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MASONRY ARCH BRIDGES LOAD CARRYING CAPACITY. Simply Supported Beam Supporting single point load. Simply Supported Beam Supporting two point load. Simply Supported Beam Supporting UDL. Suspension cable with single point load. Suspension cable with two point load.
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MASONRYARCH BRIDGES LOAD CARRYING CAPACITY
CONCEPT OF AN ARCH Concept first understood by Robert Hooke in 1865
LOAD TRANSFER MECHANISM • Horizontal thrust on sub structure • Vertical load on foundation
Analysis of Simple structures • Analysis of any structure is based on Equilibrium condition of forces- • For 3 dimensional structures- • Six conditions • ∑ Fx = 0, ∑ Fy = 0, ∑ Fz = 0, • ∑ Mx = 0, ∑ My = 0, ∑ Mz = 0, • For 2 dimensional structures- • 3 conditions • ∑ Fx = 0, ∑ Fy = 0, ∑ Mz = 0,
Determinacy of structures • Structure is determinate if no. of unknown forces (member forces/support forces) are equal to equilibrium conditions. • Structure is indeterminate if no. of unknown forces (member forces/support forces) are more than equilibrium conditions. • Stability of any structure is directly proportional to Indeterminacy. • In real life situation, most of the structure are indeterminate
If the indeterminacy is zero, structure is just stable and safe. • If indeterminacy is less than zero (-ve), structure will fail under load.
Hinges Single span- 4 hinges
Exact ASSESSMENT OF ARCH BRIDGE IS DIFFICULT? • Least understood • Not taught in academic institutions • Inadequate coverage in codes and manuals of IR • Interaction of arch barrel & fill; fill & spandrel/parapet is yet not fully understood • Inadequate knowledge of construction details • Non-availability of drawings
Construction details (not visible) • Ring thickening • Haunches and backing • Internal spandrel walls • Cross vaults and open spandrels • Materials (adjoining bridges can help) • Joints
STAGES IN ASSESSMENT • Detailed field inspections of all the bridges. • The requisite geometrical parameters obtained from field inspections. • General condition of bridges recorded.
Assessment Methods • MEXE METHOD • MODIFIED MEXE METHOD • RING • ARCHIE – M • Survey and tabulation method
MEXE METHOD • First engineering method developed by Pippard & Ashby (1939) and Pippard (1948) for use in second world war. • MEXE established in 1963 after full scale load tests carried out in 1950s. • Given in UIC code 778-3R. • Empirical Method, no scope for parametric study.
MEXE METHOD Q = Qp . K Where K = Kp . Ks . Km . Kv. Kc Kp: profile factor Ks: Shape factor Km : material factor Kv : condition factor Kc : crack factor
MEXE METHOD • Obtain Qp in KNfrom graph for specific ring thickness at crown and span
MEXE METHOD • Apply profile factor (Kp)
MEXE METHOD • Apply shape factor (KS) from graph for rq to rc ratio
MEXE METHOD • Material factor (KM) • Soft brick and soft stone = 1.0 • Hard brick = 1.2 • Mass concrete = 1.2 • Stone Masonry = 1.5