactive to the element when the relative horizontal displacement at the story under consideration has a unit value. The D-value method has been used for the analysis of seismic forces.

Moment of inertia is calculated using I = bh3/12.
Beam and column stiffness is calculated using K = I/L
Column stiffness is calculated using K̅ = (K1 + K2) / Kc (Bottom story, one end fixed) & K̅ = (K1 + K2+ K3+ K4) / 2Kc (Upper stories)

Story shear is calculated using Vn =[ Vt / ΣDn ] Dn

Moment at bottom face is calculated using Mb = VYh
Moment at top face is calculated using Mt = V (1-Y)h

COMPUTER MODELLING using ETABS
ETABS is a vast but easy to use software developed specifically for buildings and building structures. Its function includes modeling, analytical design, and detailing processes. ETABS help in analysis of large and complex buildings, even of nonlinear behavior.
ETABS has the ability to analyze the building of any possible configuration. ETABS also works on the following stages. Inserting all the relevant information, that are geometry, material properties, section properties, & loads and load cases. Assign material properties, section properties of given model. Story forces are imported by equivalent static lateral force method. Shear forces and bending moments are obtained by analyzing the model.

RESULTS

CONCLUSION
Portal method, because of its assumptions, is not as accurate as the D-value method upon comparison with ETABS results, but the approximations makes this method of analysis quite simpler and thus can be used for low rise buildings.
D-value method, being more precise, can be used for high rise buildings where the accuracy cannot be compromised.

Analysis by,
Aisha Iftikhar & team

1. 